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                  ERViRQEiffiENTAL PRCTEGTION  AOEHCY
                    QFFiCE OF TOJIiC SUBSTANCES
                    WASKIN6TDK, B.C.,   20460

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EPA 560/6-77-006
              A FIRST ORDER F>ASS BALANCE MODEL FOR THE SOURCES,
              DISTRIBUTION AND FATE OF PCBs  IN THE

                             FINAL TASK REPORT
                                Sutmitted to:

                   U. S. Environmental Protection Agency
                         Office of Toxic Substances
                          Special Projects Branch
                           Washington, D.C. 20460
                          Contract Nb. 68-01-3259
                                   Task 5
                                Submitted by:

                                 VERSAR INC.
                            6621 Electronic Drive
                         Springfield, Virginia 22151

                                July 21,  1977

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           This report has been reviewed by the Office of Toxic Substances,
U.S. Environmental Protection Agency, and approved for publication.  Approval
does not signify that the contents necessarily reflect the views and policies
of the Environmental Protection Agency, nor does mention of trade names or
commercial products constitute endorsement or recommendation for use.

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                                  PREFACE

     The continued patience and support of Mr.  Thomas Kopp of the Office of
Toxic Substances of the Environmental Protection Agency are gratefully
acknowledged.  Thanks are due to Carlos Fetterolf of the Great Lakes Fishery
Ccrnnission for the opportunity to participate in the PCB  Seminar-Dialogue
held in Ann Arbor in May 1976, which allowed the exchange of views with
Brock Neely and Dean Branson of Dow Chemical and Tom Murphy of DePaul  University.
The many suggestions that arose from several lengthy discussions with  Ian
Nisbet of Massachusetts Audubon Society, vfoich have markedly increased the
author's insight into modeling problems and the environmental properties of
PCBs, are gratefully acknowledged.  It is also a pleasure to acknowledge the
efforts directed to a critical review of this document in its final form by
Tom Murphy of DePaul University, by S. J. Kleinert of the Department of Natural
Resources of the State of Wisconsin and finally by Brock Neely of the  Dow
Chemical Company.  Needless to say errors in fact or in judgement that might
remain are the sole responsibility of the author.
     Finally, Section 6, which deals with a model of fish uptake and elimina-
tion of PCBs, was prepared by Steven Dentel.
                                     i.

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                                TABLE OF CONTENTS
EXECUTIVE SUMMARY
1.0  USTTFODUCTICN AND MASS BALAN

     1.1  Mass Balance Model - Gener
     1.2  Model Devel
                                                                    •  •
2.0  PARAMETERS FOR LAKE
          3.2.1  The Sediment Load  (M   ,)

          3.2.2  The Water Burden of
          3.2.3  Ttse Biotic Load of PCB
(Mbiota)
          3.4.1  N Sediment Zones
                                                                            Page
                                                                            •^^^^^^^^^^^^^^^^^^
                                    1

                                    2
                                    3
     2.1  Introduction  ..........................    7
     2.2  General Phsical and Hdroloical Parameters for Lake Michian  .    7
          2.2.1  Biotic Mass, G, for Lake Michigan ............    8

     2.3  Proportioning Constants/ p and ri  ................    8
          2.3.1  Biota Concentration Ratio, n	   9
          2.3.2  Sediment Concentration Ratio,  p	   9

     2.4  PCB Input Rate to Lake Michigan	10
     2.5  Evaporation Rate Constant K	11
     2.6  Summary of Physical Parameters for Lake Michigan	11

3.0  APPLICATION OF MASS BALANCE EQUATION TO LAKE MICHIGAN	13

     3.1  General Considerations	13
     3.2  Integration of the Mass Balance Equation	15
15

17

17
          3.2.4  Outflow Loss Through Mackinac Straits  (M  . fl  )   ....  17
          3.2.5  Total Input and Cumulative Mass Balance  (M. .  ,)   ....   17
          3.2.6  Co-Distillation Losses and K	18

     3.3  Effect of Organic Content in Sediments	20
     3.4  Extended Lake Michigan Model	21
                                   26
     3.5  Effect of Suspended Solids	28
     3.6  Effects to be Associated with PCB Loads Contained within
          3.6.1  Redistribution Due to Complete Mixing of Water/Sediments    29
          3.6.2  Effect of Layered Sediments - Undisturbed Sediments  ...   32
          3.6.3  Experimental Measurements on Re-solution	34
          3.6.4  Final Word on Sediments	34

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                            TABLE OF CONTENTS (CCN'T)
                                                                           Page

     3.7  Effect on Aqueous PCB Concentration Due to Parametric Variation   35

          3.7.1  General Properties of the Mass Balance Equation	37

4.0  APPLICATION OF MASS BALANCE EQUATION TO GREAT LAKES SYSTEM	40

     4.1  General Considerations	40
     4.2  Lake Superior	45
     4.3  Lake Michigan	45
     4.4  Lake Huron	46
     4.5  Lake Erie	47
     4.6  Lake Ontario	48
     4.7  Summary	49
     4.8  Effect of Point Source Inputs  	   50
     4.9  Comparison of Derived Results with Experimental Data	52

          4.9.1  Fallout on Lake Erie and Ontario	53
     4.10 Effect of Gradient in B(t)	55
     4.11 Effect of Regulatory Actions 	   55

5.0  CO-DISTILLATICN AND THE EVAPORATION RATE CONSTANT K	56

     5.1  Vapor Pressure of the Aroclors	57
          5.1.2  Self Evaporation Rates for Aroclor 1254	60
     5.2  Calculation of the Evaporation Coefficient K for Lake Michigan .   61

          5.2.1  Mass Balance at Lake Surface	61
          5.2.2  Effective Surface Vapor Pressure/Ultimate Solubility
                   Ratio	65
     5.3  Evaporation Rate Constant K	66
     5.4  Comparison With Experiment	67

6.0  AN ESTIMATE OF THE PCB CONCENTRATION IN A TYPICAL LAKE TROUT WEEN
       EXPOSED TO AN AQUEOUS PCB CONCENTRATION	68

     6.1  Development of the Model 	   68
     6.2  Determination of the Rate Constants k, and k2	70
     6.3  Effect of Regulatory Actions on Trout PCB Concentrations ....   71

7.0  FURTHER WORK	77

     7.1  Introduction of Environmental Degredation	78
     7.2  Airborne Reservoir and the Generation of a Gradient in Fallout .   79
     7.3  Introduction of Spatial (or Temporal)  Variation of Sediment  . .   81
     7.4  The Surface Layer and Co-Distillation	82
                                      111.

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                           TABLE OF CONTENTS  (Con't)
APPENDIX A: MATHEMATICAL CONSIDERATICNS

A.1.0  GENERAL	A-l

       A.I.I  6o	A-2
A.2.0  PARTICULAR APPLICATIONS TO PROBLEMS ENCOUNTERED	A-2
A.3.0  APPLICATION OF EQUATION  (A-6)      (A-7)	A-3
A.4.0  EMPIRICAL EQUATIONS  	  A-5
A.5.0  METHODS OF SOLUTION OF EQUATION  (8-3)	A-6

APPENDIX B: PARTITION COEFFICIENTS FOR AQUEOUS PCB SOLUTIONS

B.1.0  INTRODUCTION	B-l
B.2.0  MEASUREMENT OF PARTITION COEFFICIENT	B-l
B.3.0  TYPICAL PARTITION COEFFICIENTS FOR PCBs	  .  .  .  B-2

       B.3.1  Aqueous/Activated Carlson	B-2
       B.3.2  Aqueous/Soils and Clays	B-3
       B.3.3  Aquatic Concentration Factors   . .  . ^	B-3
       B.3.4  Sediment Concentration Factors	B-4
       B.3.5  Effect of Organic Content of Sediment on PCB
                Partition	B-4

APPENDIX C: E^IVIRONMENTAL PCB LOAD

C.1.0  INTRODUCTION	C-l
       C.I.I  Empirical Description of Production, Sales and
                Specific Use Categories	C-l

              C.I.1.1  Period 1930-1970	C-l

       C.I.2  Period 1971-1975 	  C-3

C.2.0  ENVIRONMENTAL LOAD OF PCBs	C-4

       C.2.1  Introduction	C-4
       C.2.2  Total Environmental PCB Load, MQv(t)	C-4

       C.2.3  Effect of Monsanto's Voluntary Ban on PCB Sales.  .  C-8

              C.2.3.1  Comparison of the  Results of Equation
                         (C-14) with the  Estimates of Nisbet
                         and Sarofim	C-8

       C.3.1  General Considerations on Mobile PCBs - M   (t)).  .  C-10
                                                       ev
       C.3.2  Effect on the 1970 Ban on Mobile PCBs (M   (t))  .  .  C-13
                                      IV.

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                           TABLE OF CONTENTS  (Con't)
APPENDIX D: CUMULATIVE E1SIVIRONMENTAL PCB LOAD AM) AN ESTIMATE
            OF THE CHLORINE SPECTRUM OF FREE PCBs

D.1.0  INTRODUCTION	D-l
D.2.0  PCB SALES BY END USE CATEGORY, PERIOD  (1930-1975)  ....  D-l
D.3.0  PCB LOSSES TO THE ENVIRONMENT	D-7
D.4.0  ESTIMATED CHLORINE SPECTRUM OF FREE PCBs	D-9

APPENDIX E:  BACKGROUND DATA USED TO CONSTRUCT THE MODEL FOR PCBs
             IN LAKE MICHIGAN

REFERENCES	F_l
                                        v.

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                                  LIST OF TABLES
Table No.                                                                Page
2.6-1     Physical and Hydrologic Constants for Lake Michigan   ....   12

3.2-1     PCB Concentrations in Lake Michigan	   16

3.2-2     Summary of PCB Mass Distribution	   19

3.3-1     Effect of Organic Content of Sediment on 3	   22

3.3-2     Effect of Organic Content of Sediment on Aqueous
            Concentration	   23

4-1       Hydrological and Physical Data, Great Lakes	   42

4.8-1     Effect of Point Sources on Lake Erie and Lake Ontario
            Estimated Aqueous Concentrations of PCBs	   51

4.9-1     Estimated PCB Load in the Sediments of the Great Lakes  ...   52

5.1.2-1   Self Evaporation Kates Aroclor 1254	   60

5.1.2-2   a Values for Aroclor 1254 (Equation 5-4)	   61
                                                       (44)
5.4-1     Bidleman and Olney Surface Concentration Data     	   67

6.2-1     Estimates of ki (Uptake Rate Constant)  	   72

B.3-1     Partition Measurements - PCBs in Water/Carbon Granules  . .  .   B-2

B.3-2     Partition Coefficients Aqueous PCB/Carbon 	   B-2
                                            IA\
B.3-3     Calculated Partition Coefficientsv ' for Aqueous Aroclor 1254   B-3

B.3-4     Accumulation of PCBs by Various Aquatic Organisms	   B-3

B.3-5     PCB Percolating Studies	   B-4

C.2.2-1   Mev(t) = Environmental Load	   C-7

C.3.1-1   Estimated Total Environmental PCB Load  [M   (t) ] and Mobile
            Environmental PCB Load in [m  (t) ]  	   C-12

C.4.1-1   Parameter Values for Equation (C-23) and Equation (C-25)  .  .   c-15

D.2-1     Proportional Use Factors - PCBs	   D-2

D.2-2     Use Categories Aroclor 1242	   D-3

D.2-3     Use Categories Aroclor 1248	   D-4
                                      vz.

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Table No.
D.2.4
D.2-5
D.3-1
D.3-2
D.4-1
D.4-2
D.4-3
D.4-4
E-l

E-2

E-3

E-4

E-5

E-6

E-7

E-8

E-9

E-10
E-ll
E-12
LIST OF TABLES (Con't)

Use Categories Aroclor 1254 	
Use Categories Aroclor 1260 	
Estimated Loss Factors for PGBs by End Use 	
PCB Environmental Load by Aroclor Type 	
Approximate Molecular Composition of Selected Aroclors . . .
Cumulative Environmental PCB Load by Chlorine Content ....
Computed Spectrum of Chlorine Content for Wild PCBs 	
Chlorine Content of Aroclors and of Environmental PCBs . . .
Concentration of PCBs in Sediments Along the Southwestern
Shore of Lake Michigan (1970-1971) 	 	
Concentration of PCBs in Michigan Streams Tributary to
Lake Michigan 	
PCBs Entering Lake Michigan From Known Industrial and STP
Discharges 	
Concentration of PCBs in Reported Michigan STP Effluents
Tributary to Lake Michigan 	
Concentration of PCBs in Reported Wisconsin Paper Plant
Effluents Discharging to Green Bay (1974-75) 	
Concentration of PCBs in Reported Wisconsin Miscellaneous
Industrial Effluents Discharged to Lake Michigan 	
Concentration of PCBs in Reported Wisconsin STP Effluents
Discharged to Green Bay (1974-75) 	
Concentration of PCBs in Reported Indiana STP Effluents
Tributary to Lake Michigan 	
Concentration of PCBs in Reported Illinois STP Effluents
Discharging to Lake Michigan 	
Lake Michigan Basin Hydrology 	
Estimates of Fish Biomass in Lake Michigan (1972-73) ....
Representative PCB Measurement 	

Page
D-5
D-6
D-7
D-8
D-10
D-ll
D-12
D-14

E-l

E-3

E-4

E-5

E-6

E-7

E-8

E-9

E-10
E-ll
E-12
E-13
Vll.

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                                 LIST OF FIGURES

Figure No;                                                                 Page

3.1-1     Graphic Description of Model Described by Equation (1-71)  ...   14

3.5-1     Plot of   7r  for p4 = 4 x 103 ................   27
3.6.1-1   Effect of Ccrrplete Removal of External PCB Sources Coupled
            with Complete Resolution fron Contaminated Sediments  ....   30

3.7-1     Properties of Equation (1-9) ..................   39

4.1-1     Schematic of Great Lakes Indicating Flow Connections  .....   41

5.1-1     Replot of Vapor Pressure of Aroclors  .............   58

5.1-2     Data in Table 5.1-1 Plotted for Low Temperature Vapor Pressure
            of Aroclor Mixtures .....................   59

5.1.2-1   Mass Evaporation Rate Aroclor 1254 from Itself  ........   62

6.1-1     Schematic Fish  ........................   68

6.3-1     Computer Plot of Equation (6-12)   ...............   74

7.2-1     Volume Element for Airborne Reservoir Computation .......   80

C.3-1     Estimate Wild PCBs, MQV(t) where t = 0, 1930  .........   C-15

D.4-1     Estimate Average Chlorine Number for Wild PCBs  ........   D-13

E-l       Locations of Sediment Sampling Stations ............   E-2
                                     viii.

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                             LIST OF SYMBOLS

A         = Area of target lake  (ft2)
A1        = Drainage area of target lake  (ft2)
B(t)      = Rate of PCB injection into system during year t  (Ibs/yr)
C.        = PCB concentration
C.        = Saturation concentration of PCB in water
 IS
C  (t)     = Aqueous PCB concentration
                                                    _2  _1
D         = Average sediment deposition rate  (Ibs ft  yr  )
E         = Mass evaporation rate for water  (Ibs/yr)
G         = Biota mass in target lake  (Ibs)
H         = Area of target lake  (ft2)
                                                     _i
K         = Surface evaporation rate constant (Ibs yr~  )
M, . . j_    - Cumulative PCB load in the biota  (Ibs)
  biota
M         = Cumulative PCB loss due to evaporation  (Ibs)
  evap.
M    «   = Cumulative PCB loss due to outflowing water (Ibs)
  outflow
M         = Cumulative PCB load in sediments  (Ibs)
  sed.
M  .   ,  •= Cumulative PCB load input to system under consideration
  total
M    ..     = Cumulative PCB load in aqueous phase  (Ibs)
M.        = Molecular weight of PCB
M         = Mass of PCB evaporated  (Ibs)
M         = Molecular weight of water
 VV
P.        = Equilibrium vapor pressure of pure solute  (PCB)  (Mm Hg)
 ' ^
P         = Equilibrium vapor pressure of water  (Mm Hg)
Q         = Water mass of the target lake  (Ibs)
S         = Rate of aqueous outflow from target lake  (Ibs yr ~  )
t         = Time (years)
t_        = Final tine  (years)
u         = Integration variable
                                     IX.

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LIST OF SYMBOLS  (OON'T)

a          = Fraction of sediments that are organic
(5          = Effective time constant for changes in PCB concentration
n          = Average biota partition coefficient
p          = Average sediment partition coefficient
p.         = Average partition coefficient for inorganic portion of sediments
p          = Average partition coefficient for organic portions of sediments
p          = Average partition coefficient for suspended solids
ty          = Concentration of suspended solids
                                     x.

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                                EXECUTIVE SUMMARY
     The work reported herein was undertaken to document and interpret avail-
able information on the transport and distribution of polychlorinated biphenyls
(PCBs) in the environment.  The model and results obtained therefrom also per-
form several important functions of a more general nature - the processes by
which refractory organic compounds are transported and distributed in the
environment are illustrated, a basis for predicting future effects of such
compounds is provided, and the types of data required to perform such analysis
are identified.  Specifically with regard to PCBs, the work should be of assist-
ance in determining potential future hazards from PCBs (free, in landfills, and
in use) and in assessing the benefits of proposed regulation and cleanup
activities.
     Ideally/ a study of the physical and temporal processes involved in the
wide dissemination of a chemical species should begin with a strong data base
which illustrates the spatial and temporal distribution of the target compound.
Unfortunately, the ability to accurately analyze environmental samples and the
recognition of the possible dangerous effects of very low levels have been very
late in coming.  Because of these factors there does not presently exist such a
body of data.  On the other hand, the inherent danger of these materials to the
biosphere precludes the slow and orderly acquisition of such a body of data.
In view of the obvious need of some effective regulatory action, and in view of
the dangers inherent in exercising such regulatory options in the absence of
guidelines suggesting the possible effects of such actions, it was deemed appropri-
ate to attempt the construction of a model describing the nature of the problem.
     The work presented here, an extension of that reported in the Versar Task I
                                 /39\
report under Contract 68-01-3259,v  ' represents an attempt to construct a plausible
scenario, based on reasonable and explicit assumptions, that is capable of answer-
ing the question "How did it come about that a compound, such as the PCBs, is so
wide spread an environmental contaminant?"  The resulting work involves the con-
struction of several mathematical descriptive models made necessary by the lack
of historical data coupled with the absence of a large base of reliable
                                     xi.

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contemporary measurements.  The work is made necessary since the measurements
that do exist strongly suggest that the PCBs are a persistent menace to the
biosphere and hence actions to control them cannot be delayed while a truly
adequate data base is obtained.

      The basic model is  constructed on a mass balance principle; that is, all
the PCB input to a restricted region of the lithosphere may be accounted for by
"storage", that is by solution or by uptake on suspended solids and by uptake
within the biota, with the remainder of the input PCBs being carried off by the
"loss" processes consisting of surface co-distillation, carry off by outflowing
streams and/or entrapment within the sediments.
      The model is somewhat complicated by the necessity of an analytic expres-
sion for the PCB input rate as a function of time; i.e., the driving function.
In the absence of a sufficient amount of data, a model has been constructed to
account for the losses to the environment, the free or "wild" PCB load and
finally for the atmospheric reservoir of PCBs.  The actual relationship of the
various parts of the model are shown in Figure I.

Environmental load Model
      Appendix C and Appendix D deal with an attempt to determine the magnitude
of the total environmental load, the free environmental load and the atmospheric
reservoir of PCBs; all as functions of time.
      The results of this analysis are:
      a.  In 1975, the total environmental PCB load is estimated to be
          3.76 x 108 Ibs. within the continental United States.
      b.  In 1975, the total free or mobile PCB load in the continental
          United States is estimated to be 8.31 x 107 Ibs.  The balance of
          the total environmental load is deemed to be encapsulated in one
          form or another in landfills, for example.
                                        xix.

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                                        Figure I

            Schematic Shewing Relationship of the Various Sections of Report*
  Environmental
   Load Model
       (C)

     Free  PCB
    Load Model
        (C)
    Atmospheric
      Reservoir
       Model
         (C)
       Surface
   Co-Distillation
       Model
         (3)
Lake Michigan
    Model
    (2) (3)
   Fish Uptake/
    Clearance
      Mode
       (6)
Great lakes
   Model
    (4)
Continental
Atmospheric
   Model
                 Sediment
                 Suspended
                  Solids
                  Model
                  (B) (3)
*The number or letter associated with each block refers to section dealing directly with
 the subject matter.
                                            Xlll.

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     c.  As of 1970, the cumulative atmospheric reservoir contained sane
         6 x 107 Ibs. of PCB indicating a rather rapid exchange between
         the total mobile PCBs and the atmospheric reservoir.
     d.  As of 1975, the PCB concentration in the air near Lake Michigan
         was of the order of 10 ug/m3.
     e.  The estimated half life for fallout from, the atmospheric reservoir
         is 0.9 years.
     f.  The average chlorine number for environmental PCBs is of the
         order of 4.32.

Mass Balance Equation as Applied to Lake Michigan
     The results of this analysis are as follows:
     a.  The generation of a plausible scenario which arrives at a present
         day PCB concentration (water plus suspended solids) of the order
         of 7-10 ppt.
     b.  The assertion that atmospheric fallout constitutes the major
         input of PCBs to Lake Michigan.
     c.  Surface evaporation or co-distillation  (the exact nomenclature
         is not known because the process is very incompletely understood)
         constitutes a significant PCB loss mechanism.
     d.  The presence of suspended solids within the water column can be
         expected to have a dominant effect on the actual (filtered)
         aqueous concentration.
     e.  The sediments should act as a significant sink for the removal of
         PCBs from the water column.
     f.  Even though there is considerable uncertainty as to the proper
         value for sane of the important parameters, the sheer bulk of the
         water mass makes the aqueous concentration essentially independent
         of these parameters over wide ranges.
                                      xiv.

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     g.  An estimate of 70 years to reduce the present PCB concentration
         by one-half in the absence of all external sources.
Application of the Mass Balance Model to the Entire Great Lakes System
     a.  The generation of a plausible scenario leading to the estimation
         of aqueous PCB concentrations which are within the range of measured
         values, i.e., less than 40 ppt.
     b.  The estimated average PCB concentration in the sediments of Lake
         Erie and Lake Ontario fall within an order of magnitude of other
         estimates(21)'
     c.  The estimated fallouts in 1974 onto Lake Erie and Lake Ontario
                                                          (21]
         both fall within a few percent of other estimates    .
     d.  Point source inputs, when introduced into Lake Erie and Lake Ontario
         lead to PCB concentrations in the aqueous phase as well within the
         sediments which are within a factor of 2 or 3 of direct observation.
     e.  An estimate of the life time of the present PCB loads in the
         absence of all sources.
Other Results
     Other results obtained somewhat incidentally to the main effort include:
     a.  An estimate of the bioconcentration rates for PCBs for a trout
         of the order of 4 x 10s.
     b.  An estimate that, for the trout, the uptake of PCBs from contaminated
         food is some 50 times more effective than from respiration.
     c.  The MacKay and Wolkoff    model for co-distillation is apparently
         not applicable in the situation where infalling PCB complicates
         the situation.
     d.  The suggestion that the significant difference in activity of PCBs
         in bulk solution compared to that in the surface layer is the driving
         force for the creation of a surface concentration gradient.
                                       xv.

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e.  A formulation is developed that suggests the possibility of an
    analysis of the continental PCB atmospheric reservoir.
                                  xvi.

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1.0  INTRCDUCTiasr AND MASS BALANCE EQUATION
     In order to discover the effeet of various possible regulatory efforts on
the distribution of refractory organics in the general environment, an attempt
has been made to determine the manner in which a specific group of such com-
pounds, PCBs, has becore so widely dispersed, to determine the dynamics of the
distribution process and to determine the changes in specific distribution that
may be expected to result from several regulatory alternatives.  Specifically,
the effect .of the voluntary ban introduced by Monsanto in 1970-71 can be
demonstrated.
     It would be most useful to construct a mathematical representation of a
suitable segment of the environment based on the existence of large quantities
of valid analytical data taken over a sufficiently long time interval so as to
allow the reliable extrapolation of the important time effects.  Unfortunately,
the necessary data are not available.  The recognition that PCBs were an environ-
mental hazard came after their prolonged and widespread use in industry.  In
addition, the ability to analyze environmental samples for very low levels of
PCBs is also a recent development.  There has been too little time since the
development of these sophisticated and exceedingly sensitive analytical techniques
to have allowed anything like a complete spatial and temporal study of the levels
of PCBs in any given region.
     In view of the serious lack of a truly adequate data base, and because of
the need to have at least a first order understanding of the physical processes
involved in the transport and distribution of PCBs, an attempt has been made to
construct a mathematical model which should contain at least a germ of the true
situation.  Specifically, the model serves to indicate something of the nature
of the problem, and of the types of measurements that will be required to con-
struct a truly satisfactory model to guide future regulatory activities.

     To test the adequacy of the resulting mass balance model,  it is first
applied to Lake Michigan for which there exists a considerable body of information
of late origin.   The results of this  analysis,  on comparison with the observed
PCB levels,  serve as a basis for the detailed examination of some of the assump-
tions introduced into the model.   Specifically,  the effect of the organic content
of the sediment and the  phenomenon of co-distillation are examined in some detail.

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     In order to extrapolate the present day observations back into the past so
as to illuminate the basic processes involved, it has been necessary to construct
a relatively primative model of the origin and dynamics of the free environmental
load of PCBs.  A significant guidepost in the construction of the free environ-
mental load model is the observation that, at least in the recent past, the most
significant PCB input route was through atmospheric fallout.  Thus the environmental
free PCB load model focuses attention on the origin and properties of the atoms-
pier ic reservoir.
     Since the primary focus on aquatic pollution rests on the effect of such
pollution on the living beings in the aquatic environment, some attention is paid
to the construction of a simple fish-load model.  Specifically, it can be shewn
that, for a trout, the body concentration of PCBs will follow that of the average
aqueous concentration  (with a suitable bioconcentration factor).  Thus, in order
to significantly reduce the PCB concentration within the higher predatory fishes
it is essential to lower the aqueous PCB concentration correspondingly.
     At the completion of tiie above consideration it is appropriate to further
exercise the model by application to a schematic Great Lakes System.  Ihe results
of this analysis are then compared to existing experimental data especially for
Lake Ontario.  Ihe outcome of this comparison is the observation that, in spite
of the necessity to make several assumptions, the theory is of some use since the
same assumptions that suffice to deal with the simple system involving only Lake
Michigan are found to be adequate to deal with the significantly more complex
Great Takes system.
     Finally, the possible effects to be derived from various possible regulatory
actions are discussed in terms of the model.

     1.1 Mass Balance Model - General Considerations
          In order to construct a mass balance model to be applied to a body
of water such as Lake Michigan, it is appropriate to determine the manner in
which an incremental increase in PCB content is distributed within the various
processes available.  In what follows, it is explicitly assumed that:
                                        -2-

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           (a)  Due to mixing and diffusional processes,  the average
               aqueous PCB  (refractory organic)  within the body of water
               is dependent  only on time.
           (b)  The PCBs  (refractory organic)  that review within the
               body of water are distributed by  solution in the aqueous
               phase, in  "solution" in the biota or within the  sediment.
           (c)  The essential loss mechanisms from the  body of water are
               evaporation from the air-water surface  and  carry-off due
               to outflowing waters, at least for short  time intervals.
In terms of these assumptions, a differential equation can be developed that
describes the time rate of change of the PCB concentration in the various phases
of the lake in terms of the input rate of PCBs.  This equation may be integrated
under various assumptions as to the time dependence of the input rate to yield
alternate expressions for the concentration of PCB within the separate phases as
a function of time.
     1.2  Model Development
          Let B(t) be the rate of injection  (Ib/yr) of the PCBs from all
sources at a reference time  t [where t (years) = 0  in  1930].  Then,  within
the interval t to t + At, an incremental amount of PCBs equal to B(t)At will be
injected into the system.  This quantity of PCBs will be partially partitioned
into the various phases, with the balance removed by evaporation and/or outflow.
                 If Q(lbs) is taken to represent the total water mass in the
Lake (assumed to be constant) and C  (t) the concentration* of PCBs in the water
*ln most cases concentration will be specified in gms solute/gm solution, i.e.
 as a dimensionless quantity.  Those exceptions will be explicitly stipulated
 when the occasion arises.

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at time t, then
                      i
which, in terms of the definition of concentration, causes an increase in soluted
PCB of magnitude*

                                          AC7
                                               ^.                        (1-1)
                 In a wide variety of environmental situations    there appears
to exist a rather definite relationship between the concentration of PCBs within
the sediment and/or the "average" member of the biota and that of the water in
which they are immersed.  Tliese general relationships are herein defined as
                                    z
                                      water
                                 n =
                                     c
                                      water  J
                                                                          (1-2)
                                    _  cdota
and are assumed to be independent of C  .    and of time.
                 Using the relationships expressed by Eq. (1-2), the incremental
increase in the mass of PCB stored in the biota is given as

                                          ACU
                             ^iota - <* AtT  At'                        t1-3'
where it is assumed that the concentration of PCBs within the biota was in
equilibrium with that in the water at time t and that G(lbs), the total mass of
the exposed biota, is .constant over the period of interest.
                 Similarily, if the rate of deposition of sediments is taken
to be D(lbs/ft2/yr) and the area of the lake to be A (ft2) , then, assuming that the
principal exchange processes between water and sediment occur within the aqueous
phase during the settling out process, the incremental PCB pickup by the sediments
is given as:
                           Amsed = ADpCw(t)At                             (1-4)
 *The term "soluted PCBs" is taken to represent the total PCBs in solution or
  attached to suspended sedimentary material.
                                      -4-

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 [where the additional term  (1/2) =~ At is considered small, especially as  At ->• o].
                 If the rate of outflow from the lake  (through the Straits of
Mackinac is taken as S  (Ibs/yr), then the loss of PCB  due to this outflow may be
taken as:

                           ^outflow - SCw(t) At •                         (1'5)
                 Finally, the mass of PCB carried out  of the system by evapora-
tion is given as:
where K is the evaporation rate constant which will be discussed below  (Section  6).
                 Now, the principle of conservation of mass requires that all
the injected PCB be accounted for,  (note that no effective degradation processes
are considered to be operative) from which it follows that

             B(t)At = Am  + Am.  .  ,  + Am   , + Am   . ...   + Am
                '       w     biota     sed     outflow     evap

Introducing the definitions of each of the incremental mass loads, and proceeding
to the limit At -> o and dropping  the subscript w since the only concentration
appearing is that of the PCB in water, the operative differential equation becomes

                        (Q + Gn) g£ +  (S + K + ADp)C = B(t)                 (1-7)

which, for convenience in what follows, may be rewritten using the substitutions,

                    _S + K + ADp
                        Q + Gn
                                                                           (1-8)
                     Q + Gn
and Equation (1-7)  becomes

                                  = YB(t) .                                (1-7')
                                       -5-

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The solution of Equation (1-7) takes the simple explicit form
r
/
                                          f
                       CCtfl = yef      B(u)eSudu              (1-9)
under the special circumstances that C(t) = o at t = o  C1930) and further that
the parameters y and 3.  Cand hence the constants introduced in Equation 1-1
through 1-6) are independent of time.
                 m the initial application of the model in Sections 3.1 and
3,2, it is further assumed that:
                  Ca)  There are no degradation processes that are
                      active for PCBs over the time interval in
                      question.
                  (b)  That all the PCBs may be treated as a single
                      chemical species.
                  (c)  That both y and 3 are independent of position
                      as well as of time.
The further development of the general mass balance model, in the latter sections
of Chapter 3 deals with the effect on the solution of Equation  (1-9) due to
spatial variations in y and 3 as well as the effects of suspended solids.  In
Sections 4.9.1 and 4.10, the effect of a spatial variation in B(u) is considered
Finally, the effect of environmental degradation of PCBs on the forcing function
B(u) and hence on the solution of Equation  (1-9) is discussed.
                 The next two chapters deal with the application of the model
to a typical test case; i.e. , to the study of PCB distribution in Lake Michigan.
                                        -6-

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2.0  PARAMETERS FOR LAKE MICHIGAN
     2.1  Introduction
          As shown in Section 3.7, the solution of the mass balance equation is
rather insensitive to the precise value of 3, at least in terms of a direct
comparison to the available in situ aqueous concentration measurements.  Never-
theless, it is altogether appropriate to attempt an estimate of the parameters,
p, r\, G and K.  In most cases, since an accurate value cannot be assigned for
these parameters, an average value will have to be used with full recognition
that, although the detailed results may well be modified as better data become
available, the general features of the model should still be applicable.  In
later sections, an attempt will be made to estimate the range of uncertainty in
the computed PCB concentrations in terms of the possible ranges of the significant
parameters.
     2.2  General Physical and Hydrological Parameters for Lake Michigan
          The general physical and hydrological parameters for Lake Michigan are
                 (2)
taken as follows:v '
          A  =  surface area of the lake = 6.24 x 1011  ft2
          S  =  outflow through Straits of Mackinac = 1.2 x 1011* lb/yr
          Q  =  water mass in lake = 1.1 x 1016 Ibs
          D  =  sediment deposition rate = 0.204 lbs/ft2 yr
          A1 =  average drainage area = 1.29 x 1012 ft2
                                        -7-

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          2.2.1  Biotic Mass, G, for Lake Michigan
                 A representative value for the biomass in Lake Michigan, recog-
nizing the relatively limited data that are available on specific species and
the absence of a detailed ecological pyramid, may be obtained from the estimates
contained in Table E-ll (Appendix E).
                 In view of the uncertainties in the details of the relative
magnitudes of the various levels of the biological pyramid, an estimate of

                                 G = 1010 Ibs.

is taken for vtfiat follows.  At the same time, it is perfectly possible that G
might actually be as much as an order of magnitude higher.  Further, it is
assumed that G ^ G(t) and, thus, has remained constant over the time interval
of interest.
     2.3  Proportioning Constants,  p and r\
          In order to determine the most appropriate values for the proportion-
 ality constants  p and r\f in  the absence of a well-founded theoretical explanation
 of the physical  processes which determine them, it is necessary to rely on in-situ
 measurements of  concentration over  wide regions' of the target water body to
 establish reasonable statistical reliability.  Actually,  such a body of data does
 not  exist for Lake Michigan  at  this time.  On the other hand, some data do exist
 for  Lake  Ontario which  should allow at least a reasonable estimate of the appro-
 priate values for Lake  Michigan.
          The essential experimental problem lies in the  observed fact that al-
 though the  concentration of  PCBs in typical  contaminated  sediments and in the
 larger fishes lie well  within the range of high accuracy  for analysis, the
 corresponding water levels lie  very near the present limits of detection.  Thus,
 since the proportioning constants are expressed as ratios of PCB concentrations,
 the  uncertainty  in c  (t) will necessarily show up as uncertainties  in the values
                    Vv
 of p and  n-  But again, the  relative insensitivity of C  (t) to the precise value
 of 3/ suggests that even these  uncertainties are not of impressive  significance to
 the  derived results.

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          2.3.1  Biota Concentration Ratio, r\
                 The brief sunmary of data displayed in Table E-12 and the
discussion which follows in Section E-5, both of Appendix E, suggests that the
value to be used for the bioconcentration ratio, n, is
                               H ~(4-8) x 10*

for Lake Ontario which, by inference, should also apply to Lake Michigan.  It
should be noted that n is taken as an average concentration ratio over all mem-
bers of the biota; thus, there will be specific species showing considerable
variation from the assumed value.
                 Since the basic physical processes that account for this
partitioning of PCB-like materials should be independent of the actual concen-
tration of PCBs in the aqueous phase  (so long as the aqueous solution is less than
saturated), it is reasonable to assume that ri is independent of time.
          2.3.2  Sediment Concentration Ratio, p
                 The estimates of  sediment concentration as compared to water
concentration that are discussed in Section E.6 of Appendix E suggest an average
value for p as applied to Lake Michigan of

                                    p~2 x 103.
This result is also subject to considerable variation, even over the confines
of a single body of water.  For  example, due to  influent effects,  there may be
considerable spatial variation in  the properties of  the sediment.   In a typical
sediment,  some portion, a, -of the  sediment is organic in nature; the remainder,
 (1-a),  is  inorganic.  The reported values  of partition coefficients for organic
and for inorganic material as compared to  water are  very different (as discussed
in more detail in Appendix B).
                 Let p  = the average partition coefficient organic/water
                     p. = the average partition coefficient inorganic/water
                     a  = organic  fraction,
 then
                      peff = apo + (1~a)  pi'                         (2"1)
                                        -9-

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 In Appendix B,  typical values of p  and p.  are derived from published experi-
 mental data.  The implications of a spatial variation in a and thus in P^f
 are  discussed in Section 3-4.  Suffice it to say again, that the insensitivity
 of 3 to  the precise value of the proportioning parameters suggests that the
 average  value selected will suffice until more comprehensive aqueous concentra-
 tion data are available for comparison.
      2.4  PCB Input Rate to Lake Michigan
           Again, the lack of historical data imposes the necessity for the
 introduction  of an assumption.  Specifically, it is assumed that the rate of
 PCB  input to  Lake Michigan follows essentially the same time dependence as
 does the estimated environmental load as given by Equation (C-24) (Appendix C)
 and  more specifically by Equation (C-40)(Appendix C).  The available background
 data for the  period 1973-1974 on tributary inputs to the lake are presented in
 Tables (E-2)  through (E-9) of Appendix E.
           A variety of fallout rate measurements have been reported^   indicating
 rates as high as 0.5 Ibs/mi2/yr = 87 ug/m2/yr in the heavily industrialized
 portion of Sweden     to the other extreme of 17.5 yg/m2/yr observed in Iceland.
 In view of the  rather heavy concentration of industry in the Lake Michigan area,
 it will be assumed that the average fallout in the 1974 era was 50 yg/m2/yr.**
           Thus, taking the area of the lake to be 5.8 x 1010 m2, the annual
 fallout should  be of the order of
                   B- ,,  4. ,,•  _u ~6.4 x 103 Ibs/yr in 1974.
                    fallout direct               /jr
           Thus, the contribution to the PCB input 1973-1974 may be sunmarized
 as follows:
           Point sources   1.6 x 103 Ibs/yr
           Lake  fallout    6.4 x 103 Ibs/yr
           Basin fallout   5.4 x 103 Ibs/yr  (where it is assumed that 50 percent
                                             of basin fallout actually enters the
                                                   (6)  *
                                             lake)( '
           Total           13.4 x 103 Ibs/vr  (1973-1974).
 *The fraction of material which falls on the watershed to ultimately end up in the
  lake depends markedly on the soil type of the watershed as well as the compound
  in  question.  In the absence of other guides, the factor 50 percent is selected.
**Treated in more detail in Section 4.9.
                                       -10-

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As shown in Appendix C,

                                 B(t) = at3'5


which for the reference year, 1974, was estimated to be


                            13.4 x 103 = a<44)3*5

                                     a = .0237
so that, in what follows,
                            B(t) = 0.0237t    •                     (2-2)
     2.5  Evaporation Rate Constant K

          This factor is the most difficult parameter to establish, primarily
 since the theory of co-distillation has received little attention.  An attempt"to

 apply the theory of MacKay and Wolkoff   ' in the special situation of dynamic

 equilibrium between fallout input, evaporation and diffusion within the surface

 layer is presented in Section 6.  In the meantime a tentative value for K is

 assigned as follows

                             K = 2.2 x 10llf Ibs/yr.


 In Section 3, the mass balance equation will be used to determine a more "correct"
 value for K.  Section 5 will deal with K in more detail.

     2.6  Summary of Physical Parameters for Lake Michigan

          The parametric values listed in Sections 2.2 through 2.4 are summarized

 in Table 2*6-1.
*The discussion in Section 2.4 and in Appendix E specifically neglects the
 large cumulative spill due to the local industry in the Waukegan Harbor
 federal navigation channel - a spill amounting to more than 100,000 Ibs
 [USEPA Survey, 16 Sept. 1976 contained in letter from C. M. Timm].  The PCB
 concentration in the outflowing waters at the north breakwater light were
 found to be less than background levels (0.1 ygAg) and thus most of this
 large spill is apparently confined to the sediments within the channel.  Thus,
 even though this is a large PCB reservoir, it is not taken into account in
 the total Lake Michigan PCB economy.  See further discussion in Appendix E.
                                        -11-

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                                   Table 2.6-1*
                Physical and Hydrologic Constants for Lake Michigan
          The values used for the various physical and hydrologic constants
for Lake Michigan are listed below: *- *
     A        = surface area of the lake = 6.24 x 1011 ft2
     S        = outflow through Strait of Mackinac = 1.2 x 10 14 Ib/yr
     Q        = water mass in lake = 1.1 x 1016 Ibs
     D        = sediment deposition rate = 0.204 Ibs/ft2yr
     ri        = biota/vater concentration ratio = 4 x 101*
     p        = sediment/water concentration ratio = 2 x 10 3
     B (1974) = FOB input rate in 1974 = 1.34 x 10" Ibs
     K        = evaporation rate constant = 2.2 x 10 1J* Ibs/yr
                    [this assumption will be discussed below in Section 5]
Then, from the data above, the various factors appearing in Equation  (1-91) may
be evaluated as follows:
                            ADp = 2.25 x 101" Ibs/yr
       Q + Gn = 1.14 x 1016  (3bs) ,  (Q + Gn) ~l = 8.77 x 10"17 (Ibs) -1
                         S + K + ADp = 5.7 x 10llf Ibs/yr
                             S + K + ADp
                         P =    Q + Gn     ~ 0.05  (yr) ~l
                            AGn
                                    -  8-77 x 10-"
*A discussion of the effect of variation of the parameters G, n and K is
 found in Section 3.7.
                                        -12-

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3.0  APPLICATION OF THE MASS BALfiNCE EQUATION TO LAKE MICHIGAN
     3.1  General Considerations
          The mass balance equation (1-9),  which is derived from the schematic
representation shown in Figure 3-1-1, may now be solved for Lake Michigan
using the parametric data presented in Chapter 2.  Several comments are in
order as to the effect of the assumptions outlined in Chapter 1.  For expli-
cidness, the model is carried through assuming that there is no spatial varia-
tion in the driving function B(t) and that there are no active degradation
processor causing the removal of PCBs.  Actually both these assumptions may be
relaxed as  shown in Chapter 7.
          Further, the assumption that all PCB's may be treated as a single
chemical species is not really necessary in the sense that the parameters n/
p and K. may, or perhaps should, be treated as averages over the various
species of PCB that are involved.  An interesting result of the enormous
mass of water involved in a body such as Lake Michigan is shown in the dis-
cussion in Section 3.7 which clearly shows the insensitivity of the solution
of Equation  (1-9) to the precise values of the parameters.
          The explicit assumptions:
          (a)  Evaporation, or more accurately, co-distillation is a signifi-
               cant process having marked influence on the mass balance and,
          (b)  the parameters 3- and Y are time independent;  seem to be
               irreducible, at least in this first order model.

          Finally, the assumption of uniformity of aqueous concentra-
tion may be removed by a simple modification of the method of solution applied
to the schematic Great Lakes System contained in Chapter 4.
                                      -13-

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                                     ^Fallout
             tEvaporation
             '[Co-distillation]
                      Point Source
*«.
                                                          Lake
                                        I
                                         Biota
                Outflow
Sediments
                                                    Figure 3.1-1
                                        Graphic Description of Model Described
                                                  by Equation (1-7')

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     3.2  Integration of the Mass Balance Equation
          In terms of the parameters for the  lake and the assumed form for
B(t) from Equation  (2-2), the differential equation for C(t), Equation (1-9)
becones:
                C(tf) = 2.08 x 10~18 e   '   ff  u3'5  e°'osUdu           (3-1)
which can be integrated by normal numerical methods but can more conveniently
be integrated by the methods outlined in Appendix A.   In any case, the approxi-
mate result of integration of Equation  (3-1) is

                      Cw(tf) ~  4.44 x  10-19tf"-5 e-°-°08tf                (3-2)

which, for (1975) (tp = 45 years) yields an aqueous PCS concentration
                    j.
estimate of 8.5 x 10~12 (8.5 ppt).  The detailed results of the numerical
evaluation of Equation  (3-2) are displayed in Table 3.2-1.
          To now examine the implication of Equation  (3.1) it  is useful  to deter-
mine the distribution of PCBs within the various portions of the lake as of 1975.

          3.2.1  The Sediment load  (M   ,)
           •                          sed
                 From the definition of the incremental sediment pickup,
Equation  (1-4), the total sediment  load in 1975 is given by (tf = 45 years)
                                             .45
                                           /    v
M   _ (1975) = ADp  /     CTT(t)dt                   (3-3)
 sed
which, on substitution of Equation  (3-2)  and integration yields

                    Msed  (1975) = 1-56 x 10" Ibs = 7.81 tons .             (3-4)
                                       -15-

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                                   TABLE  3.2-1

                      PCB Concentrations  in Lake Michigan*
                                  [Equation  3.2]
Date                   tf (years)           Cw(tf)/gm\                Cw(tf) (ppt)
                                                   \gm/
1930                    00                         0

1935                    5                   5.96 x 10~16              6 x 10""

1940                   10                   1.3 x  10 -1"               0.013

1945                   15                   7.72 x KT1*              0.077

1950                   20                   2.71 x 10"13              0.27

1955                   25                   7.1 x  10~13               0.71

1960                   30                   1.55 x 10 ~12              1.55

1965                   35                   2.98 x 10 ~12              2.98

1970                   40                   5.22 x 10~12              5.22

1975                   45                   8.52 x 10~12              8.52
                                                                                (9)
*Msasurements in 1973 indicate a range of aqueous concentration of  1 to 7.5 ppt
                                      -16-

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          3.2.2  The Water Burden of PCBs
              (Mwater>
                 The total PCB mass that is in solution in 1975 is given by





         Mwater(1975)  = Q x Cw(45)




                       = 1.1 x 1016 x 8.52 x 10~12 = 9.37 x 104 Ibs .      (3-5)




          3.2.3  The Biotic Load of PCBs
                 The biotic load of PCBs in 1975 is given by




                   M..  .  (1975) = Gn x C (45) = 3.41 x 103 Ibs •           (3-6)
                    Diota               w       	



          3.2.4  Outflow loss Through Madcinac Straits (M       )



                 From the definition of the effect of the outflowing current S,


Equation (1-5), the cumulative PCB loss due to this factor may be estimated as




                                  /•45

                    Outflow =SJ  Cw(t)dt = 8.34 x 103 Ibs .             (3-7)


                                 o




          3.2.5  Total Input and Cumulative Mass Balance  (Mtotal)



                 The total cumulative PCB mass that entered the lake is given by



                                        •45

                                           B(t)dt


                                       'o
which, on substitution of the form of B(t) from Equation  (2-1), yields the result



                                            ,45


                                                 15 dt


                                          'o



                                   = 1.45 x 105 Ibs .                      (3-8)
               r45
Mtotal " -0237J  t3'
If now the sum of Equation  (3-4), (3-5), (3-6) and  (3-7) is compared to  (3-8)  the


result shows that the net loss due to evaporation was  (cumulative)



                                  2.40 x IP1* Ibs .                           (3-9)




                                        -17-

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          3.2.6  Co-Distillation Losses and K
                 Fran Equation (3-2) and tfie definition of the average of a
function,     the average concentration (1930-1975) is given by
                                             /5
                                               u*5e-008Udw                (3-10)
which, on integration  (the exponential may be expanded in Maclaurin series
retaining only the first two terms) , yields the approximate solution

                          - 4.44 x IP"19  (45) 5'5   -<.ao68)(*5)
                       t) --  -          e
                    r     -  .
                    Cw(t) -- 35 -   5.5

                          = 1.64 x ID'12 •                                 (3-11)

 Thus, from the definition of K, Equation (1-6) , the average value of K is given
 as

               g-  (AMevap)total   2.4  x  10*        1    3  « x  u» 1K ,
                     Cw(t)At     ~ 1.64 x ID"12 X 45" "  3'25 X  10   Ug/Vr  (3-12)

 which is then to be compared with the  assumed value of K  (Table 2,5-1) of
 2.2 x 101* Ibs/yr.
                  A further estimate of the value of K may be determined by exami-
 nation of tiie incremental changes in PCB load in each of the "phases" during the
 period 1974-1975.
                           AMw = QACw = 8.36 x 10 3 Ibs
                               = GnACw = 3.04 x 102 Ibs
                                   ^A = 1'83 X 1Q3 lbs
  viiere, from Equation (3-2) , the average concentration for the period 1974-1975
  was
                          r TH             8 19 v in~12
                          Vt; 1974-1975 ~ a-^ X 10

                                        -18-

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                         Table 3.2-2
               Sumnary of PCS Mass Distribution*
                        Cumulative                 1974-1975
   Minput             1>45 x 1()5 lbs-           1<39 x  10"  lbs'
   Mwater             9'37 x i0* lbs*           8'36 x  1C)3  lbs*
                      1.56 x 104 lbs.           1.83 x  103  lbs.
                      3.41 x 103 lbs.           3.04 x  102  lbs.

   Moutflow           8'34 x 1C)3 Ibs*           9<76 x  1C|2  lbs'
   Net Mg             2.395 x 10" lbs.          2.43 x  103  lbs.

             K = 3.25 x 10:if Ibs/yr      K = 2.99 x 101" Ibs/yr
*Sunnary of results of Section 3.2.1 through 3.2.5.
                               -19-

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and the change in concentration during the same period
                         *V(t? 1974-1975
Furthermore, the input to the Lake system during this same time interval was
                                           .45
                                          /
                                  = .02371   t3'1
                                         J/->
AM.     = .0237/   t3*5dt
  input
               ro
                                  = 1.39 x 10* Ibs .

Hence, the net loss of PCBs due to evaporation during the period 1974-1975 is
equal to the net input less the accounted for deposition in the other "phases";
i.e.
                       AM              = 2.43 x 103 Ibs
                         evap!974-1975
whereupon                  _  ._   ina
                       K = 3 12 x lir12 = 2>" x lollf ^/y63* •            (3~13)

A further discussion of the K values, Equation (3-12) and (3-13), will follow
later; in the meantime another important parameter must be dealt with.

     3.3  Effect of Organic Content in Sediments
          Returning to the formal solution of the mass balance equation,
Equation (1-9) and the definitions in Equation (1-8), which will be rewritten here
for convenience

                         C  (t.) =ye~3tf /  fB(u)eeudu                     (1-9)
                          vv  J—
and                             B = S + K + ADp
                                     Q + Gn
                                      1
                                Y =
                                    Q + Gn
                                      -20-
                                                                           (1-8)

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          It has been shown in Section (1-5)  that the effect of variation of
 the decay constant 3/  is to produce rather small changes in the resulting
 concentration.   Specifically, from Equation (2-1),  it is found that the value
 of p  to be used in a given situation depends markedly on the organic fraction
 a of  the sediment.  In Appendix B, it is demonstrated that appropriate values
 for pQ = 10s  and for p.^ ~ 10, so that the specific value of p ff may vary
 from 10 for entirely inorganic sediments to 10s for entirely organic sediments.
 Table 3.3-1 illustrates the effect of organic content on p ff and thence on 3-
 In addition,  the effect of variation in organic content on the resulting con-
 centration to be expected in Lake Michigan is summarized in Table 3.3-2.
     3.4  Extended Lake Michigan Model
          Suppose that the lake actually consists of two distinct regions in
that the organic content of the sediments are very different in the taro
regions.  The  lake may then be divided into two segments, denoted by I and
II with rapid  interchange between the aqueous portions of the segment such
 that the aqueous concentrations are identical at all times.  Thus, the mass
 balance equation for the segments becomes:
(3-15)
                  Gin          +si + Ka + DAipi   Ci(t) = Bi(t)


                  G2n]  S|^ +[S2 + K2 + DA2P2J  C2 (t) = B2 (t)
but'         d(t) = c2(t) ,   [QI + Gin]  + [02 + G2n] = Q + Gn;
                             Si + S2 = S

                             Ki + K2 = K
                        and  Bi(t) + B2(t) = B(t).
 Adding the Equations  (3-15) yields the resulting overall mass balance equation

                               +  fs + K + D  (Aipi + A2p2)j  C(t)=B(t).   (3-16)
                                        -21-

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                                  TABLE 3.3-1





                  Effect of Organic Content of Sediment on 8



                      Peff                  ADpeff                  3  (Eg.  1-8)





0.001                 102                 1.27xl013                    .0314




0.01                  103                 1.27 x 101"                    .0404



0.1                   10"                 1.27 x 1015                    .1417



1.0                   10s                 1.27 x 1016                   1.145
                                       -22-

-------
                                 TABLE  3.3-2
       Effect of Organic Content of Sediment on Aqueous Concentration
peff
0
10
102
10 3
5 x 103
10*
10 5
6
.0298
.0298
.0314
.0404
.0853
.1417
1.145
Co
0
0
0
0
0
0
0
C20 yrs
(ppt)
.297
.297
.29
.28
.25
.19
.004*
C30 yrs
(Ppt)
1.76
1.76
1.67
1.61
1.28
0.91
0.003*
C40 yrs
(PPt)
6.13
6.13
5.70
5.43
4.01
2.52
0.001*
C45 yrs
(PPt)
10.17
10.17
9.39
8.87
6.30
3.77
0.002*
* Because of convergence problems these values are to be considered as essentially
  zero.
                                      -23-

-------
As before
                          8 = S * K + D
                           '   Q + Gn
     Equation (3-16) has the formal solution
                                    Q + Gn
                                                                           (3-17)
                         Cw(t) = ye^f  /   e3uB(u)du
                                        o
where u is a symbolic integration variable.  On substitution of the values for
Y and the form of B (u) from Equation (2-1) ;
                                              S*
                                              /    e6uu3'5du .
NOW
                   Cw(t) = 2.08 x 10~18 ef     euu3'5du .               (3-18)
   , the values of tf which are of interest are in the range

                          0 < tf < 45     (1930-1975)

hence, the series solution of Equation (3-18)  can be shown to converge sufficiently
rapidly to be of practicable value

                                    3 < 0.4 .
          By suitable manipulation of the defining equation for 3 , Equation (3-17) ,
it can be shown in the case that the areas of the two segments of the lake are
equal,

                      3eff = .0298 + 5.6 x lQ-6(pi + p2).                  (3-20)

Now, by way of illustration select *

                    Pi = 10, i.e. entirely inorganic sediment
                    pa = 4 x 103, i.e., 4% organic matter in sediment
The average organic content of lake Michigan sediments is of the order of 4%
  (actually this is based on a total organic carbon measurement).

                                       -24-

-------
then

                                  3 = 0.0522




and, suitable evaluation of Equation (3-18) for this specific value of 3 yields


the approximate form for C (t)





                        Cw(t) = 4.62 x i0-19t'"5e"0088t                   (3-21)




from which Cw(1975) = 8.49 x 10~12  (which compares favorably with the values


tabulated in Table 3.3-2).  Hence, the total mass balance may be computed  (for


the period 1930-1975) as follows:




          AM           •     i
            water = QC .(45)

                                = 1.14 x 1016 x 8.45 x 10~12 = 9.68 x 1Q1* Ibs


          ^iota = GnCw(45)





          ^outflow = S/Cw(t)dt = 1.2 x 101* x 6.89 x 10"11 = 8.27 x 103 Ibs





                      Pi Tcw(t)dt = 6'24 x ^°	x -204 (10) x 6.89 x 1011 = 43.85 Ibs






          AM—-  = ^ P2/*Cw(t)dt                                    = 1.75 x 10"
and the total input is as before  (Equation 3-10)




                           AM.    . = 1.45 x 105 Ibs •
                             input       •




Hence, the evaporation loss is, in this case,




                            AM     = 2.24 x 10" Ibs
                              evap   —————



which is to be compared to the value obtained in Equation  (3-9)
                                        -25-

-------
The special significance of the large variation in PCB partition coefficient
allowed for each of the two zones is demonstrated by a computation of the average
concentration of the sediment deposited during 1975 for each of the two zones:
                      KEconc    - M(PCB) sed     _
                              sed   Deposited mass   A.D.


where                 A.^ = area covered (assumed to be ^ )

                      D. = deposition rate = 0.204 Ibs/ft2/yr
                           (assumed to be uniform over the entire lake)
          In zone I, p = 10 (no organic)
                    — — —         44
                    Clsed(1975) ~ 6.37 x lb10 = 6'91 x 10~
                                 1.75 x 10k
                                                        ,-7
                    C2sed(1975 - i.37 x lO10 = 2'75 x 10

Thus, in this case, the relative concentrations within the sediment in the two
zones differ by several orders of magnitude.  The total sediment load is approx-
imately 1.75 x 101* Ibs to be compared to the value listed in Equation (3-4).

           3.4.1  N Sediment Zones
                 To extend the model to  a system partitioned into N zones  of
differing  sediment constitution  (i.e., different percentage  of organic material)
it is only necessary  to replace  the factor ADp which occurs  in 3 by the  sum

                                   E VlPl
                                   i=l

where provisions have been included to provide  for varying deposition rates,  D^.
                                        -26-

-------
10 '_
Plot of
                 .
               Cw(t)
                    Figure 3.5-1


                      for p^ = 4 x 103
                   (Equation 3.26)
                     -27-

-------
    3.5  Effect of Suspended Solids
         Suppose that there exists a concentration fy of permanently suspended
solids characterized by a partition coefficient p, within the body of water
of mass Q.  Then the total mass of water plus sediments is

                                M = Q(1-H(;).                       (3-23)

If now the concentration within a filtered water sample were C T  (t) then that
associated with the suspended sc
"soluted" PCB would be given as

                        M(t).

On the other hand, the effective concentration of the PCBs within the suspension
as given by Equation  (3-2) for Lake Michigan is taken as C  (t) and the mass of
PCB within the suspension is

                            M(t)PCBSol=QCw(t)'                 (3-25)

Equating Equation  (3-24) with (3-25) indicates that
                                              •                   <3-26'
associated with the suspended solids would be p .C   (t) and the total mass of
                            PCB SOI
Hence, given the suspended solids concentration and the percentage of organic
material contained therein, it is possible through Equation  (3-26) to relate the
                                                      i
C  (t) from Equation  (3-2) with the actual measured C   (t) of filtered aqueous
solutions.
    3.6  Effects to be Associated with PCB Loads Contained within Sediments
         One serious question that might arise deals with the possible effect
of re-solution of entrapped PCBs from sediments deposited during an earlier
                            0.2 )
epoch.  It has been asserted     that one nasty effect to be associated with
attempts to eliminate sources of PCBs to such bodies as the Great Lakes lies
in the fact that the sediments contain large reservoirs of PCBs which would
have to be removed prior to any lessening of the aqueous concentration within
the lake.  Several comments on this question are appropriate.

                                       -28-

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          3.6.1   Redistribution Due to Complete Mixing of Water/Sediments
                 Suppose that at the end of 1976, all external sources of PCB
to Lake Michigan were suppressed and, further, that all the PCBs stored in the
sedimentary layers were available for re-solution.  What could be expected to be
the time before the aqueous concentration  fell to 50 percent of its 1976 level?
                 It is assumed that the partition coefficient between water and
the sediment is 2 x 103 (as assumed before) and that the sediment rate is
AD = 1.27 x 10X1 Ibs/year and has been constant during the entire interval from
1930, then the total PCB load at the end of 1976 within the sediment is given as
mr6,(
ADp I   C  (
   J    W
                   Msed(PCB)  = ^P '   C-(t) =  1'32 x 10  ^              (3--27)
 where C (t)dt is given by Equation  (3-2) .  Also, at the end of 1976, the total
        W
 load in the aqueous plus biotic phases is given by

                   MpQ^w) =  (Q + Gn)Cw(46) =1.06 x 105 ]Jos             (3-28)

 thug,  the total "available" PCBs is 2.38 x 10s Ibs at the reference date.  To
 compute the resulting concentration in the water after mixing
                                               _
                                       ADpt + (Q + Gn)

 where ADpt = (ADp)(46) = total mass of contaminated sediment.

                 Thus, immediately after mixing the aqueous concentration will
 be
                            Cw(46)eff = 10.3 x 10~12.

                 During the succeeding year, the losses from the system result
 ing from evaporation plus outflow are given as

                         Mloss =  (K
                                       -29-

-------
                         Elapsed Time (yrs)
                        Figure 3.6.1-1
     Effect of Complete Removal of External PCS Sources
Coupled with Complete Resolution from Contaminated Sediments

-------
To a first approximation then

             Mlosg(47 year) =  (3.4 x 10   ) (C^(46))=  3.5 x 103  Ibs;

thus, the remaining PCB is just 2.38 x 105 -  3.5 x 103 =  2.345 x 105  Ibs.
Meanwhile, the sediment load has increased by an amount AD = 1.27 x 1011 Ibs,
so that the concentration in the water at the end  of the  47th  year  is approxi-
mately
                           Cw(47) - 10.0  x 10~12.

Proceeding in this stepwise manner results in the  following approximate con-
centrations in succeeding years as shown  in Table  3.6.1-1.

                                 TABLET 3.6.1-1
              ESTIMATED AQUEOUS  CCNCENTRATICN IN LAKE MICHIGAN
                        t  (from 1930)   Concentration
46
47
48
49
50
51
52
53
54
10.3
10.0
9.78
9.53
9.30
9.08
8.86
8.65
8.45
x 10-"
x 10"12
x 10-12
x 10-12
x ID'12
x 10~12
x 10-12
x 10"12
x lO"12
In order to best utilize the results obtained above, a standard regression
analysis yields the relationship (see Appendix A)
                                              -1 «22
-------
          3.6.2  Effect of Layered Sediments - Undisturbed Sediments
                 The above calculation is highly simplified in the sense that
the situation within the sediment is such that only a small part of the entire
PCB load would be available for resolution in an undisturbed sediment.  Actually,
the sediment must be considered as being made up of layers deposited in earlier
epochs each with a concentration appropriate to the aqueous concentration during
the time of deposition.  Under these circumstances, it would be expected that
diffusion of the PCBs would tend to diminish the concentration gradient with the
result that the top  (most recent) layer would, in  fact, exhibit a concentration
less than would be expected as a result of the aqueous concentration at the
time of its formation.  To illustrate the effect of diffusion on reduction  of
the concentration gradient through the various layers of  the sediment, consider
                                                                             (13)
the expression for the rate of mass transport along a concentration gradient
                                                                           (3-301
where A is the area of the layer (cm2)  of thickness d (cm)  across which there
exists a concentration (gm/cm3)  difference Cz-Ci.  D is the diffusion coefficient
   9
 cm
^sec^ of ^^ solute ^ the solution.  Applying Equation (4-3)  to Lake Michigan
sediments during the period 1930-1975, the parameters of use are
                     A  = 5.8 x 101" on2
                     b  = 5 on (0.1 cm/year)(14)
                     Ci = 0
                     C2 ~ 2.8 x 10"8 gm/cm3 [from Equation (3.2)  with
                                             suitable change in dimensions]
In order to estimate D, it is noted that     typical diffusion coefficients for
organics in water are of the order of 10"5 cm2/sec or, in terms of t in years,
        cm.
D ~ 3.5     .   Substitution of the numerical values into Equation  (3-30) yields

                           (gms/yr) ~ 2.25 x 106 Ibs/yr.                   (3-31)
                                       -32-

-------
The value deduced from Equation (3-31) is obviously much greater than the total
available sediment load; a result that can only be understood if it is assumed
that, due to this diffusion, the actual concentration of the surface layer is
significantly below that specified as due to the aqueous concentrations.  With-
out undertaking the complex problem of applying the diffusion equation in its
differential form to the problem, it is evident that on the time scale involved
herein, the concentration within the  total layered sediment should tend to some
uniform value which would be expected to be below the average value for the
precipitated layers over the period (1930-1975); lower than the average since
the layers deposited prior to the earliest injection of PCBs (1930) were
originally at zero concentration of PCBs.  The result to be expected from all
this is that, essentially, the PCBs contained within the sediments are actually
not available and hence, in the event that all external sources were shut off,
the only processes active would be the losses due to outflow, to evaporation
and to the material carried off by the newly forming sediments.  Under these
circumstances, the applicable differential Equation is Equation (1-7) with
B(t) = O
for which the solution is

                                  C = CQe " - .                             (3-32)

Introducing the value of B = 0.05, the time required for C(t) to fall to 1/2
its value in 1975 is

                         = 13.7
                                        -33-

-------
           3.6.3  Experimental Meaauflananta on Re-solution
                 In a laboratory study of a number of sediment samples from
 Lake Michigan, among other sources, Fulk et al     report that as a consequence
 of resuspension of PCB contaminated sediments in water
           a.  The amount of soluble pesticide material added to the
               water column by disposal of the sediment interstitial
               water is negligible at sediment-to-water ratios of
               1:10 or less.
           b.  The amount of pesticide  (material) desorbed from
               suspended solids is negligible at sediment-to-water
               ratios of 1:10 or less."
 In view of these observations it would appear that, in the absence of residual
 suspended  solids which contain PCBs from the sediment, that the estimates of the
 previous two sections of this report tend to exaggerate the effect of re-
 suspension of the sediment.

           3.6.4 Final Word on Sediments
                 It can be inferred from the above that, in the absence of some
 catastrophic event involving the re-suspension of the complete contaminated
 sediments, PCBs that have been carried down with forming sediments are, for all
 intents and purposes, permanently removed from participation in future contami-
 nation processes.  This observation can  be expected to be significantly less
 forceful when applied to the moving sediments in a river since re-suspension
                               (171
 is often a significant process.
               A further point in  the context of sediment re-solution is  in
order.  In those  cases wherein the  sediments are essentially undisturbed,  the
                      •
further formation of new sediment should, in the event that the aqueous concen-
tration (through which  they are transferred to the bottom) is decreasing in
time,  further isolate the more heavily contaminated sediments.
               All in  all, it appears that, in the absence of  significant
natural or biological degradation processes, sediment fixation  is  the primary
process acting  to remove PCBs from active participation  in biological processes.

                                         -34-

-------
     3.7  Effect on Aqueous PCS Concentxation Due to Parametric Variation
          As pointed out above the parameters G, n and K have been assigned some-
what arbitrary values.  It is important to note that the time constant 3, defined
by Equation (1-8), directly affects the numerical value of the computed aqueous
KB concentrations as is shown by  the solution of the  mass balance Equation
(see Equation A-9).  It thus becomes important to discuss the possible range of
the parameters G,  n and K, and the variations introduced in the computed PCB
concentrations that result from the extreme situations.
          The average biological portion coefficient, n, has been taken to be
4 x 10^ but, depending on the nature of the biota could easily be significantly
different.  For the purposes of this analysis,

                       1 x 10" < n ^  5 x 10s                              (3-33)

          It has been suggested^14' that the total mass of the biota, G, which
has been taken as 1010 Ibs, could very well be an order of magnitude greater, that
is,
                          1010 < G < 1011                                  (3-34)

          Finally, the parameter K, which is the surface co-distillation rate
constant has been more or less arbitrarily assigned a value of 2.2 Ibs/yr.  Actual
mass balance computations, in Section 3.2.5 suggest a value for K of the order of
3.0 x 10J1* Ibs/yr.  Further, the theory of co-distillation of MacKay and Vfolkoff,
if applied directly to the situation in Lake Michigan, suggests that K might be
as high as 3 x 1016 Ibs/yr.  Thus, the possible range of K is

                         0
-------
          The other parameters, Q, A, D, and S which appear in 3  are established
parameters.   The remaining parameter p, which characterizes the sediment partition
ing is established by the organic content of the sediment and is treated in some
detail in Section 3.3.
          Returning to the definition of 3 ,

                                  a _ K + S  + ADp                          n  R>
                                  3 -   Q +  GH —                          (1 8)

it is clear that the minimum value of 3 occurs when K = 0, Gn is maximum; i.e. ,

                             ?*n ' 1 1          - °-0075  '               (3-36)
On the other hand, the maximum, value of 3  would occur when K is vaximum and Gn
is ininimum, i.e. ,
                                  K    + S + ADp
                           ^ - <™— - '•«                    <

Compelling arguments, presented in Section 5.2, djndicate that the MacKay and
Wolkoff  '  theory of co-distillation cannot apply without modification in a situ-
ation wherein there exists a surface layer of enhanced concentration.   Thus, it
would seem that the upper bound on K is of the order of 5 x 1011* Ibs/yr, hence
the maximum value for 3

                                   3    = 0.049
                                    max

Summarizing the above, the probable range of 3 for Lake Michigan is

                                0.0075< 3 < 0.049  .                       (3-38)

The situation for 3 near the lower limit could be characterized as storage dominated
in that the factor (Q + Gn) is significantly larger than the loss factor
(K + S + ADp) .  The upper bound for 3 may, with some justification, be referred to
as loss dominated.
                                        -36-

-------
          3.7.1  General Properties of the Mass Balance Equation

          Frcm the form of Equation (1-9) it can be seen that, if there were
to exist an equilibrium state then gr - o.  Hence, from Equation  (1-9)

                                  3C = yB(t)

                              or  C=jB(t).                           (3-10)
                                   etj   p

But B(t) is a function of t, hence

                         dC       d
                                             °' hence
the system cannot be in equilibrium unless B(t) is no longer time dependent.
Further, in the special case that B(t) = o after t>t , then Equation  (1-9)
becomes, for t>t ,

                                 dc  + RP - o
                                 at  + ec " °'
                         or  C(t>tQ) = C(tQ)e p^  V-                     (3-11)

From the form of Equation (1-11) it is clear that 3 is the effective time
constant of the system.

          .The general solution of Equation  (1-9), given in Appendix A,  is
of the form
                                                                   (A 9)
vfcere B(t) = at .                                                  (C-40)
                                       -37-

-------
          In the following section an attempt is made to determine the proper
magnitude of the two partition coefficients, p and n and to estimate the total
bicmass, G as well as the evaporation rate constant K, all in order to determine
the appropriate value for 3 as defined by Equation (1-8).  It is instructive to
examine the effect of various values of 3 on the solution of Equation (A-9)
as follows:
                      C(t) yat       = Y>l)n   C3t)n
                          1      J     ~     Tr(6+l+n)                    (3-12)

which can be evaluated for o<_ 3 £ 0.1 and for t = 45 years.  The results of
this calculation are shown in Figure 1.2-1.
Further,
                                               n  n(3t)n
                                        n=o
                                                 n(n-l)(3t)n
                                        n=o

In a manner similar to the evaluation of Equation (3-12) , Equations (3-13) and
(3-14) have been evaluated for t = 45, o<3£ 0.1 with the results presented in
Figure 3.7.1-1.

          Clearly, the effect of 3, within the range Q<$
-------
-10
                                                            — .30    o
                                                             _1.00
                                                             0.14
                      Figure 3.7-1

        Properties of Equation  (1-9)
                              -39-

-------
4.0  APPLICATION OF MASS BALANCE EQUATION TO GREAT LAKES SYSTEM
     4.1  General Considerations

     The detailed procedure to be applied to the entire Great Lakes System
follows exactly that used for Lake Michigan with due account being taken of the
interconnection between the Lakes.  A decided difficulty arises when it is
noted that there is very little data available to allow an estimate of the
biological mass, G, for the lakes other than Michigan..  In order to obtain some
useful approximation for the biotic masses, it has been assumed that the total
biotic mass of each lake is proportional to its surface area.  Thus, the values
given under the heading Gn in Table 4-1 were derived from the estimated biotic
mass of Lake Michigan.
     In a similar manner, the evaporation rate constant K was derived.  Since
the thermodynamic theory of co-distillation ^ indicates that the rate of
evaporation of the solute  (PCB) is proportional to the water mass evaporation
rate and that the proportionality factor depends on physical constants, it is
appropriate to derive the K values for the lakes from that found in Lake
Michigan, allowance being made for the individual water mass evaporation rates
CEj).
                                      (18)
     The physical and biological data     appropriate to the lakes are listed
in Table 4-1 which follows.  For each individual lake, it is assumed that the
input PCB is the sum of the fallout contribution plus the inflowing streams
from the upper contaminated lakes.  Point sources are neglected, except insofar
as they contribute to the fallout itself.  Then the general differential
equation for each lake is given by
                   JP  (t)                                  n        /-H
         (A + Gn)i ^4r-  + (K + S + ADp) .D. (t) = B. (t) +  £  S. .C. 
-------
     The solution of equation (4-1) where C,(t)  = 0 at t = 0,  is given as
                                                               du
          cj(t) = «rr
(4-2)
where
             (K + S + ADp.
         •    <^
         D    (Q
                     j
                         -   where the elements of 3  are listed in Table 4-1
and where u is simply an integration variable,  u = t.

Now, the geographic conditions that obtain in the Great Lakes  are illustrated
in the schematic, Figure 4-L.l, which follows:

cs(t)
Bm(t)-1
M.
\
Cm(t)

Ss


Sm







i
Hun
s





•>n
h(t



r-B, (t) B6tt) B (t)
1
1 1
q G g
h Erie e Ontario o St.
) * Cg.(t) CQ(t) Lawrence
                                Figure 4 -1"!
                            Schematic of Great Lakes
                           Indicating Flow Connections
                                      -41-

-------
         TABLE  4-1
Hydrological and Physical Data
          Great  Lakes
1
N)




Lake
Superior
Michigan
Huron
Erie
Ontario
(ft-Ji
8.87
6.18
6.41
2.78
2.07
(ft2)t
22.55
18.93
20.85
7.39
9.70
E
(Xb/yr)
xlO"1"
0.97
0.837
0.868
0.485
0.302
Q
(Ibs)
xlO"16
2.70
1.076
0.781
0.101
0.36
P
xlO"3
4.21
4.31
4.0
4.65
6.786
ADp
(lb/yr)
xlO~13
1.91
22.4
12.4
49.5
10 32
Sout
(lb/yr>
xlO-1*
1.95
0.086
3.69
3.94
4.71
Sm,, « Su 2
(Ib/yr) llb/yr)
xlO~11* xlO~l
—
— —
1.95 1.02
4.45 —
3.98 —
Gn
(Jb)_llt
5.7
4.0
4.15
1.80
1.34
K
xlO~llt
3.48
3.00
3.11
1.74
1.08
3
.0204
.056
.0978
0-893
0.183

-------
Thus, from Figure 4.1-1  it is clear that Equation (4-2)  for Lake Superior and


Lake Michigan assumes the simplif ied form
                                                                          (4-3)
where j = S* m.




For Lake Superior, using the data in Table 4,1-1
                                               ,-

                 c.(t> ' i.K x 10" •-"'*]  Bs
-------
     4.2   Lake Superior
          In terms of the defined input functions, Equation  (4-4) may be
written as
                 C (t) = 1.32 x 10~18 e-°2Qltt/  u3*V0201fUdu
                                               /
                                               o
which has the solution (see Appendix A for details)
                       C (t) = 2.93 x io-19t"-5e—0037t.                    (4-4)
                        5
To check mass balance, note that the total input in the interval 1930-1974, is
given by
                     t            44
             Qin = /   B(u)du =  I   .0365u3'5du = 2.23 x 10s Ibs.
                   o             o
On the other hand, the total losses are given by
                                              -t
                        Qloss =  (ADp + K + S) /   cs(u)du
                                             o
                              = 3.727 x 104 Ibs,
while the stored PCS is given by
                  (Q + Gn)C  (44) = (6.84 x 10"12)(2.757 x 1016)
                          s
                                = 1.787 x 10s

or total input = 2.23 x 10s Ibs; amount accounted for is 2.16 x 105-lbs.
                                       -44-

-------
    4.3   Lake Michigan

                                                ,t

                                        -3»(t) /         B u
which, in terms of the numerical values in Table 4.1, yields the form



                                            r*

              Cm(t) = 8.96 x ID'17 e-05st  /  (.0283)u3'V056Udu


                                           o




                    = 2.54 x 1(T18 e-°S6t /  u3-V056Udu
 for which the approximate solution is*
                        C  (t) = 5.64 x l(T19e-009 V'5.                   (4-6)
                         m
 Again, check the mass balance,



                               44
-/
                       Q.  = /   B  (t)dt = 1.56 x 105 Ibs,
                        in   /    m       	
 The net loss =  (K + S + ADp) /  C  (t)dt = 4.999 x 1(T Ibs,
 and the stored material =  (Q + Gn)Cm(44) = 1.052 x 1(T Ibs.




 Hence, total input = 1.56 x 105 Ibs, total accounted for is 1.552 x 10s Ibs.
*Results in this  section differ slightly from those derived in Section 3.2.

 Since K is taken K =  3  x  10llf  Ibs/yr.
                                       -45-

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    4.4    Lake Huron



          Since Lake Huron is seen to have two additional inputs,  from Lake


Superior and from Lake Michigan, the solution for C, (t)  takes the  general form



                                   .t



                                                                    * du
                TWT  e^h/   K(u) + SsCs(u) + SmCm(u)}  **"*
                                 Cs(t)dt + 1.02 x 10ll+/
= .0305 /  t3<5dt + 1.93 x 10llf /  C^(t)dt + 1.02  x 10ll+ /   Cm(t)dt
    = 1.685 x 10s + 1.29 x 101* +  8.19 x 103 = 1.896  x 10s  Ibs




                        44


Losses = (ADp + S + K) /  C^tjdt =  6.84 x 10** Ibs
and stored material =  (Q + Gn)Ch(44) = 7.64  x IP1*  Ibs.



          Input 1.896 x 10s Ibs, accounted for 1.44 x 105 Ibs.
                                        ^46-

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    4.5   Lake Erie

          Since Lake Erie has  input from Lake Huron as well as from non-point
sources,  the solution  for C (t)  takes the form
                           £
                          '/(
                                                           3  (u)
                                         Bg(u) + Su)  e £   du
which, on substitution of the appropriate forms and values becomes
C£(t) = 8.40 x
                                       r*
                          ri6e-0.893t /  |<
                               + (4,45 x 101[t)(8.24 x 10"19 ) u"' 5e-IOltUj-e '89 3t .  (4-8)
\diich, on integration yields the approximate form

              C(t)  = 3.69  x HT1 V5e~0'075t  l + 0.0303te"'0 ist   .      (4-8)
               £
Now, the total PCB input to Lake Erie  from 1930-1974 was

                      44               44
              Q.   + f   B (t)dt + S^ /  C (t)dt = 1.0196 x 10" Ibs
                            44
Losses Q1 = (ADp + S + K) /  C£(t)dt = 9.08 x 10* Ibs
while the stored PCB = (Q + Gn)C£(44)  = 7.06 x IP3 Ibs:

                        Total input =  1.0196 x IP1* Ibs
                        Total accounted for = 9.79 x 10** Ibs
                                       -47-

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    4.6   Lake Ontario
         Again,  this lake has input from Lake Erie as well as from non-point
sources,  hence the solution for C (t) takes the form
               Co(t)  - (0-       e        {Bo(u) + SeC£(u)}
which has the solution

                       CQ(t) = 7.4 x lO'19^'5^0'013* .                   (4-9)

The cumulative input to Lake Ontario  (up to  1974)  is given by
          44              .  44
  Q.^ = /   B (t)dt + S^ /  Cjt)dt =  6.91 x 104 + 3.37 x 101* = 1.03  x 10° Ibs.
The stored material in 1974 was
                         (Q + Gri)C  (44) =  4.26  x 1(T  Ibs
and the cumulative losses were

                                  •44
                    (ADp + K + S) /   C  (t)dt = 5.96  x 1(T  Ibs.
                        Accounted for = 1.022 x 105  Ibs
                        Input -  1.03  x  10s  Ibs
                                       -48-

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   4.7   Summary
         To summarize the results of the previous calculations, for the assumed
situation that the only PCB input to the Great Lakes has arisen from fallout,

                       Cs(t)  = 2.93 x iQ-19 t*-5e"0037t                    (4-5)

                       Cm(t)  = 5.64 x io-i9t"-5e-009t                     (4-6)

                             = 8.24 x icT19t'f*5e~"J18t                     (4-7)
                       C£(t)  = 3.69 x 10'1*V5e-°-075'-                    (4_8)

                       C (t)  = 7.45 x IQ"19^'^'0'01^                    (4-9)
                        o
          The results, in terms of estimated concentrations for the lakes, are
given in Table 4.7-2

                                  TABLE 4.7-1
                Estimated PCB Concentration for the Great Lakes
                                   (in PPT)
Lake
Superior
Michigan
Huron
Erie
Ontario
1930
0
0
0
0
0
1940
0.09
0.16
0.22
0.70
0.21
1950
0.2
0.34
0.41
0.86
0.41
1960
1.2
1.9
2.13
2.79
2.24
1970
4.1
6.4
6.5
5.11
7.17
1975
6.9
10.3
10.0
6.1
11.4
                                       -49-

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    4.8   Effect of Point Source Inputs
          It is not reasonable to assume that the only input to the lakes is
from fallout, when in fact there is reason to believe that, especially for Erie
and Ontario, there has been considerable point source input. ^19^  The concen-
tration as a function of time for these latter lakes can be written in parametric
form,  where [the coefficient a£ or aQ is taken to represent the constant part of
the input function, the time dependence is assumed to be the same for fallout as
for point sources].
                                B£(t)  = a£t3'5

                                Bo(t)  =aot3'5

then
          C (t)  = 3.15 x l
-------
                      Table 4.8-1
Effect of Point Sources on Lake Erie and Lake Ontario
       Estimated Aqueous Concentrations of PCBs
Percent Point
Source
0
20
40
75
100
200
<*£
.0117
.014
.0164
.0205
.0234
.0351
C£C421
(PPtl
5.54
6.03
6.82
7.93
8.72
11.91
C£C451
(ppt}
6.1
6.78
7.49
8.70
9.56
13.0
ao
.0125
.015
.0175
.0219
.025
.0375
Co(42>
(ppt)
8.70
10.4
12.2
15.2
17.4
26.1
CQC45)
(ppt)
11.4
14.4
16.8
21.0
24
36
                          -51-

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     4.9   Comparison of Derived Results with Experimental Data
          In a recent extensive review of the PCB contamination of the Great
Lakes and their tributaries by the Canadian Environmental Contaminants Committee
there are presented estimates of the PCB inputs to the four Canadian lakes as well
as some estimates of the average sediment PCB concentrations and estimated total
sediment  PCB loads.  Although these data are somewhat fragmentary and derived from
the immediate past, it is possible to compare the estimates to those derived from
                                                          (21)
the model.   Table 4.9-1 is derived partially from Table 28
of Section 4 of this study.

                                 TABLE 4.9-1
           Estimated PCB Load in the Sediments of the Great Lakes
     and from the results
                   CANADIAN ESTIMATES
                                     (21)
MODEL ESTIMATES*


Lake
Ontario
Erie
Huron
Superior
Average
Sediment
Concentration
(ppb)
100
100
4.25
30

Load
(Ibs)
6.6 x 10s
4 x 106
3.5 x 104
7.9 x 10*
Average
Sediment
Concentration
(P?b)
13.4
9
8
6.4

Load
(Ibs)
6 x 10"
9 x 10*
7 x IQk
3.7 x 101*
    *Frcm Equations (4-5)  through (4-9)  and the data in Table 4-1.

                                                                      (21)
          In the discussion that preceeds the presentation of Table 28     it is
pointed out that the data from which the average concentration of PCBs within the
various sediments are not complete and titius the estimates of average concentration
may well be considerably in error, probably on the high side.  In addition, the
existence of marked variations in sediment thickness and the extreme variations
                                        (21)
in PCB concentrations found in Lake Eriev  ' make an estimate of average concen-
tration and PCB load very difficult.  The comparison demonstrated in Table 4.9-1
is further confused since the estimates of sediment concentration derived from
the normal [Equations (4-5) through (4-9)] are based on fallout as the only source
of PCB to the lakes; an assumption that is surely not correct.  If point sources
                                      -52-

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are included as is discussed in Section 4.8, the average water concentration
derived from the model is increased and so is the PCB concentration within the
sediments.
          If it is assumed that the average sediment concentration on Lake
Superior was as high as 30 ppb in 1974, then the corresponding average water
concentration over the interval 1930-1974 would have been

                            —
                       C^ -SS2.  ,.  7.13 x 10"12  .
But, in general
                            C  (t) ~ at*'5   ,
                             o       o
and
                               44
                                  '5du = 7.13 x 10~12
                          a   *
                        = -5! /  u"
Hence
                       C  (t) ~ 1.58 x lO'18^'5                             (4-12)
                        s
Evaluation of Equation (4-12) for 1974  (t = 44) yields

                           Cs(44) ~ 38.7 ppt    .

With an aqueous PCB concentration as high as 38 ppt, it could logically be  assumed
that the higher preditators could easily exhibit PCB concentrations in the  range
of hundreds of parts per million.
                                                (21)
          T3ius, it would seem that the Canadian     estimate of the sediment PCB
loads for the Great Lakes is probably high.

          4.9.1  Fallout on Lake Erie and Ontario
                                        (21)
                 In the Canadian reportv    it is suggested that the atmospherically
derived input to Lake Erie and to Lake Ontario was of the order of 103 kg/yr =
2.2 x 103 Ibs/yr.
                                      -53-

-------
                 From the assumed fallout rate of 1.023 x 10~8 Ibs/ft2/yr, the
input to the individual lakes as derived f ran the model was
                 Fallout input to Lake Erie ~ 2.8 x 103 Ibs
                 Fallout input to Lake Ontario ~ 2.12 x 103 Ibs,
values that are very close to those estimates quoted above, thus the assumption
of a(t)  = 50 ug/m2/yr = 1.023 x 10~8 Ibs/ft2/yr for the Great Lakes region seems
to be in agreement with other estimates.
                 If it is now assumed that the fallout rate was essentially
uniform over the Lakes region, as in Section 4.1, then the fallout during 1974
onto Lake Superior was of the order of

                        AQ input - 2 x 101* Ibs.

On the other hand, returning to Equation  (4-12), the aqueous PCB concentration
in 1973 and 1974 were

                        C  (1974) ~ 39.3 x 10~12
                        C  (1973) ~ 35.4 x 10~12

hence
               AQ.,. 	, =  (Q + Gn) AC - 1.08 x 105 Ibs.
                 stored.
while
               AQ,      +  (K + ADp + S) C ~ 2.14 x 10" Ibs.
                 losses
It is clear that AQ ^    , + AQ,      > AQ input, from which there are  two con-
                   stored,     losses
elusions; e'ither
           (a)  There were very large point source inputs of PCBs to Lake
               Superior during 1974,'
or         (b)  The estimated^  ' average PCB concentration of the sediments
               in Lake Superior are too high.
                                      -54-

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    4.10  Effect of Gradient  in B(t)
         A major assumption implicit in the treatment of the entire Great
Lakes system lies in the assertion that the fallout is essentially the same
over Lake Superior as over Lake Ontario.  In light of the absence of data
to the contrary, there seems to be adequate justification for this simplification.
When data are available that allow an estimate of the spatial as well as the
temporal variation in fallout, the present model can easily be modified to
deal with the more accurate information.
    4.11  .Effect of Regulatory Actions
         As can be seen above, the effect of point source discharges (assumed
to be all sources other than fallout)  is to sharply increase the concentration
in Lake Erie and Lake Ontario.  It is assumed that the actual situation in
both these bodies involves considerably more input than simply that due to fallout,
so that the data in Table 4.7-1 seems to represent the best possible situation,
one that would be expected to arise as a result of complete elimination of all non-
fallout sources of PCBs.
                                     -55-

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5.0  CO-DISTILLATION AND THE EVAPORATION RATE CONSTANT K
     Solutions that involve poorly soluble solutes usually exhibit properties
which differ significantly from predictions based strictly on the mole fractions
of the components.   Recent work by MacKay and Wolkoff ^   has suggested the
type of correction required to deal with surface evaporation of the solute fron
such a solution.  Their principal result    is

                             dM.     EP. M.
                             	i _     is i   _                           ,c ..
                             dt	MPC.   ci                          (5-1}
                                      W W IS

where, applied specifically to Lake Michigan, the parameters are

     E   = mass evaporation rate of water  (8.36 x 1013 Ib/yr)
     P.  = equilibrium vapor pressure of pure solute
     M.  = molecular weight of solute (325-Aroclor 1254)
     G1  = mass of water from which evaporation occurs
     M   = molecular weight of water (18)
     C.  = saturation concentration of solute
      -LS
     P   = equilibrium vapor pressure water  (23.7 mm Hg)
     C.  = concentration of solute in the evaporation layer
     P.  = effective vapor pressure of solute in solution

Comparison of Equation (5-1)  with the definition of K from Equation (1-6)
makes clear that,  to the degree that Equation (5-1)  applies,
                                      EP. M.
                                  K = 55-^1 .                    (5-2)

In order to estimate K from (5-2)  it is necessary to determine the vapor
pressure of the PCBs.
                                     -56-

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        5.1  Vapor Pressure of the Aroclors
             Data published by Monsanto^  ' giving the vapor pressure of the
   several Aroclor mixtures over the temperature range 150-300°C may conveniently
   be extended to cover the lower temperature ranges by using the general  relation-
   ship(23>
                                    log(VP) = a - |-
   viiere VP is in mm Hg, and T is the absolute temperature.  By standard regression
   analysis  (Appendix A), the appropriate values of a. and 3 were computed  as dis-
   played in Table 5.1-1.   in addition, the vapor pressure at 760 mm Hg occurs  at
   the normal boiling point, so that a check of the validity of the extrapolation
   may be made by comparing the estimated boiling temperature in Column 5  with  the
                   (24)
   published value     of the boiling range in Column 6.

                                    Table 5.1-1
                   Vapor Pressure Parameters for Aroclor Mixtures

                                                     T
Aroclor      Clf          o_             6_              boil  (Est.)        Boiling  Range
                                                                           325-366°C
                                                                           340-375°C
                                                                           365-390°C
                                                                           385-420°C

                                                             (22)
   The actual vapor pressure curves, as reported by Monsanto     are plotted in
   Figure 5.1-1 with the extension to lower temperatures, using the parameters  in
   Table 5.1-1 in Equation  (5-2), plotted  in Figure  5.1-2.
        If the PCBs in solution in the water are assumed to be Aroclor 1254, the  vapor
   pressure, at ambient temperature 20°C, should be

                              (VP)2()OC - 1.5 x 10"* mmHg
1242
1248
1254
1260
3.65
4.22
5.34
6.48
20.496
19.448
20.36
19.557
8.088 x 103
7.793 x 103
8.537 x 103
8.445 x 103
311 °C
335°C
349 °C
380°C
                                         -57-

-------
500
                                                Peplot of Vapor Pressure of Aroclors
                                                Monsanto Report 0/PL - 306A(22)
100
 SO
 20
 10
   17
              13
19
        * 10
                                       f (°
                        21
22
                                                23
                                                             24
                                          -58-

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                                       Figure 5.1-2

                                       Data in Table 5.1-1 Plotted
                                       For Low Temperature Vapor
                                       Pressure of Aroclor Mixtures

                                       Data from Table 5.1-1
2.5   2.6   2.7   2.8    2.9    3.0

                         i  x 103
3.1   3.2   3.3   3.4    3.5    3.6
3.7
                                   -59-

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          5.1.2  Self Evaporation Rates for Acoclor 1254
                 In order to verify the validity of the computed vapor pressures
displayed in Figure 5.1-2 it is appropriate to examine the published data on the
evaporation rate of Aroclor 1254 from a free surface of the pure material.  Mon-
santo^    has  published evaporation data at 60°C and 100°C while Hague et aV
have studied self evaporation at 26°C with the results tabulated in Table 5.1.2-1.
                                  Table 5.1.2-1
                      Self Evaporation Rates Aroclor 1254

                      T(°C)           dm/dt (gm/cm2/sec)
                        26°              2.315  x 10"11
                        60°              9.95  x 10~10
                      100°              1.47  x 10~8

                 In order to extend these data to temperatures other than those
at which measurements have been made, it is appropriate to have recourse to the
                             ( 27}
kinetic theory of evaporation v  ' which suggests that the rate of condensation
of a gas of molecular weight M, at an absolute temperature T and a vapor pressure
P is given as
where
     R = universal gas constant = 8.317 x 10 7 ergs/°K/mole
     M = molecular weight in gms/mole
     T = absolute temperature in °K
     P = vapor pressure at temperature T in dynes/on2

The factor a expresses the probability that the colliding molecule will stick
to the surface rather than simply rebound; clearly a <_ 1.  The relevance of
Equation (5.4) to the problem of evaporation derives from the fact that, at
equilibrium in a closed system, the rate of condensation of molecules on the
                                     -60-

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surface must exactly equal the rate at which they leave the surface.  Thus, if
the system were rearranged so that the evaporated molecules were completely
removed while all other parameters were kept constant, then the rate of evapo-
ration would be given by Equation  (5-4). ^
                 Introducing the measured evaporation rates from Table 5.1.2-1
into Equation  C5-4) results in the computed values of a as shown in Table
5.1.2-2.

                                 Table 5,1.2-2
                   a Values for Aroclor 1254 (Equation 5-4)
                             26°C      a = 0.905
                             60°C      a = 0.907
                            100°C      a = 0.905

The consistency of the computed a values, as shown in Table 5.1.2-2 may be
                                                                    (25 26)
taken as evidence of the excellent precision of the measured values    '    and
also of the validity of the extrapolated vapor  pressure curves shown in Figure
5.1-2.
                 The specific measured as well  as several computed -=£• values for
Aroclor 1254 are plotted in Figure 5.1.2-1.

     5.2   Calculation of the Evaporation Coefficient K for Lake Michigan

          5.2.1  Mass Balance at Lake Surface
                 In Section 3.2, the detailed balance of PCBs within the Lake
in 1975 was computed.  If the results are particularized into fluxes in
gm/onVsec, the effects at the surface may be summarized as follows:

                 Fallout        1.59 x 10"16 gm/cm2/sec
                 Evaporation    6.34 x 10~17 gm/cm2/sec
                 Net PCB input  9.51 x 10"17 gm/cm2/sec
                 Simultaneously
                 Net Water Evaporated  2.13 x 10"6 gm/cm2/sec

Now, from the above, the PCB concentration in the vapor state (ratio of PCB
evaporation flux to the water evaporation flux)
                                      -61-

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I
                                     x Haque Data
                                     9 Gorcuted
      10 "_
      10 12_
      10'1
                           40        60
                             Temperature (*C)
                            Figure 5.1.2-1
                    Mass Evaporation Rate Aroclor 1254
                            from Itself
                                 -62-

-------
                          6-34 xl(T17 = 2>98 x 10_n   (1975)              (5_5)
                          2.13 x 10~6

The concentration shown in Equation  C5-51 is clearly not to be interpreted as
the ambient air concentration over the lake, only as one component thereof;  there
is. also the airborne load which is the origin of the fallout.

          It is tentatively assumed that the surface (aqueous) concentration is
equivalent to the vapor concentration, and further, from Equation (3-2), the
bulk aqueous concentration was 8.5 x 10~12 (in 1974) , then

                                  C  = C
                                   s    vap;

                           and,   Cs = YCW

                           where  Y =  2'98 X ^"^ ~ 3.4                  (5-6)
                                       8.5 x 10"12

Then, using the cortputed value of C. and y/ it can be shown that (from Equations
(3-2)  and (5-6)
                        AC. (1974-1975) ~ 3 x 10"12 yr~
                            {±.y it—J-y i->i  ~ j A xO    "—
                        At"
or,
                         ACi\ sec"1 = 9.68 x 10'20 sec'1
Thus, the total gain in the "dissolved" PCS within the surface layer of thickness
£ was

                     (AM),     ~ 9.68 x ID"20 C gms/sec/cm3.               (5-7)
On the other hand, a layer of thickness § with a concentration gradient
                                  AC
                                  r
                                       c -c
                                  AC    s  w
                                      -63-

-------
will experience a diffusion current^ 9' given by
                            /<3m^          - n Ac                             rs-R}
                            ( :33T /            D ~F"                             \3 °)
                            ^'diffusion     T
                                                          2
where the cross-sectional area is taken as 1 on2 r D in	and AC is  gm/cm3.
                                                       ScC
 (Note, most of the concentrations used in this paper  have been in terms of
gni/gm, i.e., dimensionless.)

          Introducing the concentrations and thus the concentration gradient,
and taking D to be of the order of 10~5 cm2/sec, which is the  usual magnitude  for
organic solutes in water  °

                              dm        2 x 10"16
                              _	                              (5_9)
                              at diff     ^

If the sum of Equation  C5-7) and  (5-8) is equated to  the net PCS  gain in 1975,
the resulting equation may be solved for £

                   9.68 x 10~20 £ + 2 x 10"16 = 9.51  x 10~17               (5-10)
                                      5

                      ?2 - 9.82 x 102 5 + 2.066 x 103 =  0

from which,
                            £ = 2.2 cm  (or 980 on)  ,                       C5'11)

Since the layer of enhanced surface concentration is  usually assumed  to be very
thin,     the value 5 = 2.2 on is selected in what follows:
          From Equation (5-7), the net gain during 1975  of  the solute load
within the layer was

                     (|jr)      ~ 2.13 x ID'19 gm/on'/sec                   (5-12)
                         layer
                                      -64-

-------
Correspondingly, the loss from the layer due to diffusion into the bulk water was

                                     -1 x 10"17 gm/cm2/sec                  (5-13)
                        dif fusion
And the sum of these are
                         -r  ~ 9.12 x 10"17 gm/cm2/sec

which compares to the net loss to the surface and bulk of 9.51 x 10~17 gm/cm2/sec.

Further, from Equation (5-13 J it is seen that a total of

                           (f )     = 3840 Ibs/yr
                           Vflr/bulk
entered the lake during 1975  from the diffusion of fallout material through the
surface layer.

          5.2.2  Effective Surface Vapor Pressure/Ultimate Solubility Ratio
                 If Equation (5-1) is now used to compute the rate of effective
vapor pressure to solubility limit, using Equation  C5-1) ;
                           'eff.

On the other hand, for the "pure" Aroclor 1254,(32)

                                      ~ 2.33 x  103                          (.5-15)
                                'pure

                 The physical meaning of the result shown in Equation  (5-14) is
not clear but it can certainly be stated that both the effective vapor pressure
and the effective limiting solubility within the surface layer are higher than
the corresponding values for the bulk solution.
                                     -65-

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                                           /p. \
                 It is true that the ratio I •—• )     is used by MacKay and
Vfolkoff    as a measure of the activity of the PCS in solution in water; hence,
one should perhaps consider the ratio in Equation (5-14) as a measure of the
activity of PCB within the surface layer.  If this is true, then it should be
possible to demonstrate that a layer of enhanced concentration is, in fact
formed by these differences in activity within the bulk solution and within the
layer.  In this case,  the equilibrium concentration within the layer would arise
as a consequence of the combined effect of an activity gradient enhancing the
layer concentration while ordinary concentration dependent diffusion plus surface
codistillation would tend to decrease the layer concentration.  This point merits
further detailed consideration.
     5.3  Evaporation Rate Constant K
                                                            /Pis\
          In view of the uncertainty in the determination of IT;— /within the
                                                            \cis/
surface layer, it is clear that the determination of K from Equation (5-2) is
not possible.  Thus, K, the surface evaporation rate constant must remain as
an empirical parameter to be determined by an iterative processes such as is
used in Section 3.
          When applied to other lakes, the corrected evaporation rate constant
is determined by

                                K\    /K\                         (5-10)
                                TT /    \ TJ1 i
                                  'i   \   / Mich

as has been done in deriving the data in Table 4-1.
                                      -66-

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      5.4  Comparison With Experlmant
                             (33)
           Bidleman and Olney   'reported a series of measurements of PCB concen-
 trations within the surface layer (150 microns) and in the corresponding sub-
 surface regimen.  Their Table 2(33*  is partially reproduced below:
                                    Table 5.4-1
                  Bidleman and Olney Surface Concentration
Site #2
1
2
3
4
5
6
7
f fv i n^ ^\
^SL ** '
11.2
4.9
8.3
3.8
5.6
5.0
8.4
CbuUc (x 1Ql2)
3.6
<0.9
1.0
<0.9
1.6
1.8
<0.9
si/n
3.1
5.4
8.3
4.2
3.5
2.8
9.3
From which  SL   = y = 5.2
           SxdJc
                                                           (33)
It is recognized that the measurements cited in Table 5.4-lVJ-;>'  were made in
sea water where it is to be expected that C.   will be less than for fresh water
due to the competitive effects of the solvated ions with the poorly soluble PCB
molecules.      This reduction in C.  can only result in an increase in the
                                   is        •*
tendency to retain PCBs on the surface.  In this case one would anticipate that
the ratio of surface layer concentration to bulk, concentration might well exceed
that for the case of fresh water systems.
          A comparison of the Bidleman and Olney     results with those derived
in the discussion leading to Equation (5-5) suggests that the assumption that
the PCB concentration in the evaporated material (water plus PCB) is not very
different from that found in the uppermost boundary is realistic.  It should
also be noted that the situation in Lake Michigan differs from that treated by
MacKay and Wolkof f ^    in that the latter discussion dealt with the situation
wherein the only source of solute was that initially present in the solution;
whereas the case treated here has the additional complication due to the fallout
input.
                                     -67-

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6.0 AN ESTIMATE OF THE PCB CDNCENTRATION IN A TYPICAL LAKE TROUT WHEN EXPOSED
    TO AN AQUEOUS  PCB CONCENTRATION

    6«1  Development of the Model
         Consider  a fish with PCB intakes and outputs as represented schematically
                                    cfe(t)
                                     M(t)
                                                R (t)
                                               •- o
                         FIGURE 6.1-1.   SCHEMATIC FISH
where:     F (t)  = PCB intake due to the inclusion in food per unit fish ness
          F (t)  = PCB output contained in food wastes per unit fish mass
          R_ (t)  = PCB intake with respiratory intake water per unit fish mass
          R (t)  = PCB output with respired water per unit fish mass
          M(t)   = PCB output by lipid turnover, metabolism or other clearance
                  routes per unit fish mass
          Cf (t)  = PCB concentration in the edible portion of the fish
          C (t)   = PCB concentration in fishes' aqueous environment.
           W
Now, the mass balance implied by Figure 6.1-1 may be summarized by the equation,
in the limit At -»• o,
                    (t) - FQ(t)
                                                 - RQ(t)  - M(t)
                 dCf(t)
                 •at"
In order to simplify Equation (6-1),
       -~—  = AFx(t)
                                          - M(t)
(6-1)
let
AF(t) = kfCw(t)
ARCt) = krCw(t)
M(t)  = kC  (t)
      and k  + kfH
                                                                            (6-2)
                                      -68-

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With these substitutions, Equation  (6.1) takes  the form

                          dC.(t)
+kCf(t) = kaCw(t)   .                        (6.3)
                                     2

m order to solve Equation  (6-3) multiply both sides  of the equation by exp (k2t)
to yield

                    g| fcf (t) es?)  (kzt)j = kiCw(t)  exp (kzt)

for which, the solution is
       Cf (tz) exp  (k t ) ~ Cf (t  ) exp  (k  t )= k  /  C^(u)  exp (k u)du,         (6-4)

                                                 ti

      u has been introduced as an integrating variable.

      The general solution of Equation (6-1) is given as

                                 t2
             Cf(t2) =kle-k2t2f Cw(u)ek^du + Cf(t1)e-^(t2-tl)  .            (6_5)
If it is asserted that the average age of consumable fish is  T,  then the limits
of integration in Equation  (6-5) become t -  T and t. With the additional assumption
that
                     Cf (t - T) =0, Equation (6-5) becomes
                   Cf(t) =kie'22    Cw(u)ek2Udu + k3e'2    ,                (6-6)

                                   t-T
                                      -69-

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Now, following the definition of parameters ki and k2  (from Equation  (6-2)), the
ratio Cf (t)/Cw(t)  will approximate the bioooncentration factor as t ->• °°.   Stated
more precisely, for any Cw(t) = ytn where n is an integer > 0,
                                                   - kf                      (6"7)

since e l/J^z « 1 in the limit.

     6.2  Determination of the Rate Constants k, and k2
          The difficulty in application of Equation (6-6) lies in the selection
of appropriate values for ki and k2 which relate respectively to PCB uptake and
clearnace rate constants, as can be seen from Equation  (6-3).  Experiments by
               (35)
Branson et. al.     have determined these constants, for lake trout, to be
                             ki = 1.04 x 10s yr-1
                             k2 = 10.95 yr"1
(6-8)
!Ihe procedures used to determine these values     involved only a PCB-contaminated
aqueous environment and a non-contaminated food source.  Hence the ki value cited
in Equation (6-8)  is actually the kR in Equations  (6-2) and therefore reflects a
minimum value of kj.  In point of fact, the kp component of ki is likely to be
significantly larger than kR since substantial bioaccumulation of PCBs may already
have occurred up to the tropic level of the fish diet, particularly for predatory
fishes.
          If one assumes the Branson^35)  value for k  value to be equal to ki
 (i.e., k,. = 0) , a conputation of the Cf  (1970) , for lake Michigan yields
                                                                        (37)
Cf (1970)  ~ 29 ppb, a value far below the measured values for that era.
          Experimental determination of the rate constant kR would be difficult
and does not appear to have been attempted.  On the other hand, if the empirical
values for Lake Michigan are inserted in Equation  (6 -5) , the result will  lead to
an empirical estimate of k:  and, using Branson's value of k^, to an estimate  of
kf as follows.   Using the measurements of Cf (t) on spot  (Leiostomus Xanthurus)
                                      -70-

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                    (38}
 by Willford et.  al.     corrected by the 1:3 ratio of whole  fish concentration
 to muscle concentration as used by Branson et. al.     and by Hansen,  et.  al.
 and the expression for Cw(t) derived in Section 3  [Equation  (3-2)], Equation
 (6-5)  is solved by the method indicated in Appendix A  (Section A. 5) with the
 results indicated in Table 6.2-1.  From Table 6.2-1, the average value of  ki is

                              k~i = 4.28 x 106 yrs"1                           (6-9)

 Clearly, a comparison of the average kj, from Equation  (6-9), with the value of
 kj^ given in Equation (6-8), kp » kR so that, the trout intake from its  diet is
 about 50 times that due to respiration.
           Further, a comparison of ki and ka, through Equation  (6-7) suggests  a
 bioconcentration factor
              nw ir-  ~ 3.9 x 10s (edible)  ~ 1.17 x 10s (whole fish)          (6-10)
                  K-Z
Using Willford's  data     and the estimated aqueous concentration from Table  3.2-1,
the estimated bioconcentration factor,

                                n ~ 1.33 x 10s  .
Further, Veith     reports maximum concentration factors for the trout to be  of
the order of 1.5  x 10s.

    6.3,   Effect of Regulatory Actions on Trout PCS Concentrations
          The differential equation, Equation (6-5), particularized for trout
becones
                                          t
              QrCt) = 4.28 x 106e-10*9st/   e10'95UQT(u)du + k3e~1Q'95t       (6-11)
               f                         J           w
                                        t-T

**iich,  following  the method outlined in Appendix A  (leading to Equation  (A-13),
may be solved numerically to yield the results shown in Figure 6.3-1 for  two
different values  of 3,  where 3 is defined in terms of the differential equation

                             dC,(t)
                               "L   + k2C-(t) = St1"5   .                    (6-12)
                               Q*C        i
                                       -71-

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                      TABLE 6.2-1




           ESTIMATES OF ki (UPTAKE RATE CONSTANT)
Date
9/28/72
9A9/73
10/9/74
T
(yrs)
42.75
43.37
44.77
Cfe
xlO6
4.3
6.3
7.6
T
6.38
5.93
6.08
Cw(t)
x 1012
12.3
13.1
15.2
a
468
479
490
R
36.36
37.79
38.68
6
398
414
424
I:*
xlO~6
2.1
2.4
2.9
I2**
xlO23
0.049
7.76
1.64
x 10" 6
3.55
4.61
4.67
- T-f
     J
              e
**
  I2 =
                          -72-

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Note that the  log [Cf(tJ]  is plotted against the date in Figure 6.3-1.
         The  plotted curves in Figure 6.3-1 represent the concentration in the
edible portion of a trout as a function of time, specifically/ for a trout born
in 1930.  To discern what would happen to an animal  born at a later date, the
operative differential equation may be written
                           dC(t)
                                  = kiCw(t) - k2Cf (t)  .                      (6-13)
If it is assumed that at birth Cf = o, then because of the large value of ki and
the non-zero value of C (t)  for t > o (later than 1930), the rate of change of Cf(t)
is initially very large.  Eventually, any given fish, regardless of its time of
initial injection into the poluted water, will arrive at the limiting concentration
shown in Figure 6.3-1.   Clearly, from Equation (£-13) when

                                KiCw(t)  = k2Cf (t)

or                                 Cf(t)
                                   Cw{t)   k7

then                               dCf (t)

Now, suppose that, at t = tQ, Cw(tQ) = GW(O) and Cf (tQ) = ^ GW(O)  .

Further, suppose that,  as a result of regulatory activity, the input of PCBs were
to be decreased so that

                           Cw(t > to) = Cw(o)e~Y(t " V                      (6-14)

Substitution of Equation (6-14) into Equation (6-13)  results in the formal solution
                                        fT
               C,(T)ek2to = klC (o)eYto    e(kz ' Y)udu   .                    (6-15)

                               "
                                       -73-

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-J
•U
                 -15
                     17"
                                     19 IS
             Figure 6.3-1
   COMPUTER PLOT OF EQUATION  (6-12)
Which is written in the form
f(t) + af(t)=6tlf-5
f(t) = o, 1930;   a = 10.95
[Numerical  integration via 3rd order
           Runge-Kutta]
                                                                          IS'75
                                                         Tims in Years (Date)

-------
Several cases are obvious:

     a)  Suppose y = o,  i.e.  for T > t  , C  (T) = C  (t )
                                     o  w      wo

        ek*TK (T) -&LC  (o)'k
             I r      K.2.  w

which/  on simplification yields
                          cf(T) =kTcw(0) =cf(to}
as required.
     b)   Suppose y 7* o but/ since any practical regulatory effort will take a
number of years  to reduce the PCB concentration to I/  of its value at t ,
                                                    e                  o
Y « 1 and hence 7 « ka: under these circumstances , Equation  ( -15) becomes/  after
integration  and  sinplification,
          Cf (T) =  JL Cw(o)e-2   -     l-e              C(o)eo   .      (6-17)

Note that/ for T t*  t , Equation  (6-17) reduces to

                               Cf •<»,
                         C  (T*») =   Lr  (oJe         . o,                   (6-18)
                          t
Ihus,  from a comparison of Equation  (6-18) with  (6-14) , it is clear that the rate
at which the PCB concentration decreases in the trout is exactly the rate at
vMch the PCB concentration decreases in the aqueous surroundings.
     c)   Suppose that a trout with PCB concentration Cf (t _) is suddenly removed
from PCB contaminated water and introduced into clean water.  Under these
circumstances/ for t > t  / Equation  (6-13) becomes

                             dC.Ct)
                             -ar   =-k*cf(t)  •
                                      -75-

-------
fee which the solution is

                         Cf(t > to) = CjCt^e'

and the time interval (t-tQ)  = (At)1/2 required for a 50 percent reduction in
concentration is
                                                                              (6-19)
                                       -76-

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7.0 FURTHER WORK
    The results  presented in this work have been derived under a number of
assumptions  which are justified primarily because much of the basic information
needed to  avoid such assumptions is simply not available.  In this category are
included such  factors as total biotic mass, the average biological partition
coefficient, the  details of biological uptake and clearance of refractory con-
pounds and the nature of the surface layer at the air-water interface and the
driving forces which are responsible for the concentration gradient across the
layer. Further,  there exists no real historical base of data that could be used
to establish bench marks to check the validity of the many extrapolations that
have been  used.
    Other of  the assumptions have been introduced for the sake of physical or
mathematical simplification.  In this category should be included the assumptions
that the Aroclors act like a single compound; that there is no degradation of the
PCBs in the  environment; that it is proper to characterize the sediments by a
single partition  coefficient and that the fallout areal density is independent of
the latitude.   This category of assumptions can be removed from the model at the
expense of some increase in mathematical complexity.  Several examples of the
manner in  which these assumptions can be removed are given below in schematic
form.   It  would be of considerable practical interest to further explore these
avenues.
     In addition, the mass balance model, while it has been explicitly applied to
the PCB problem,  should be capable of extension to the study of other refractory
conpounds, for example to mirex.  It should also be pointed out that this type
model presents many points that should lend themselves to direct experimental
testing from which more accurate models may be evolved.
     The fact  that the model is capable of being expressed in the form of con-
tinuous functions of time with an explicit functional form for the driving
function is  of significance in an attempt to ascertain the effect of alternative
regulatory actions.  The effect of any regulatory activity will be felt in terms
of an alteration  of the PCB input to the target region.  If this alteration can
be expressed as a function of time (in a reasonably well-behaved functional form),
                                      -77-

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the mass balance equation can be integrated to estimate the time scale required
to obtain  the desired reduction in PCB concentration in any phase of the system.
This ability is of prime importance in comparing the effects of several alterna-
tive regulatory activities.
     The next several sections represent, in schematic form, the methods that
may be used to remove one or another of the assumptions that have been introduced
for physical or mathematical convenience.

     7.1   Introduction of Environmental Degredation
          If it is assumed that the species of PCB with chlorine numbers of
three (3)  or less are degraded by environmental processes, then the forcing
function B(t) may be rewritten

                            B(t) = Bi(t) + B2(t)                             (7-1)

where Bi(t)  refers to the lower, degradable species, and B2(t) to the higher,
non-degradable species of PCBs.  As before the functional form of the B. (t) is
taken
                                Bi(t) = a.                                    (7-2)

If it is assumed that the decay of BI (t) may be expressed by a decay constant X,
then

                                                 -1                           (7-3)

where the second term on the right hand side of Equation  (7-3) describes the
additional input to the reservoir of the lower species while the first term on
the right describes the decay of the material already in the environment.   On
integration of Equation (7-3)
                                                                              (7-4)
So that, the driving function B (t) becomes

                       B (t) = Olt? l  1 - --   + cut  2                      (7-5)
                                      -78-

-------
As before & i  and $ ^ are derived fran the environmental load model exhibited in
Appendix C using data from Appendix D.  The parameters on and ct2 are derived from
experimental  data taken recent times and X is derived from the known degradation
data.
         In  addition to the required modification in the driving function, the
two partition coefficients, p and n are, in general, dependent of the molecular
structure of  the partitioned species.  Thus, it is to be expected that both will
exhibit quite different values for the lower chlorinated FOB species as compared
to the higher chlorinated species.
         Further,  the surface evaporation rate constant K, which appears to
depend on vapor pressure as well as limiting solubility, will be different for
the taro species of PCBs.  Thus, the time constant, 3/ will be different for the
two species.   In terms of the solution of the mass balance equation, it is clear
that, since there is no coupling between the two species, there should then be
two separate  differential equations, one for its lower species, the other for
the remaining PCB species.
         It  remains to be pointed out that the additional complexity of treating
each level  of chlorine substitution as a separate species could also be intro-
duced.  The resulting complexity would hardly be justified.

     7.2 Air-borne Reservoir and the Generation of a Gradient in Fallout
         The assumption that a(t) is constant over a large region such as the
Great Lakes may be removed by a procedure similar to the following:
         Consider a column of air of uniform density and of height h  (h is
selected so that the surface pressure due to the weight of gas equals the normal
atmospheric pressure) located at a position  (x, y) on the surface of a flat earth.
Let the area  of the base of the column be (Sx) (6y) as shown in Figure 7.2-1.
Let the average (constant) air velocity, v, be directed parallel to the x axis
and let the PCB concentration of the air entering the column be C (x,t) and that
leaving be C(x(t)  + 6x,t).  It is explicitly assumed that C is not a function of y.
                                      -79-

-------
                  V
                       x, y)
                                            (x + Sx, y + <5y)
                                      (x + 5.x, y)
                             FIGUEE  7.2-1
            Volume Element for Airborne Reservoir Computation
          Then in the time interval At, the  amount of PCB entering the column is
                                       C(x,t)At
and that leaving is
                            = v(Sy)h C(x + Sx, t)At
Thus, the net change per unit time is
                   AM
                      = v(5y)h C(x,t)  - v(
-------
Further,  it is taken that there exists a surface distribution of PCBs, described
by p(x,t)  from which a fraction a(x,t) is vaporized in unit time.  Hence the
contribution to the mass of PCBs within the column is given by

                     (H    }- a te't) P (*» t) ($ x) GS y)                         (7-9)
                     \  evap/

So that the mass balance, obtained by summing Equation (7-7) , (7-8) and (7-9)
becomes
                     v
                                                 3C(x t)
It is appropriate to note that the definition of — sr~  requires

that t be treated as a constant, so that Equation (7-10) may more properly be
written as

                           i)+ XC(x,ti) = 2l£&-} p(x,ti)                   (
With a suitable definition of a(x,ti) and p(x,t..) , Equation (7-10 ') may be solved
to indicate the variation of the airborne concentration of PCBs with position at
a fixed time, i.e.., the comparison of the results of measurements taken at widely
separated locations at the same time.  If Equation (7-101) were solved for a
nunber of different t. , then the resulting set of solutions may be used to con-
struct the time dependence of C(x,t) so as to define the entire function.  From
such an equation, the fallout may be derived as a function of position and time.

     7.3  Introduction of Spatial (or Temporal) Variation of Sediment
          In Section 3.3,  it was shown that even complex contours of spatial
variation of sediment rate or sediment partition coefficient could "be incorporated
into the mass balance equation.  The essential simplifying assumption is that of
conplete mixing of the water column.  If it becomes necessary to consider temporal
variations in either sediment deposition rate or chemical content, the complexi-
ties introduced are considerable for, in this case, the time constant, 3 , becomes
time dependent.  The solution of the mass balance equation must then be accomplished
                                     -81-

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by a series of summations over small time intervals; there is little likelihood
that so siitple a solution as expressed by Equations  (A-8) or  (A-9) can be
obtained.

     7.4  The Surface Layer and Co-Distillation
          As is apparent from the discussion in Section 5, the existence of a
surface layer of enhanced concentration is not readily understood.  It would
appear that the origin of this layer is bound up in the very high activity of
a solute such as a PCB in water as compared to the activity such a molecule
would exhibit at the air-water interface.  Thus, it seems that the driving force
to produce the enhanced concentration is just the difference in activity in the
bulk as compared to that on the surface which, combined with the loss due to
evaporation establishes a dynamic equilibrium constant.  Since it appears that
this process is of great importance to the mass accounting of a body of water
and since, this also could be a significant process for the injection of
materials into the atmospheric reservoir, it obviously merits more study.
                                     -82-

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        APPENDIX A
MATHEMATICAL CONSIDERATIONS

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                          MATHEMATICAL CONSIDERATIONS

 A, 1.0  GENERAL
     The  evaluation of definite integrals of the form


                               I =  /   X?eSxdx       ,                      (A-l)
                                   o
where t is finite, 6  may be either positive or negative and 3 is non-integer,
are of considerable interest in the context of this work.  It is appropriate to
consider both cases with respect to the sign of 5  (the case where 6  = 0 is, of
course, trivial).

     A.1,1  5<0
            By substitution of W = 
-------
Thus,  the series represented by Equation (A-4)  is absolutely convergent for all
finite t and 5 .

    A.I. 2  5>o
            In the event that 5  is non-negative , evaluation of the integral in
Equation (A-l) proceeds by the usual expansion of the exponential in the
                 (2)
Maclaurin series ,    integration of the resulting series term by term and sub-
sequent collection to yield
                          >o
                                      n=o
which is also convergent in the limit as rc*», since, as before
                                      la I
                                      '  n1
A.2.(L  PARTICULAR APPLICATICNS TO PROBLEMS ENCOUNTERED
     Of specific interest in this work are the two integral forms
                             I:=eul-/   Jfe^cbc                         (A-6)


and

                                    £ J- I   OS,,
                                                                          (A-7)
which occur as solutions of the mass balance equations, as for example Equation
 (3-1).
     A general form for the solution of these forms may be obtained by the
procedure outlined in Section A-l followed by expansion of the pre-factor
exponential in Maclaurin series, subsequent multiplication of the series, col-
lection of terms involving like powers of (St) and ultimate simplification.
                                     A-2.

-------
Thus
                        m=o                 m=o

which, on introduction of the notation  for the truncated product


                  n

may be reduced to the tractable foim
                         Tl =
                          1
In exactly the same way,
                                           n   (3 + 1 + n)
                                      n=o   n
                                                   XM T- 1 + n) '             (A"9)
                                      n=o


Further, both series (A-8) and (A-9) are seen to be absolutely convergent  for

all finite 61.


A.3.0  APPLICATION OF EQUATION (A-6) AND\A-7)

     To illustrate the utility of the series solutions, several cases are  treated.

Consider the integral
                              Ea = e
                                         t
                                    at '
which may be directly integrated by elementary methods to yield


           I _ eat-l _ 1V^ (at)m   1 _ 1 V^ (at)m _
                 a     a / y~ml     a   a / ^~ml
	                             /  ^ '(m-+ 1)1
m-o               m=l           m=o
                                      A~3

-------
On the other hand, i& is of  the form of Equation (A-6)  with 6=0, hence, from


Equation (A-8),                        ^



                             I    - t V <°*),n
                             a     * Z_j n  (n + 1)
                                      n=o
                but  1   (n + 1) = (1) (2) (3)	(n + 1)  = (n + 1)!
                             Xa =t2^^rT1^T                          ^~±1}
                                    n=o

vfaich is exactly the form of Equation (A-10).


A second, perhaps more instructive  example comes from the evaluation of the


integral in Equation (3-1)




                                                /•**

                  C(tf) = 2.08 x  10"18  e-°-°5t /   u3-5e0'05Udu
      is obviously of the form of I2  (Equation (A-7) )  for which the solution is ,


 from Equation  (A-9) , given as
n fo.

n
                                                        05
               C(tf) = 2.08 x 10-  tf-5      (-l)       (       n).         (A-10)
                                           n=o
Consider now, only the sum, which on expansion yields the first several terms as
             x     |b.05 tf)     (0.05 tf\z        (0
.05
     T r

                   "T • « • •
            4.5 "  (4.5)(5.5)    (4.5)(5.5)(6.5)   (4.5)(5.5)(6.5)(7.5)
           = 0.222 - .00202 tf +  .0000155  tf2  - .0000001036 tf3 	,





a result which clearly converges  quite rapidly for tf < 50 years,  which is the


time span of interest.  Thus, C(45)  ~ 9.2  x 10"12  if one considers only the


first three terms in the series.  Actually,  the result depicted in Table "3.2-1


were carried out utilizing the first five  terms of the expansion.





                                     A-4.

-------
A.4.0 EMPIRICAL EQUATIONS
     As  is frequently the case, concentrations expressed as functions of time,
as for example Equation (A-10), have in the course of additional computations,
to be integrated.  Examples of this vould include Equation (3-10).  In this
circumstance, the series expansion, such as Equation (A-10) is somewhat
cumbersome.  To simplify this process, recourse has been had to empirical methods
whereby the concentration computed from equations of the form (A-9) are fitted
to the equation

                        ln(Cw)  = a +  6 +D Int-xt

which corresponds to the assumption that

                             Cw(t) = at? + V*

The fit is accomplished by a least squares    fit to obtain the best value of
a1 and T.
     The actual form of Equation  (3-2) was obtained in the indicated manner.
                                      A-5.

-------
A.5.0  METHODS  OF SOLUTION OF EQUATION (8-3)
          In general,  the form of Equation  (8-3) requires a solution given by
Equation (8-6)  which is of exactly the form of Equation  (A-7) which has been
shown  to have a solution of the form given by Equation (A-9).  Unfortunately,
the value  of k2u is so large that the ^convergence of Equation  (A-9) makes the
latter quite unsuitable for eavaluation.  In this case the most useful approach
requires a series of transformations as follows:
    Equation (8-3) is re-written after substitution of Equation  (5-6) for the
C (t)  for  Lake  Michigan (in terms of the exponantial, the factor k2u » .09t, so
 l™
that the latter is ignored), then
        Cw(t) = Yt*-
                                                                            (5-6)
whereupon
Now:
                    cf(t)
                                                 +  j_
                                 t-T>0
                                                   (8-3)
                 = e
/
 T-T>O
r    ek2V-5du
                                                              :k3   -k2t
 If the following substitutions are made
          Let u = Tx
              a = k2T
             du = TdX
     R =  T-T
     u =  RY
     k2R=  6
     du = RdY
 then
        Cf(t)
         ]
  5-k2tJ
                                                 ,-k2t
                                                         (A-ll)
                                       A-6.

-------
                                                        '5dY +  L- e        (A-ll)
A further series of substitutions

          - Z = X-l                    - S = Y-l
            X = 1-Z                      Y = 1-S
           dX = - dZ                    dY = dS

transforms Equation (A-ll) into the form

   C,(t)
= T
               n   e-^Cl-ZJ^dZ-R^e^y   e'
                                 P
More generally,  assume C (t) = yt , then by the same series of transformations, for
the case t > T ,

                                                1
                                        - R^1/"  e-^^e-^Vdy        (A-13)
                                              J
Note that,  for k2T >> o and P > -1, the second integral is considerably smaller
than the first.  On the other hand, for very small T, the contribution from the
second integral is of importance.
                                     A-7.

-------
APPENDIX A REFERENCE


 (1)  "Modern Analysis," E. T. Whittaker and G. N. Watson, Cambridge, 1948,
     Chapter 3, pp. 235-264 especially pp. 341ff.

 (2)  "Advanced Calculus," I. S. Sokolnikoff, McGraw, New York, 1939, pp. 290ff.

 (3)  "Treatment of Experimental Data," A. G. Worthing and J. Geffner; Wiley,
     New York, 1943, pp. 56ff.
                                       A-8.

-------
                   APPENDIX B
PARTITION COEFFICIENTS FOR AQUEOUS PCB SOLUTIONS

-------
B.I.O  nmoDueTiaN(1/2) *
       If a given solute,  A, is soluble in two immiscible solvents S and S1,
then at equilibrium
Equation (B-l)  expresses the distribution of the available solute A into each of
the separate solvents and may be described by the equilibrium constant
                                   P =                                      (B-2)
                                       |A(S) I

which is known as the partition or distribution coefficient for the given solute
in the two solvents.

B.2.0  MEASUREMENT OF PARTITION COEFFICIENT
       Suppose a solute, A, was originally present in solvent S with a concentration
Cm-  After mixing the original solution with a second solute, S', and allowing
the  (immiscible) solutions to separate, it is found that the concentration of A
in S is Ci, in S1 is C2.  If the mass of S is M  and that of S1 is M2, then

                              MiCio = MiCi + M2C2  •                        (B-3)

By suitable rearrangement and the introduction of p from Equation (B-2) , Equation
 (B-3) becomes

                                  o   . = Cl° " Cl                          (B-4)
                                  pSiSf      Ci                             v   '

or alternately

                                     = Ml r     r
                               PSiS'   M2  10 " Cz '                         (B-41)

Thus, the partition coefficient for two solutes may be determined either from the
concentration change of the solute in the initial solvent due to the "extraction"
by the second solvent or by the comparison of the initial concentration to the
concentration in the second solvent after the "extraction".

* All references for this Appendix are listed on page B-5
                                      B-l.

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B.3.0 TYPICAL PARTITION COEFFICIENTS FOR PCBs

      B.3.1  Aqueous/Activated Carbon
              Hager and Rizzcr ' have studied the effect of granulated activated
carton on PCB solutions (made up in Acetone and diluted with water).  Their study
included both Aroclor 1242 and A]
be summarized as in Table B.3-1:
included both Aroclor 1242 and Aroclor 1254 PCB preparations.   Their data    may
                                  TABLE B.3-1
             PARTITION MEASUREMENTS - PCBs IN WATER/CARBON GRANULES

        Carbon Dosage                       Aqueous Concentration (ppt)
           (mg/1)	1242	1254
          Control                            45                 49
            2.0                              7.3                37
            5.0                              1.6                17
           10.0                              1.1                4.2
           25.0                              ND                 1.6
           50.0                              ND                 1.2


Analyses of these data using Equation (B-41) yields the partition coefficients
displayed in Table B.3-2:

                                   TABLE B.3-2
                    PARTITION COEFFICIENTS AQUEOUS PCB/CARBON
        Carbon Dosage                          Partition Coefficient
            mg/1                             p(1242)	p(1254)
2
5
10
25
50
2.58 x 106
5.43 x 10s
3.99 x 10s
	
__ _
1.1 x 105
3.3 x 10s
9.7 x 10s
1.1 x 106
0.73 x 10s
                                     B-2.

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      B.3.2  Aqueous/Soils and Clays
                         (A)
             Haque et al  ' have studied the partition coefficients for aqueous
Aroclor  1254  solutions with a number of soil type materials.  The results of
                               /4\
their work (from their Figure 2V ') may be summarized as follows in Table B.3-3:
                                  TABLE B.3-3
                    CALCULATED PARTITION COEFFICIENTS
                              AQUEOUS AROCLOR 1254
                                  (4)
                                     FOR
                 SORBENT
                                     AQ/SORBENT
       Silica Gel
       Sand (Del Monte)
       Kaolinite Clay
       Montxnorillonite Clay  (#26)
       mite Clay (#35)
       Wbodburn Soil (Loam)
                                        0.2
                                        0.02
                                        1.0
                                        1.5
                                        3.0
                                       10
       B.3.3  Aquatic Concentration Factors
              A number of authors have computed concentration factors for
aquatic species.  For example, Stalling and Mayer1   , as a result of a number of
determinations of accumulation of PCBs, presented the results shown in Table
B.3-4:

                                   TABLE B.3-4
                ACCUMULATION OF PCBs BY VARIOUS AQUATIC ORGANISMS
   Species
Catfish

Bluegill

Fiddler Crab
Pink Shrimp
Aroclor
 1248
 1254
 1248
 1254
 1254
 1254
   Time
60 da
60 da
60 da
60 da
30 da
30 da
Concentration Factor
7.2 x 10"
7.6 x 10*
6.37 x 10*
1.28 x 10*
2.29 x 10" - 3.4 x 10"
6.9 x 10*  - 1.2 x 10*
                                      B-3.

-------
In addition there are reports of fish uptakes equivalent to partition coefficients
of 4 x 10* to 9 x 105 in Lake Ontario,(6'7)  to 1.9 x 10" in Lake St. Clair,  (8)
7 x 103 to 2 x 103 for the Hudson River^9)  and 4 x 10" to 5 x 10* in the Atlantic
      (10)
Ocean.
       B.3.4  Sediment Concentration Factors
              The large number of measurements of sediment concentration factors
nay be fairly represented by the measurements of Haile, et al
in 1974 which indicate
                                                              (6)
                                        on Lake Ontario
                       psed/water ~  1.7 x 103  to 2.5 x 103

       B.3.5  Effect of Organic Content of Sediment on PCS Partition
              The experiments with soil leaching characteristics reported by
Tucker/ et al     show the marked effect of organic carbon on the aqueous
partition.  The manner in which the  experiment was conducted and the nature of
the explicit results precludes the direct calculation of partition coefficients
but the data in their
are quite suggestive.
                      (11)
Table II, which is reproduced herein as Table B.3-5,
                                    TABLE B.3-5
                            PCB PERCOLATING STUDIES
                                                    (11)
    NORFOLK LOAM
  (1% Organic Carbon)
        RAY SILTY LOAM
       (1% Organic Carbon)
  DRUMMER LOAM
(6% Organic Carbon)
Elution Vol.
(1)
1.3 - 8.1
10.1
13.5
25.5
. 48.1
PCB Cone.
(ppb)
ND
ND
23
63
63
Elution Vol.
(1)
2.7 - 16.4
20.7
27.6
51.9
98.1
PCB Cone.
(ppb)
ND
65
92
153
136
Elution Vol.
(1)
1.6 - 9.9
12.5
16.6
31.4
59.2
PCB Cone.
(ppb)
ND
ND
ND
ND
ND
                                       B-4.

-------
APPENDIX B  FOOTNOTES

(1)  "Separation Methods in Chemical Analysis," J.M. Miller, Wiley, New York,
      1975, pp. 32ff.

(2)  "Quantitative Inorganic Analysis," G. Chariot and D. B^zier; Methuen,
      London, 1957, pp. 155ff.

(3)  Hager, and Rizzo.  EPA Tech. Transfer Session, Atlanta, April 19,  1974.

(4)  Hague, R. , D.W. Schmedding and V.H. Freed.  Environ. Sc. Technol. , 8, 439
      (1974) .
 (5)  Stalling, D-L- ar^ F-L- Mayer, Jr.  Environ. Health Perspectives, 1, 159
      (1972) .

 (6)  Haile, C.L. , G. Veith, G. F. Lee and W.C. Boyle.  EPA-660/3-75-002 ,
      June 1975, U.S. EPA.

 (7)  Kaiser, K.L.  Sci. 19, 523  (1974).

 (8)  Michigan Department of Agriculture, Bureau of Consumer Protection, 1973,
      Great Lakes Environmental Contaminants Study.

 (9)  Quoted by D.J. Ruoff and V.J. DeCarlo - Private Communication.

(10)  Harvey, G.R. , H.P. Miklas, V.T. Bowen and W.G. Steinhauer, J. Marine Res.,
      3£, 103 C1973).

(11)  Tucker, E.S. , W.J. Litschgi and W.M. Mees.   "Migration of PCBs in Soil
      Induced by Percolating Water, " Bull. Enviro. Contamination  & Technol. , 13,
      No. 1, 1975.
                                       B-5.

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      APPENDIX C
ENVIRONMENTAL PQ3 LOAD

-------
C.1.0  INERDDUCTICN
       In this Appendix a model is presented that proceeds from published^ ' *
data on the production and sales of PCBs within the United States.  The sales
figures are further subdivided into various use categories.  With the introduction
of estimated loss factors for each use category, it is possible to construct an
equation describing the total environmental PCB load M  (t).  With the further
introduction of use life factors for the major use categories, it is then possible
to estimate the mobile environmental PCB load, Mev(t).  Finally, the introduction
probabilities of vaporization, it becomes possible to construct a model of the
atmospheric reservoir.  The results of the various steps in this computation are
                                  (2)
compared to the Nisbet and Sarofim    estimates.

       C.I.I  Empirical Description of Production, Sales and Specific Use
              Categories
              From the data supplied by Monsanto,    a portion of which is pre-
sented as Table C.I. 1-1, it is possible to construct empirical descriptions for
the total production, sales and uses in specific use categories.

              C.l.1.1  Period 1930-1970
                       From the Monsanto    sales data for PCBs, it is possible
to fit an empirical expression for each category which, to a satisfactory degree,
represents the time dependence of that parameter.  In each case, it is assumed
that the relation is of the general form:

                             In Q(t) = a + n In t.                         (C-l)

                        (a)  Total Production
                            The derived empirical expression for the yearly pro-
duction takes the form, for the period 1930-1970,

                               = 2.94 x 102t3
*The references for this Appendix are listed on page C-21.
                                      C-l.

-------
The appropriate empirical expression for the yearly sales, for the period
1930-1970,  takes the form
                         Qsales(t)  = 311 t3'39 Ibs/yr.                     (C-3)

The corresponding expressions for capacitor sales and for transformer sales are
(for the period 1930-1970)
            Capacitor sales:    Q^ (t) = 2.03 x 102 t3*289 Ibs/yr

            Transformer sales:  Qfc) = 2.02 x 103 t2*37 Ibs/yr
(C-4)
                       In the above expressions, it should be noted that it is
explicitly assumed that
                       (a)  the given Monsanto data are accurate and
                            represent the great preponderance of PCB
                            production and sales within the U.S.
                       (b)  the trends rated in the interval 1954-1970
                            are simple continuations of earlier trends,
                            so that the curves which fit the period
                            1954-1970 can, in fact, be used to cover
                            the entire interval, 1930-1970.

                       Information reported elsewhere    suggests that the
second assumption above might result in low estimates for total U.S. sales;
therefore, the results derived from this analysis must be considered as a lower
bound on the actual situation.
                       In any case, numerical evaluation of expressions  (C-3) and
(C-4) suggest that a weighted average for the proportion of PCB sales that were
employed in electrical applications is of the order of

                             B =0.62 (i.e., 62%).                           (C-5)

                       The remainder of the sales during the period 1930-1970 was
for non-electrical applications.
                                      C-2.

-------
      C.1.2  Period 1971-1975
                                                          (4\
             In 1970,  Monsanto instituted a voluntary ban    on the sales of
PCBs restricting their use to electrical applications.  As a result of this ban,
the empirical relationship appropriate for sales in the post 1970 period is
                        Q'galegft)  = 3.31 x 107 Ibs/yr.                    (C-6)

              In addition, during this period essentially 100 percent of PCB
production was used for electrical applications; i.e.

                             3 =1.00 (1970-1975).                         (C-7)

              To determine the total sales and total electrical system usage for
the period 1930-1975, Equation (C-3) may be combined with Equation (C-6).  Inte-
gration over the appropriate time frame yields

                          1975
                                     = 9.33 x 10e
                          19 30
and for total electrical system usage, Equations  (c-4) and  (C-5) with  (C-7) may
be combined and, on integration, yield,
                     19 75
                          Q i  4. •   i (t) = 7.12 x 10 8 Ibs.
                          ^electrical      -
                     19 30
The balance, 2.21 x 10 8 Ibs, was used in non-electrical applications.
                                      C-3.

-------
C.2.0  ENVnOSMENTAL IDAD OF PCBs
      C.2.1  Introduction
              PCBs,  or for that natter any other refractory chemical compound,
may exist in the environment in two distinct states:  (a)  that material which is
in a form such as to remain localized and thus is not actually available to enter
the sensitive portion of the environment, i.e. , the biota; and (b)  that material
v&ich  is not so constrained and is thus free to enter the sensitive portion of
the environment.  This latter portion of the environment load will be referred
to as  "free" or "wild" PCBs.  The significance of the first category lies in the
fact that the containment is not of infinite life and thus material in category
(a) can and will eventually become a component of category (b) .  For those com-
pounds for which there exists relatively high rates of degradation within the
environment, the category (a) is of somewhat lesser importance than for those
refractory compounds for which the only inactivation mechanism is the entrapment
with non-available forms, for example, in deep ocean sediments.
              In order to estimate the rate of accumulation of PCBs in category
(b) , it is first necessary to determine the rate of entry of PCBs into the
category (a) .  This will be followed by an analysis that suggests the nature of
and the relative importance of the processes by which this total environmental
load eventually becomes wild PCBs.

       C.2.2  Total Environmental PCS Load, M(t)
              It is assumed that, in any time interval t to t + At, a fraction
a < 1 of the total sales during that interval was directly lost to the environ-
ment due to transport losses, spills and manufacturing losses, for example.  It
is further assumed that a fraction B < 1 of the total sales was used in the
inanufacture of long lived electrical components.  If the average lifetime of
these electrical components (time of service prior to their being discarded as
obsolete)  is y  years, then during the time interval t to t + At, an amount
              i
                                 3 C- (t-Y )  At                              (C-8)
                                    5    1
                                      C-4.

-------
will enter the environment as part of category  (a) .  In addition, the direct
entry is given as

                                  a Qs(t) At,                               (C-9)

              The remaining sales (l-a-3) Q(t) was used in the production of
relatively short-lived products, such as carbonless paper, hydraulic fluids,
etc. , which are assumed to have an average lifetime y  years .  Thus , the entry
                                                     2
of this material into the total environmental pool is given by

                              (l-a-6) Q  (t-Y ) At.                          (C-10)
                                       S    2

              If the three components of the total environmental load, M  (t)
are summed, the resulting differential equation for M  (t) becomes, in the
limit as At ->• o

               dM  (t)
                        a Q (t) + (l-a-6) Qjt-Y ) +S Qjt-y )  .          (C-ll)
                    .       s               s    2       S    i
              To evaluate Equation (C-ll) it is important to note that the term
 (1-a-g)  Q,,(t-Y ) does not contribute to dM  (t) until a time t >Y  where
         S    2                           ® '*'                     2
                                           at~
t = o = 1930.   Similarily, the term 3 Q  (t-Y ) does not contribute to the change
                                       s    i
in M  ,(t)  until a time t > Y  where t = o = 1930.  Hence, the solution of
    ev                      2
Equation (C-ll)  is given as


                   t                   f*                 t
        Mev(t)=al  Qs(t)dt + (l-a-6) I    Q^t-^dt + 3 /  Qs(t-Y2)dt.   (C-12)
                                                            1
              In order to obtain a numerical evaluation of Equation
it is appropriate to note that 3, the fraction of initial sales utilized for
electrical applications, is given by Equation  (C-5) for the period 1930-1970,
and by Equation (C-7) for the post 1970 period.
                                      C-5.

-------
            An estimate of the factor a, the fraction of  direct losses, can be
obtained by noting that
             (a)   approximately 10% of the electrical material
                  was lost during transport, production and
                  processing,  '
             (b)   approximately 30% of the non-electrical
                  material was lost during transport, pro-
                  duction, processing, and use.
Hence,
                       a = (0.1)  (0.52) +  (0.30)  (.38)
                       a = 0.17.
                                                                           (013)
It is further assumed that
                                             (7)
                                  = 20 years
                                i
                               Y  = 4 years(8)   .                          (C-131)
                                2
When the expression for Q (t) given by Equation  (C-3),  coupled with the estimates
of a, 3 / Y, and y / are introduced into Equation  (C-ll),  the total
                2                   _ . _.
load at some time after 1930, M   (t) may be cotoited in three  time
                              ev
(a) o < t < Y , M  t(t)  » 12.04t**39 Ibs.
            2   Sv
                                      39              *m 39
        t < Y, Mev(t)  = 70.84  0.17t-   +  (0.21) (t-4)  m
                                                                                    (C-14)
(c)
      < t    , M  (t) - 70.84{o.l7t*-39 +  (0.21) (t-4) ^ 39  + (0.62) (t-20) ^ 39} Ibs
    i           ev            l                                               /
   numerical results are sumuarized in Table  2.2-1.   It should be noted that, in
   radistinction to euations such as Equation  (C-3) ,  which represent the yearly
 ales, Equations (C-14) represent the cumulative load in pounds
                                           C-6.

-------
 Date
                                 TABLE C.2.2-1

                        M  (t)  = Environmental PCB Load
[From Equation (C-14) ]

     M(t)  (Ibs)
                                                      [From Equation (C-14/C-16)]
Mev(t) (Its)
1930
1935
1940
1945
1950
1955
1960
1965
1970*
1975**
1980**
0
5
10
15
20
25
30
35
40
45
50
0
1.42 x 101*
3.35 x 10s
2.32 x 106
9.1 x 106
2.52 x 107
6.23 x 107
1.31 x 108
2.54 x 108
4.58 x 108
7.79 x 108
0
1.42 x 10*
3.35 x 105
2.32 x 106
9.1 x 106
2.62 x 107
6.23 x 107
1.31 x 108
2.54 x 108
3.76 x 108
5.12 x 108
 *This value of the total environmental load estimated to be of the order of
  2.5 x  108 Ibs in 1970 is to be compared to the estimate of 7.8 x 108 Ibs by
  Nisbet and Sarofin(2).   See Section C.2.3.1 for a fuller discussion of this
  conparison.
**Equation (C-14)  is not actually valid for the post 1970 period, but if the
  voluntary ban had not been iirposed, the estimated M  (1975) would have been
  as recorded  in Table 2.2-1.
                                     C-7.

-------
       C.2.3  Effect of Monsanto 's Voluntary Ban on PCS Sales
              In the actual situation, as a result of the voluntary Monsanto ^
ban on PCB sales, the expression MQV(t) given by Equation (C-14) must be modified
to account for post 1970 sales levels.  Thus, for the period 1971 and later,
                                       -t                    44
        Mev(t > 40)  = MQV(t = 40)  + a1/   Q^tjdt + (l-a-6)  /   Q(t-4)dt
                                       40                 "40
                     Q(t-20)dt
44               40
                         1^1)/   Q^t^dt+B/
which, on noting that (1-a1-^ 1) = o for the period after 1970  (t=40) , and
substitution of the forms of Q(t) and Q1 (t) , becomes on integration/

Mev(t > 40)  = Mev(t = 40) +  (0.1) (3.31 x 106) (t-40) +  (0.21 (|i^.) f(40) "' 39-(36) "' 39]


                    + (0.62)  (^^(t^O)4'39  - (20)1*'39]   .             (C-15)
Equation (C-15)  may be simplified to yield (t > 45) ,

        M  (t>45)  = 3.75 x 108 + (3.3 x 10s) (t-40) + 43.92(t-20) "' 39 .     (C-16)
         ev

              C.2.3.1  Comparison of the Results of Equation (C-14) with the
                       Estimates of Nisbet and Sarofim(^)
                                                   (2)
                       In 1972, Nisbet and Sarofim    provided a rough estimate
of the losses of PCBs to the North American environment up to the year 1970 to
have been:   3 - 4 x 106 Ibs to the atmosphere (largely Aroclor 1254 and 1260
from plastics and 1242 from burning of dumps) ; 8 - 9 x 106 Ibs to fresh and
coastal waters (Aroclor 1242-1260) ; and 4.4 x 10 7 Ibs into dumps and landfills
(largely Aroclor 1242) ; other losses were assumed to be small.  The cumulative
losses in the period 1930-1970 were estimated to be
                                      C-8.

-------
             Atmosphere    6 x 107 Ibs

             Water - fresh and coastal    1.2 x 108 Ibs

             Dumps and landfills          6 x 108 Ibs


making a total  environmental acs^umulation (M  (t)  of an estimated 7.8^ x 108 Ibs.


On the other hand,  returning to Equation (C-3), integration over the period
1930-1970 yields the result
                                 40

                              11   t3'
                  Qs(40)  = 311 /   t3'39dt = 7.64 x 108 Ibs,
clearly then, the Nisbet estimate exceeds the cumulative United States sales up

to 1970.

                       Returning to Equations (C-4) which express the capacitor

and transformer sales as functions of time, it is clear that, with an average

service life of 20 years, the net amount of PCS still in service in 1970 was

                                                     40

               (Q   )                  =2.03xl02/  t3'289dt
                 cap in service (1970)             J
                                                   20
                                       = 3.35 x 108 Ibs;


while for transformers
                                                       40

                                         = 2.02xl03/   t*'37dt
                       in service (1970)
                                                     20
                                                      /  t*'
                                         = 1.36 x 108 Ibs.
                                      (1)
Hence,  in 1970 of the total U.S. salesv '  of 7.64 x 10s Ibs, a sub total of

4.71 x 108 Ibs were still in service and thus could not participate in the general

environmental pool.
                                     09.

-------
                       If the material still in service in non-electrical
applications  in 1970 were ignored, the general environmental pool could not have
exceeded

                   7.64 x 10s - 4.71 x 108 = 2.93 x 108 Ibs,

a value which compares favorably with that indicated in Table C.2.2.1.

C.3.0  MOBILE OR FREE ENVTEOJMENTAL PCBs, m  (t)

       C.3.1   General Considerations on Mobile PCBs - Mev(t)
              To consider the processes by which the general environmental load
of PCBs (Mgv(t) I becomes free, i.e., the processes by which m  (t)  is generated,
it is necessary to consider that some fraction of the direct losses are in a
form such  that the lost material immediately becomes mobile; i.e.,  spills and/or
evaporation losses.  Further, the non-mobile material is usually encased or
enclosed in some sort of container which will eventually be degraded thus allowing
the subsequent escape of the component PCB.
              The fraction of the total sales that is waste occuring in all
production uses of PCBs is oQ_(t) of which some fraction e is immediately mobile.
                             5                                               . .   ...
Thus, in the  time interval t to t + At, this component  introduces an amount

                                   eoQ (t)At                               (C-17)
                                      5

into the free environmental pool.  The remainder (l-e)aQ (t) which enters the
                                                        5
environmental reservoir is contained in a state such that the PCB content is
gradually  released with a time constant T  = I/A .  Thus, within the reference
                                         2      2
interval t to t + At, an amount
                                A (l-e)oQe(t)At                            (C-18)
                                 2       S
enters the mobile pool.
              Further, a fraction $ of the yearly sales was used to manufacture
long lived electrical components, assumed to have a useful life of y  years,
after which the components are scrapped.  Thus, the contribution of this source
to the general environmental pool is

                                      C-10.

-------
                                 8 Qs(t-y )At                               (




•The electrical containers in which the PCB is enclosed will eventually decay,


with a half life T  = 1/X .  The additional component entering the mobile res-


ervoir will be, during the reference time interval,



                                X 3 CL(t-y )At   .                          (C-20)
                                  i5    i



Finally, the remainder (l-a-6 )Q (t) was used in the construction of products
                               s

assumed to have a useful life of y  years, after which they are discarded, thus


contributing a component to the general environmental pool:



                              (1-cHS) Q(t-y )At   .                         (C-21)
                                       S    2



If as before,  it is assumed that these products have a lifetime T = 1/X  against
                                                                 2     2

decay, then the contribution to the mobile environmental pool will be



                             X (1-a-S) Q(t-Y )At   .                       (C-22)
                              2         S    2



              On combining Equations  (C-17) , (C-18) ,  (C-20) and C-22) , in the


limit At ->• o, the differential equation for mev(t) becomes
                               (t) + X2(l-e)oQg(t) + X^Qgft-Y^) +




                               X  (l-a-6)Qe(t-Y )                            (C-23)
                                2        S    2




           = fea+ X. (l-e)al Q (t) + X  (l-a-6 ) Q_ (t-y ) + X SQ  (t-y  )
             I      2       JS       2        S21.S1




       from Equation (C-3)  Q  = Silt3*39.
                            S



On integration of Equation  (C-23) and the substitution of the parameters  from


Table C.3.1-1, with the exception of e, the result is
                                      C-ll.

-------
                                 TABLE C.3.1-1
                Estimated Total Environmental PCB Load {M   (t) ]

                 and Mobile Environmental PCB Load in  [m   (t) ]
                                                        .(2)       M   ,^	(3)
Date
1930
1935
1940
1945
1950
1955
1960
1965
1970
1975
1980
1990
t
(years)
0
5
10
15
20
25
30
35
40
45
50
60
&\) v ' ev WJJ.A.
(Ibs) (Ibs)
0 0
6.49 x 103
1.40 x 105
8.62 x 10s
3.14 x 10s
8.54 x 106
1.89 x 107
3.86 x 107
7.01 x 107 7.01 x 107
1.19 x 108 8.31 x 107
1.90 x 108 9.04 x 107
4.30 x 108 1.07 x 108
1YJgV v w ^Ji-j-
(Ibs)
0
1.42 x 10"
3.35 x 10s
2.32 x 10s
9.1 x 106
2.62 x 107
6.23 x 107
1.31 x 108
2.54 x 108
3.76 x 108
4.66 x 108
8.41 x 108
Notes:  (1)  From Equation (C-24)
        (2)  From Equation (C-25)
        (3)  From Equation (C-15)
                                     012.

-------
             mev(t)  = 10.84e(t)'t'39 + 1.204(t) "'39 + 1.49(t-4) *'39

                                    + 0.44(t-20)'t*39                        (C-24)

where the term t-4 is taken to be zero when t <  4, and that continuing t-20 to
be zero when t < 20.
              In order to evaluate mev(t) it is  necessary to determine a useful
value for e as follows:  From the definition of  e as that fraction of  the initial
losses, due to spills, transportation accidents, manufacturing wastes, etc., is
immediately free,  it would appear that a reasonable choice ^  of e is_40%_of .the
initial losses.   Thus,  in terms of this choice of e, Equation (C-24)  becomes

               mev(t) = 5.54t4*39 + 1.49(t-4)'t'39 + 0.44 (t-20)1"39.        (C-25)
The detailed evaluation of Equation  (C-25) is enumerated in Table C.3.1-1 which
also includes the tc
comparison purposes.
also includes  the total environmental load M  (t) from Equation (C-15) for
                                            ev
       C.3.2  Effect on the 1970 Ban(4) on Mobile PCBs  (M   (t)
                                                         ev
              It is now appropriate to discuss the effect that the partial ban
established in 1970 can be expected to have on the mobile PCB load, roev(t).  The
operative change occurs as a result of the substitution of Equation  (C-6) for
Equation (C-3) in the time interval after 1970.  The resulting expression for
m  (t>40)  is given as (recalling that the ban also stopped sales for non-
electrical applications):
                         40
                   » eoS /   t3*
       mev(t > 40)  » eoS    t3*39dt + ea*5'
                         t                            t<44
                   ex S /   (t-y )3<39dt +  (l-cH3)A<5 /   (t-y  )dt           (C-26)
                     ')       '                   2J
                                      C-13.

-------
which, on integration and evaluation of the coefficients, becomes, using the
parametric values listed in Table 2.4.1-1,

        mev(t<45)  =J7.59 x 107 + (0.44)  (t^O)**39 -I- 1.32 x 106  (t-40)] lbs(C-26')

Numerical values derived from Equation  (C-25') are listed in column 4 of Table
2.4.2-1.  Again, the effect of the voluntary partial ban of 1970-71 is apparent.
              It will be useful in what follows to express the numerical relation-
ship given by Equation (C-251)  in the approximate empirical form  (formed by
regression analysis of the tabulated values of Equation  (C-261)
                             mev(t<40) = 4.83^
                        m
                         ev(t > 40) = 1.69 x
                                                        Ibs.
                                                                           (C-27)
              Equation (C-27) suggests that, in 1970, the cumulative mobile PCB
reservoir, m., (40)  was of the order of 7.82 x 107 Ibs whereas the Nisbet and
       (2)
Sarofxnr   estimate for mobile PCBs (water plus atmospheric load) was of the
order of 1.8 x 108  Ihs.  A plot of Equation (C-27) is presented on Figure C.3-1.
C.4.0  ATMDSPHERIC  TRANSPORT
       C.4.1  Atmospheric Reservoir of PCBs, m.a(t)

              Suppose that some fraction 0 of the instantaneous addition to the
mobile environmental material is vaporized.  Then within the interval t to t + At
                                                                            (C-28)
dm. (t)
CL
- o *fc,(t
0 at
Further, suppose that the material contained within the mobile pool  is vaporized
with a time constant T
reservoir is given by
with a tiros constant T  = 1/X ,   then the additional component of the atmospheric
                      3      3
                              dma(t)
                                                                            (C-29)
                                      C-14

-------
o
ft
5
d
    ISO
    160
    140
    120
    100
    30
    60
    40
    20
Qarw = 8
     1930      1940      1950
                                1960
                                  DATE
                            1970      1980
                          Figure  C.3.1
                          Estimate Wild PCBs,
                     M-(t)   where t = 0,  1930
                      £V
                          Equation (C-27)
                                  C-15.

-------
                                 Table C.4.1-1



          Parameter Values for Equation (C-23) and Equation (C-25)





    a =  0-17                        £ = 0.40                     a1  = 0.1


    6 =  0.62                      1-e = 0.60                     
-------
Finally,  suppose that the lifetime, T   = 1/X ,  of the atmospheric reservoir
                                     "*       »f

results in a decay of m  (t) given as
                       cl
                                    = X  in (t).
                                        t   a
               (C-30)
              The total change in m (t)  with time is then given as
                                    cL
din (t)
cl
~~dt 	
din (t)
cL
— at"
+
a
din (t)
a.
"" dt~
+
b
dma(t)
dt
                                                                             (C-31)
which on substitution of the appropriate expressions yields the differential


equation for m  (t) as follows:
                   dm  (t)
X  m (t) = 0
 "t  a
                                                        mev(t)
               (C-32)
for which the general solution  is


                             J:
              ma(t, =
dm   (t)

  ev    + X  in   (t)
   dt      3  ev   _
dt
                                                (C-33)
After substitution of the expression for m  (t)  from Equation  (C-27) the result


of the integration by parts  is
                 _ > en
                 - 4.83
                                    21.74
                                                 _
3.5 ^  (3.5)(2.5)
                                    (3.5)(2.5)(l.i
                                             g
                                                               .5
       dt>    (c-34)
                                       C-17.

-------
                    In order to evaluate Equation  (C-34),  it is  appropriate to return
      to the source term for ma(t) , vis,, Equation  (C-28) and (C-29),  then

                                     /*   f  dm   (t)                 "1
                             ma(t) =J    I 9—3t~ +X3 me.v(t)   dtj            (C~35)
                                     o

      yfriich,upon substitution of the form of mev(t) from Equation (C-27),  yields the
      expression

                                ia(t) = 7.82 x 107 <9 + 7.27X31 Ibs                (C-36)
                          19 30
      If now,  the Nisbet and Sarofim  '  estimate of total atmospheric load of  6 x 10 7
      Ibs is introduced, using the same factor of 3 to account for the overestimate,
      and assuming that 9 = .05, Equation  (C-36) may be solved for X3 to yield

                                     X3 = 0.0283 yr"1

                                  or T3 = 35.3 years .

                                                            (2)
      Thus, it appears that the modified Nisbet and Sarofim   estimate of the
      cumulative atmospheric load requires that the time for the evaporation losses of
      the environmental load to reduce the latter to 1/e is of the order of  35.3  years.

             C.4.2  Atmospheric Concentration of PCBs
                    If Equation (C-35) is evaluated for t = 45 and also for  t  = 44,  then
2
                                      m  (t) = m  (1975) - 2.51 x  10"  Ibs
                                       cl       Si
                    19 30         19 30
     "Whereupon, returning" to' Equation (C-34) and evaluating at t = 45 with the
      appropriate  substitution for 0 and for X3, yields the expression for Xi*
                             X'? - 1.23X? + 0.15X* - 0.117 =o                     (C-37)
                                            C-18.

-------
which is in the form




                             X3  + bX2 + cX + d = o





foe which °-Q*




                A = 18 bod - 4b3d + b2c2-4c3-27d2 = -0.3696 < o




hence, only one of the roots of Equation  (C-37) is real, and that real root is




                               Xi, = 1.1865 yr'1






                             i- - T* ~ 0.843 yrs.                           (C-38)
                             Ait




Beturning to Equation (C-34), substituting for 0, X3 and Xi», and evaluating the


integral by the methods of Appendix A, yields




                             m (45) ~ 2.-05 x 106 Ibs .                       (C-39)
                              Si



If it is now assumed that the air concentration over the continental United


States is uniform, and that the atmosphere is of uniform, density and hence of


height'11'




                           h.   ~ 8.18 x 103 meters.
                            is



The area of the continental United States'  ' ~ 7.827 x 1012m2; whereupon~the


concentration of PCB in 1975 should have been




                               2.05 x 106 x 454
                     C .  (45)~
                      air'  '  8.18 x 10° x 7.82 x
                   C1~~'(1975) = 1.45 x 10"8 gra/m3 ~ 14 ng/m3
                    air
or in the usual concentration terms, gm/gm,
                               !—(1975) ~ 11 ppt.
                                      C-19.

-------
Actual measurements by Murphy <13) in 1975-1976 have shown that ambient PCB
levels were of the order of 3-6 ppt indicating that the estimate in Equation
(C-37) is within a factor of two to three of the measured values.  This reason-
able agreement suggests the validity of the estimates for the various particulates
used in  this analysis.

C.5.0 TIME DEPENDENCE OF a(t) and B(t)
      Returning to Equation  (C-34) and introducing the definition of a(t) as

                                o(t)A = X 1,111 (t)                             (C-38)
                                           CL

where A  = area of continental United States.

By iterated calculation of Equation (C-38) for various times from t = o (1930)
to t = 40 (1970)  and by standard regression analysis of the result, the
empirical form for q (tl is

                                 a(t)  = a t3'5                              (039)
                                         o
and. since,  at least for the Great Lakes, fallout constitutes the major PCB input,
the forcing function, B(t) is taken to have the form

                                 B(t)  = aI1t*'5.                            (C-40)
                                      020.

-------
ftEPENDIX C REFEKbfciCES

(1)  Monsanto Industrial Chemicals Company, "PCB Manufacture and Sales-Monsanto
    Industrial Chemicals Ccmpany - 1957 thru 1964."  (unpublished data), 1974a.

    Monsanto Industrial Chemicals Ccmpany, "PCB Manufacture and Sales-Monsanto
    Industrial Chemicals Company - 1965 thru 1974."  (unpublished data), 1974a.

(2)  Nisbet,  C.T.,  and A.F. Sarofim.  Environmental Health Perspectives Exp 1:
    21-38,  1972.

(3)  •Versar  Inc., TCBs in the United States:   Industrial Use and Environmental
    Distribution"  NTIS PB-252 4Q2/3WP.  February 1976.

(4)  Monsanto Industrial Co., Testimony, FWPCO(307) Docket No. 1, Presented by
    Mr. W.B. Papageorge.

(5)   Ibid, Reference 3, Section V, 3.1 and 3.2.

(6)   Ibid, Reference 3, Section V, 3.5.

(7)   Ibid, Reference 3, Section V, 3.1 and 3.2.

(8)   Ibid, Reference 3, Section V, 3.5.

(9)   Ibid, Reference 3, Section II, 5.0.

(10)   I.S.  and E.S.  Sokonnikoff. "Higher Mathematics for Engineers and Physicists,"
     MoGraw, 1941,  New York.

(11)   Iso Density Atmosphere.

(12)   Annan., World Almanac, Washington Star News, Washington, D.C., 1975.

(13)   Murphy, Thomas.  Private ccmmunication.
                                       0-21.

-------
                  APPENDIX D
   CUMULATIVE ENVIRONMENTAL PCB LOAD AND AN
ESTIMATE OF THE CHLORINE SPECTRUM OF FREE PCBs

-------
D. 1. 0  MERDDUCTION
      It has been assumed,  in the development of the ness balance model, that
there are no significant degradation processes, either environmental nor
biological, operative for free PCBs.  It will be shown in what follows that the
often cited  '  '    observation that, in spite of the fact that Aroclor 1242 was
used in many applications which should tend to allow its escape into the environ-
ment, the observed KB spectrum from, many biological and environmental specimens
most clearly resembles that of 1254, it is not necessary to involve degradation
or metabolic processes to account for this observation.  In point of fact, it is
possible  to construct a model of the free PCB chlorine content simply from the
Mansanto  data on sales and end use coupled with estimates of yearly loss factors
for each  end use category.

D.2.0- PCB SALES BY END USE CATEGORY, Period (1930-1975)
       The production and sales figures for the principle Aroclors for the period
1957 through 1975 indicate that, by far the principle species manufactured and
sold were the Aroclors 1242,  1248, 1254 and 1260.  These mixtures will be the
only ones considered in what follows.
       It will be necessary to estimate the PCB production and sales in the
period 1930 through 1956, a time span for which there appear to exist no official
figures.      This extrapolation is accomplished by fitting the published produc-
tion and sales figures, by Aroclor category, for the period 1957 through 1970 by
an expression of the form

                              Q(t) = atn (Ibs/yr)                            (D-D

and then assuring that this expression fits the corresponding production and
sales figures back to 1930 when t = 0 in 1930 (t in years) .  The Monsanto released
sales figures  ^  also allow the estimate of the proportional use factors for each
end use for each of the Aroclors.  The results of these calculations are displayed
in Table P. 2-1 which follows.
       From the computed use factors in Table D.2-1, and the sales by end use
category it is possible .to estimate the quantities of each of the significant
*The references  for this Appendix are listed on page D-15.

                                       D-l

-------
          TABLE D.2-1

PROPORTIONAL USE FACTOES - PCBs
                       (4)
        [Monsanto Data]
                          Transformers
Date
1930-1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
Heat Transfer &
Hydraulic Fluids
0.025
0.049
0.059
0.086
0.072
0.109
0.107
0.118
0.121
0.113
0.102
0.100
0.128
0.165
0.154
0.136
0.028
	
___
MSC
Industrial
0.156
0.022
0.029
0.050
0.044
0.056
0.044
0.040
0.038
0.036
0.030
0.023
0.020
0.016
0.022
0.015
	
	
— —
&
Capacitors
0.806
0.784
0.760
0.718
0.707
0.592
0.614
0.600
0.614
0.626
0.640
0.653
0.632
0.552
0.555
0.766
0.972
1.00
1.00
Plasticizer
Applications
0.013
0.145
0.15
0.146
0.177
0.242
0.235
0.241
0.230
0.226
0.228
0.214
0.221
0.245
0.267
0.082
	
	
	
               D-2.

-------
Aroclors utilized in end use.   The results of these estimates  are shown in
Tables D.2-2 through D.2-5.   It is to be noted that after the  voluntary ban(  '
on PCB sales for non-closed  end uses in 1970-1971, the form of the empirical
description  of the various sales categories  is
                                 Q(t) = 6
    Ibs/yr
(D-2)
and was esentially constant.
                                      Table D.2-2
                              USE CATEGORIES ARQCLOR 1242
(4)
                                  (Thousands of Pounds)
                           [Proportional Usages from Table D.2-1]
Date
1930-1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
Heat
Transfer
(Ibs)
—
—
—
—
—
—
82.6
278
495
757
1,187
1,550
1,149
2,043
2,624
1,932
20.4
__
	
Hydraulic
Fluids
(Ibs)
2,050
893
616
1,169
1,310
2,161
2,127
1,907
2,357
2,806
2,848
3,186
3,992
5,448
4,907
924
	
_
	
Misc.
Industrial
(Ibs)
12,790
401
303
680
801
1,110
2,127
740
896
1,135
1,187
990
897
726
1,069
315
	
	
	
Transformers
(Ibs)
—
7,289
2,287
2,597
4,094
3,311
4,337
3,535
4,196
5,266
5,973
7,621
7,884
8,172
9,183
6,426
	
	
	
Capacitors
(Ibs)
—
9,603
5,650
7,166
8,770
8,426
8,344
7,571
10,277
14,474
19,343
20,494
20,363
17,025
17,783
9,660
	
	
	
Transformers
& Capacitors
(Ibs)
66,075
16,891
7,937
9,763
12,865
11,738
12,681
11,106
14,473
19,740
25,316
28,115
28,347
25,061
26,966
16,086
708
6,200
6,207
Plasticizers
(Ibs)
10,657
1,000
1,567
1,985
3,221
4,798
4,854
4,461
5,421
7,126
9,019
9,214
9,913
11,123
12,973
1,722
	
	
	
Petroleum
Applications
(Ibs)
—
	
	
	
	
—
	
	
	
	
	
	
	
953
	
	
	
	
	
                                       D-3.

-------
                                     D.2-3
                       USE CATEGORIES AROCLOR 1248

                         (In Thousands of Pounds)
             [Proportional Uses Calculated from Table D.2-1]
HYDRAULIC &
HEAT TRANSFER
Date
1930-1957
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
Fract.
.128
.227
.248
.305
.246
.268
.270
.268
.272
.254
.218
.238
.270
.315
.259
.312

Amt.
(Ibs)
2,043
404
635
1,032
695
1,078
935
1,343
1,425
1,414
1,093
1,120
1,321
1,780
1,055
81
	
PLASTIC! ZER
APPLICATIONS
Fract.
.804
.671
.63
.515
.605
.595
.615
.628
.625
.644
.691
.688
.670
.643
.685
.582

Amt.
(Ibs)
12,830
1,194
1,612
1,753
1,710
2,394
2,130
3,148
3,274
3,584
3,465
3,236
3,279
3,635
2,790
152
	
MISC.
INDUSTRIAL
Fract.
.067
.102
.122
.177
.150
.138
.115
.104
.103
.103
.091
.074
.061
.042
.056
.106

Amt.
(Ibs)
1,069
181
312
599
424
555
398
521
540
573
456
348
299
237
228
28
	
1974
                                     D-4.

-------
                   TABIE D.2-4

           USE CATEGORIES AKKIOR 1254

            (In "thousands of Pounds)
tProportional Factors Derived From Table D.2-1)
Date
1931-1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
Heat
Transfer
(Ibs)
	
	
	
	
	
	
25.3
89
132
186
211
241
341
442
671
429
98
	
	
Hydraulic
Fluids
(Iba)
629
219
395
581
438
686
651
611
628
689
507
496
791
1,179
1,255
205
	
	
	
Misc.
Industrial
(Ibs)
3,923
98
194
338
268
352
278
236
239
279
211
154
178
157
273
70
	
	
	
Trans formers
(li>s)
	
1,704
1,465
1,290
1,674
1,051
1,328
1,129
1,118
1,292
1,062
1,185
1,583
1,768
2,348
1,426
	
	
	
Capaci tors
(Ibs)
	
2,351
3,620
3,559
2,934
2,675
2,555
2,418
2,738
3,551
3,440
3,187
4,037
3,654
4,546
2,144
	
	
	
Trans formers
& Capacitors
(Ibs)
20,271
4,135
5,085
4,849
4,304
3,726
3,884
3,547
3,856
4,843
4,502
4,372
5,619
5,422
6,894
3,570
3,397
7,976
6,176
Plasticizers
(Ibs)
327
1,000
1,004
986
1,078
1,523
1,486
1,425
1,444
1,749
1,604
1,433
1,965
2,406
3,316
3»2
	
	
	
Petroleum
Applications
(Ibs)
	
000
	
	
	
	
	
	
	
	
	
	
	
206
	
	
	
	
	

-------
                  TABLE D.2-5

          USE CATEGORIES AROCLOR 1260

             (Thousands of Pounds)
[Proportional Factors Derived From Table D.2-1]
Date
1930-1956
1957
1958
1959
1960
1961
1962
196S
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
Hydraulic
Fluids
(Ibs)
423
493
293
569
528
713
679
900
1.033
659
599
706
672
732
807
235
8.5
	
	
Plasticizers
(Ibs)
220
400
897
966
1,297
1,583
1,550
1,838
1,963
1,318
1,340
1,373
1,161
1,088
1,306
141
	
	
	
Transformers
(Ibs)
13,529
6,085
4,546
4,752
5,182
3,872
4,049
4,576
5,240
3,650
3,760
4,190
3,319
2,450
2,714
1,321
296
	
	
Misc.
Industrial
(Ibs)
2,638
258
173
331
323
366
290
305
324
210
176
150
105
181
108
26
	
	
	
                      D-6.

-------
D.3.0 PCB LOSSES TO THE ENVIRONMENT
      Now in order to estimate the amounts of the various Aroclors that have
escaped  to the environment,  it is appropriate to introduce a reasonable estimate
of the yearly losses associated with each end use.  The loss factors, listed in
Table D.3-1 include spillage losses accompanying manufacture or use of the PCB
containing end product as well as losses due to inadequate disposal methods.

                                  TABLE D.3-1
                 ESTIMATED LOSS FACTORS FOR PCBs BY END USE^
                                                 % of Yearly PCB Use
              Use Category                       Lost'to-'Environment
      Closed electrical systems
            (transformers and capacitors)                  5%
      Hydraulic and heat exchange fluids                60%
      Plasticizers                                      25%
      Miscellaneous industrial applications             90%
      Each of the assigned loss percentage factors can be the subject of con-
siderable controversy.  Suffice it to say that the choices made appear to be
reasonable based on the widely varying information considered.
      Now, the quantities of PCB of the separate Aroclor mixtures given in
Tables D.2-2 through D.2-5,  may be combined with the loss facotor from Table
D.3-1 to yield an estimate of the yearly PCB losses to the environment as well
as an estimate of the cumulative total losses.  The results of these calculations
are listed in Table D.3-2.
      The tabulated results in Table D.3-2 may be fitted by the empirical
relationship (1930-1970)

                    (Q«Pcumulative = 8'Q X'10' *''" *»                  (1>3)
                                     D-7.

-------
              TABLE D.3-2
PCB ENVIRONMENTAL LOAD BY AROCLOR TYPE
        [In Thousands of Pounds]

              Aroclor Type


1930-56
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1242

18,709
1,991
1,431
2,298
2,955
4,082
3,992
3,648
4,597
5,928
7,010
7,442
7,789
9,182
10,072
3,232
48
310
310
1248

5,395
704
1,065
1,597
1,226
1,745
1,452
2,062
2,160
2,260
1,932
1,794
1,881
2,190
1,536
112
-
-
—
1254

5,003
676
917
1,142
989
1,295
1,222
1,166
1,224
1,456
1,247
1,158
1,615
2,172
2,575
717
229
399
309
1260

3,559
932
783
1,118
1,191
1,347
1,258
1,503
1,664
1,096
1,041
1,111
954
997
1,044
266
20
-
—
1016 Total
PCBs
32,466
4,303
4,196
6,155
6,361
8,469
7,924
8,379
9,645
10,740
11,230
11,505
12,239
14,541
15,227
167 4,494
1,045 1,342
1,177 1,886
1,098 1,717
                  Grand Total -          172.8 x 106 Ibs.
                  D-8.

-------
D.4.0  ESTIMATED CHLOKDSE SPECTRUM OF FREE PCBs
       The approximate molecular composition of the Aroclors displayed in
Table D.4-1.   From the compositional data in Table D.4-1 and the estimated losses
by Aroclor -type from Table D.3-2 it is possible to estimate the losses as a
function of chlorine number.  The results of these estimates are displayed in
Table D.4-2.
       Finally, the estimates contained in Table D.4-2 may be converted to
estimates of the average molecular makeup of the environmental PCB load.  The
results of such computations for selected years between 1930 and 1974 are dis-
played in Table D.4-3.

D.5.0  RESULTS
       By comparison of the estimated molecular composition of the environmental
PCBs given in Table D.4-3 with the measured composition given in Table D.4-1 it
is evident that the wild PCBs approximate the composition of Aroclor 1248.
       The comparison of the estimated chlorine content of the known Aroclors is
shown in Table D.4-4.
                                      D-9.

-------
            TABLE  D.4-1
APPROXIMATE MOLECULAR COMPOSITION
      OF SELECTED AROCLORS^
             Aroclor Type or Grade
Chlorobiphenyl
C12H10
C12H9C1
C12H8C12
C12H7C13
C12H6C14
C12H5C15
C12H4C16
Cu i"i
1 ? "3 "7
C12H2C18
C12H1C19
C12C110
1221
11
51
32
4
2
0.5
ND
ND
ND
ND
ND
1242
(pe
<0.1
1
16
49
25
8
1
<0.1
ND
ND
ND
1248
rcent cc


2
18
40
36
4




1254
mpositi
<0.1
<0.1
0.5
1
21
48
23
6
ND
ND
ND
1260
on)





12
38
41
8
1

1016
<0.1
1
20
57
21
1
<0.1
ND
ND
ND
ND
                D-10.

-------
           TABLE  D.4-2

CUMULATIVE ENVIRONMENTAL PCB LOAD
       BY CHLORINE CONTENT
      [In Thousands of Pounds]


1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974

—1
561
621
664
733
822
944
1064
1173
1311
1489
1699
1922
2156
2431
2733
2837
2881
2938
2992
Cl
2
2540
2813
3020
3351
3760
4326
4874
5389
6030
6846
7796
8799
9850
11088
12428
12880
13073
13324
13561
Cl
3
6210
6894
7487
8417
9465
10922
12301
13693
15369
17436
19747
22154
24674
27639
30735
31723
32131
32663
33165
Cl
4
8221
9174
10130
11584
13070
15135
17048
19095
21473
24315
27328
30406
33673
37543
41462
42624
43086
43700
44272
Cl
5
8936
10070
11311
13086
14805
17128
19279
21575
34160
27123
30097
33080
36376
40368
44523
45657
45782
46046
46265
cic
— 6
4017
4709
5419
6388
7344
8529
9640
10835
12153
13391
14568
15754
17053
18625
20362
20840
20928
21076
21193
Cl
	 /
1759
2182
2558
3085
3632
4162
4751
5437
6192
6728
7230
7755
8243
8782
9365
9517
9539
9563
9582
C10
— 8
285
360
423
512
607
715
816
936
1069
1157
1240
1329
1405
1485
1569
1590
1592
1592
1592
Cl
9
36
45
53
64
89
89
102
117
134
145
155
166
176
186
196
199
199
199
199
Total

32,565
36,868
41,064
47,219
53,580
62,049
69,973
78,352
87,997
98,735
109,966
121,471
133,710
148,251
163,478
167,972
169,314
171,204
172,821
               D-ll.

-------
                                   TABLE  D. 4-3

                          COMPUTED SPECTRUM OF CHLORINE
                              CONTENT FOR WILD POBs


                                    [In Percent]
                     Weight Percentage of Isomers  Containing Cl

1956
1960
1965
1970
1974
C1-L
1.7
1.5
1.5
1.7
1.7
ci2
7.8
7.0
6.9
7.6
7.8
<*3
19.1
17.7
17.7
18.8
19.2
^4
25.2
24.4
24.6
25.4
25.6
—5
27.4
27.6
27.5
27.2
26.8
^6
12.3
13.7
13.6
12.5
12.3
9?
5.4
6.8
6.8
5.7
5.5
0*
0.9
1.1
1.2
1.0
0.9
^9
0.1
0.1
0.1
0.1
0.1
Average      1.6      7.4       18.5     25.0     27.3    12.9     6.0    1.0     0.1
 Values
                                       D-12.

-------
                            7.00
2
OJ
                            6.40
                           H6.00 -
                           35.40 .
                            5.00
                            4.4C
                            4.0C
                      la I

        Data 1975 (5.00)' '


X Computed Using only (5.01)


  Cl, - Cl, fron Table
    4     7
                                                                                            Aroclor 1260
                                                                                            Aroclor 1254
                                                                                            Aroclor 1248
                                                                                            Aroclor 1242
                            3.401-
                                                                                                                                -4-
                                      1930    1934      1938    1942     1946     1950    1954     1958     1962    1966     1970     1974
                                                                        Figure  D.4-1


                                                     Estimated Average Chlorine Number for  Wild PCBs

-------
                                  TABLE  D.4-4
                         CHLORINE CONTENT OF AROCLORS
                           AND OF ENVIRONMENTAL PCBs

    Aroclor                     Chlorine Content (atoins/nolecule)
      1242                                     3.67
      1248                                     4.22
      1254                                     5.35
   Environmental                              4.32

Thus,  from this sinple computation it is clear that the spectrum of the environ-
mental PCBs may have arisen simply from the mechanics of the dispersal of the
individual  Aroclor mixtures and does not necessarily require the invoking of
metabolic or environmental degradation processes.
                                     D-14.

-------
APPENDIX D - REFERENCES

(1)   Nisbet, C.T., and A.F. Sarofim.  Environmental Health Perspectives
     Exp 1: 21-38, 1972.              	

(2)   Peakall, D.B., "PCBs and their Environmental Effects", CRC Review
     5_, Issue 4, 1975.

(3)   Glooschenko, W.A., et al,  "Distribution of Pesticides and PCBs  in
     Water, Sediments and Seston of the Upper Great Lakes", Pest. Monit.
     J., 1£, 61(1976).

(4)   Monsanto Industrial Chemicals Company, "PCS Manufacture and Sales-
     Monsanto Industrial Chemicals Company - 1957 thru 1964."   (unpublished
     data), 1974a.

     Monsanto Industrial Chemicals Company, "PCB Manufacture and Sales-
     Monsanto Industrial Chemicals Company - 1965 thru 1974."  (unpublished
     data), 1974a.

(5)   Ibid, Ref. D-l

(6)   Versar Inc., "PCBs in the  United States: Industrial Use and Environmental
     Distribution" NITS PB-252  402/3WP. February 1976.

(7)  Hutzinger, 0., S. Safe, and V. Zitko, "The Chemistry of PCBs",  CRC
     Press, Cleveland, Ohio, 1974.

(8)  Murphy; Thomas, DePaul U., personal communication.
                                      D-15.

-------
            APPENDIX E
DATA BASE FOR LAKE MICHIGAN MODEL

-------
                                  APPENDIX E
                      BACKGROUND DATA USED TO CONSTRUCT
                     THE MODEL FOR PCBs  IN LAKE MICHIGAN
                                  Table E-l
                     Concentration of PCBs in Sediments          m**
       Along the Southwestern Shore of  Lake  Michigan (1970-1971) (  '
     Sample locations                    	PCBs (ppb)	
Along SW  shore of lake;   sampling         13.09 A               15.24 B
1-3 mi. off-shore*  (See Figure E-l).      6.73 A               16.09 ?
                                          11.81 ?               12.69 ?
                                          26.07 A               23.53 A
                                          87.98 A               17.53 A
                                         130.27 ?               36.7 ?
                                          26.61 B               58.81 A
                                          64.32 A               41.06 A
                                           3.72 A              132.61 A
                                           3.87 A               80.63 ?
                                          35.8 A               29.29 A
                                           8.31 A               13.34 A
                                                  Total = 896.01
                                             Ave. (PCB) =  37.3
NOTE:  Estimated location of sampling sites with respect to thermocline:
                          A - Above thermocline
                          B - Below thermocline
                          ? - Questionable
*Sampling sites are located in an area with several known STP discharges.  Data
were not available on PCB concentrations in these STP effluents;  however,
judging from PCB data for other area STPs, it is probable that these plants dis-
charge PCBs, thereby producing higher concentrations in the adjacent sediments.

**The references for this Appendix are listed on Page  E-17.
                                     E-l

-------
     Wisconsin.
     iUlinois
           Kellogg Creek 4.33
              Bull Creek  22.1 •!
                                                                N
           Doad River 18.59
  Unnammed Channel 636.04
     Waukegan River 505.0
     Pettibone Creek 405.4 •

    Ravine Park Ravine 3.85  •
    x 13.34
 /x Waukegan STP 29.29
    x 80.63

 x  North Chicago STP 132.61


x 41.06
 x  Lake Bluff STP 58.81

    x 36.7
 x  Lake Forest STP  17.53
                                                                         10
                                                         Scale  In ml 1«»
                                                           LAKE MICHIGAN
Ferry Hall School Ravine 18.68 _
  Stone Gate Lane Ravine 11.22 •
           Barat Ravine 7.28 •

                            \    x  16.09
        Park Avenue Ravine 5.86 «\ x Highland Park  & Park Avenue STP 23.53
        Ravine Drive Ravine 6.38 •
         Gary Avenue Ravine 20.00 ux
  Lake_Counjty_	J
  Cook County                    \   x 8.31
                                    x 15.24
                                             E-l
PCBs  in  sedinents of Lake  Michigan and in Tributary stream   and  ravine
sediments in 1971:   Total  of Aroclors 1242  and 1254 in parts per billion
on a  dry weight basis.  (1)
                                           E-2

-------
                                    TABLE - E-2

                        Concentration of PCBs in Reported        ,,,
             Illinois STP Effluents Discharging to Lake MichiganUJ
                                                                      PCB Load
gTP Location                     Flow (mgd) *            pPCBJ (ppb) **     (Ib/day)
Waukegan                             0.002               2.635          .00004
North Chicago Plant                  1.2                 0.831          .0083
    Total                           1.202                             0.00834

    PCB Load = 8.34 x 10~3 Ib/day = 3.04 Ib/yr.
*  Data for 1975
** Data for 1971
NOTE:     A major potential source of PCBs released to Lake Michigan has been
identified in Waukegan, Illinois.     An industrial plant located approximately
one mile from Lake Michigan used PCBs in die casting machines for about 20 years,
closing in 1972 when PCBs were no longer  available in Monsanto.   Direct dis-
charges -from this plant occurred into the Waukegan Harbor and into a unnamed ditch

(a)  Great Lakes Surveillance Branch, PCB's in the Bottom Sediments of Waukegan
    Harbor, Waukegan,  Illinois - sample!;  May 12, 1976  and June  9,  1976.
    U.S.E.PVA: Region  V.
                                    E-3

-------
discharging directly into Lake Michigan.  Quantitative estimates of the fate of
the PCBs used in this plant are speculative, but more than 100,000 Ibs. of PCBs
may have been discharged by this plant into drainage ditches and sewers(a).  High
levels of PCBs have been found in the sediments of the harbor,  the ditch,  and of
the Waukegan River which drains into Lake Michigan just south of the harbor.

          Recent measurements of FOB concentrations in the sediment of Waukegan
Harbor vary from 4200 rag/kg at the upper end of the harbor near the industrial
discharge point to 11 mgAg at the lower end of the harbor. ^   Concentrations
of PCBs in the connecting channel sediments are 1 to 3 mg/kg/ 2nd t^6 concentra-
tion of PCBs in the sediment off the end of the piers was measured at 0.1  mg/kg-
There is little water flow through this harbor, the drainage area being no more
than a few times the water area of the harbor.  The high gradient in concentra-
tions of PCBs from the upper to the lower end of the harbor is  consistent  with
the hypothesis that PCBs are strongly bound to the sediments and that the  sedi-
ments, when undisturbed, provide a reliable sink for the PCBs.   (Note:  rapid
exchange of PCBs between the sediment and overlying water would be expected to
be reversible.  This would result in a fairly even concentration of PCBs through-
out the harbor due to diffusion, since water flows through the  harbor but  sus-
pended solids settle rapidly at the upper end of the harbor).

          Although it is not directly connected to the drainage area of the in-
dustrial plant that released PCBs to the Waukegan Harbor, the Waukegan River also
has been noted as  having appreciable levels of PCBs in the sediments and  water.
It has been estimated ^'  that the concentration of PCBs in Waukegan River water
(a)   Great Lakes Surveillance Branch,  PCB's in the Bottom Sediments of Waukegan
     Harbor, Waukegan,  Illinois - sampled;   May 12, 1976 and June 9, 1976.
     U.S.E.P.A.   Region V.
(b)   Robert a. Schacht, Pesticides in  the Illinois Waters of Lake Michigan,  EPA
     Report 660/3-74-002, Jan.,  1974.   See particularily Table 7 of this report.
                                     E-4

-------
showed a maximum of about 2.6ppb (total of 1242 and 1254) in 1971.  If the vital
parameters of the river are taken to be  ^cl
                 Drainage area 9.68 mi2
                 Annual rainfall runoff 10"/yr.
Then the total outfall of water per year from the Waukegan River into the lake
was:
         QUVyr) = 9.68 (mi*) x (5.28xl03)2 (ft2/mi2)  x j§-[^ft)
                         X62.4 lb/ft3
                  = 1.4 x 1010 (Ibs/yr)
Therefore, in terms of the reported maximum PCB concentration ^) , the total
input of PCBs to Lake Michigan during 1971 from the Waukegan River was on the
order of 36.5 Ibs.  Clearly, this contribution is not trivial, but on the other
hand is small compared to the other input of PCBs that are discussed above.

          The fact that so small a portion of the PCBs that are available within
the sediments are actually found in the overlying waters seems to bear out the
often repeated conclusion of this paper that such materials that  are contained
within the sediments are probably "removed" frcm further participation in biolog-
ical processes.

          The third possible source of PCBs to Lake Michigan in the Waukegan
area is a drainage ditch which runs from the PCB using plant directly with Lake
Michigan north of Waukegan harbor.  This ditch is about ten feet  wide and three
feet deep  and carries storm sewer runoff from part of the city of Waukegan.  In
addition, this ditch received the floor drainage from one half of the PCB using
plant during the years that PCBs were used.  The sediments in this ditch have
been found to contain PCBs at a concentration greater than that in the sediments
 (b)  Robert A. Schacht, Pesticides in the Illinois Waters of Lake Michigan, EPA
     report 660/3-74-002, Jan., 1974.  See particularily Table 7 of this report.
 (c)  Private communication frcm Ms.  Lathrop, U.S. Geological Survey, Reston, Va.
                                      E-5

-------
in Waukegan Harbor.  However, because of the scouring action of occasional heavy
flows in this ditch, much contaminated sediment may have been carried into Lake
Michigan.  Measurements of PCB levels in the lake sediments show elevated concen-
trations of PCBs around and particularly south of Waukegan (See Figure E-l).  Tliis
would be the pattern expected if occasional flows of heavy PCB-contaminated sedi-
ments were  carried into the lake by storm water runoff.  The fact that the PCB
oontamination of the lake sediments is found to be still fairly localized six years
after PCBs use has stopped, suggests that the PCBs are fairly immobilized in the
sediments.  However, since no good estimates of PCB in flow to the lake from the
drainage ditch are available, the figures we have used as the basis for total PCB
inputs to Lake Michigan must be judged  on the basis of reasonableness, and must
be considered as subject to possible major revision as more data becomes available.
                                      E-6

-------
                                    Table E-3
                    Concentration of  PCBs in Michigan Streams
                        Tributary to  Lake Michigan(2'3f4)
  Stream
St.  Joseph
Kalamazoo
Grand
Muskegon
Manistee
Boardman
Elk
Portage
    TOTAL
PCS
ppb; mean 1971-72)
0.013
0.065
0.041
0.010
0.014
0.017
0.012
0.47*
Stream
Discharge
(CFS)
4,204
2,162
5,814
2,489
2,047
187
575
18
17,478
(1974)
(M3D)
2,716
1,397
3,756
1,608
1,322
121
371
12
11,291
PCBs
Ib/day Uo/yr
0.29 105.9
0.75
1.28
0.13
0.15
0.02
0.04
0.045
275.1
466.5
47.5
54.8
7.3
14.6
16.5
988.2
    *Qne-tiire measurement taken in  1972.
                                      E-7

-------
                                    Table  E-4
                        PCBs Entering Lake Michigan From
                      Known Industrial and STP Discharges*

  State                        PCB Load  (Ib/yr)                      Source
Michigan                            217.2                              STPs
Wisconsin                          1170.1                           Industries
Wisconsin                           130.3                              STPs
Indiana                             122.3.                              STPs
Illinois                              3.1                              STPs
      Total                        1643
*See Tables E-5 - E-9 for tabulations of the individual waste discharges.
                                    E-8

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                                 TABLE E-5



                     Concentration of PCBs in Paported
Michiaan STP
STP location
Albion
Battle Creek
Benton Harbor,
St. Joseph Plant
Menominee
Muskegon
Niles'
Portage
East Lansing
Escanaba
Holland
Jackson
Kalamazoo
Lansing
Effluents Tributary
Design Flow
(MGD, 1974)
4,0
22.0
13.0
1.2
10.0
10.0
3.6
8.5
2.2
4.5
20.0
34.0
34.0
to Lake Michiaan u''/;
[PCS]
(ppb, 1971-72)
0.44
0.39
0.65
0.35
0.28
0.68
1.9
0.5
0.29
0.6
<0.1
0.66
0.18
PCB Load
(Ib/day)
0.015
0.017
0.070
0.004
0.023
0.056
0.057
0.035
0.005
0.022

0.186
0.051
   Total                      147.0*                                   0.595*





   PCB Load = 0.595 Ib/day = 217.2 Ib/yr.
Total does  not include flows with [PCB]  <0.1 ppb.
                                   E-9

-------
                                   TABLE E-  6
Paper Plant Effluents
Plant
Badger Paper Mills
Soott Paper
Marinette
Ooonto Falls
Shawano Paper
John Strange Paper
Bergstrcm Paper
Kimberly Clark
Thilniany Paper
Fort Howard Paper
Mill Effluent
Dsinking
Deinking & Mill Effluent
Merican Can
Sulfite Sewer
Paper Mill lagoon
Charmin Paper
Green Bay Packaging
Discharqinq to
Flow (ragd)
4.78

5.91
11.03
2.43
1.11
5.22
4.30
25.1

7.3
11.04
18.1

2.23
10.35
16.3
1.77
Green Bay (1974-75) ^
[PCB] (ppb)
<.l

<.l
<.l
<.l
4.00
28.40
0.28
<.l

2,60
6.40
7.07

0.1
0.14
0.14
0.45
>;
PCB Load
(Ib/day)

-
-
-
0.037
1.26
0.010
-

0.158
0.586
1.06

0.002
0.012
0.019
0.006
     Total*                           77.65                              3.15






     PCB  load =3.15 Ib/day = 1,150 Ib/yr.
* Total does  not include flows with [PCB]  <0.1 ppb.
                                     E-10

-------
                                    TABLE E- 7
                   Concentration of PCBs in Reported Wisconsin
        Miscellaneous Industrial Effluents Discharged to Lake Michigan
        Plant
MDtor Casting Go.
Grey Iron Foundry, Inc.
Howmett, Corp. - Crucible Steel
Maynard Steel Casting Corp.
Milwaukee Solvay Coke Co.
Briggs & Stratton
Wshr Steel Co.
EST Co.
Milwaukee Die Casting Co.
Msta-MDld Daton Malleable Inc.
Babcock & Wilccx Co.
   Tubular Products Div.
     Total**
Flow  (nvgd)
  0.22
  0.339
  0.796
  0.133
  4.3
  1.523
  0.228
  0..069
  0.012*
  0.033*
[PCS] (ppb)
  <0.2
                                    (5)
PCS Load
(Ib/day)
  <0.2
  <0.1
   2.95
  32.2
 170.3

   0.9
 0.001
 0.003
 0.047
     PCB load = 0.055 Ib/day =20.1  Ib/yr.
 *   Average of two readings.
 **  Total does not include flows with [PCB]<0.1 ppb.
                                       E-ll

-------
 * Total does not include flows with [PCB]<0.1 ppb.
                                     TABLE E-8

                   Concentration of PCBs in reported Wisconsin  (c.}
                STP Effluents  Discharged to Green Bay  (1974-75)(  '

                                                                        PCB Load
    STP Location                    Flow (mgd)          [PCB] (ppb)
Marinette
Portage
Oshkosh
Neenak-Manash
Appleton
Kaukauna
DePere
.Green Bay
Kewaunee
Two Rivers
Manitowoc
Sheboygan
Port Washington
Milwaukee  (South Shore)
Milwaukee  (S. Milwaukee)
Racine
Kenosha
     Total                           119.8*                               0.357*

     PCB load = 0.357  Ib/day = 130.3 Ib/yr.
2.5
0.736
8.49
12.75
11.05
1.25
23.45
30.64
0.315
2.28
9.3
11.04
1.59
66.7
2.42
16.92
18.88
<0.1
5.0
0.1
0.16
0.12
<0.1
0.5
<0.1
0.18
0.2
<0.1
1.1
0.2
0.29
0.12
<0 . 1
<0.1

0.031
0.007
0.017
0.011

0.01

0.001
0.004

0.11
0.003
0.160
0.003


                                     E-12

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                                     TABLE E-9
STP Location
Michigan City
Valparaiso
Hobart
Hammond
East Chicago
Chestertown
Gary
South Bend
Mishawaka
Elkhart
Goshen
Nappanee
Kendallville
La Grange
Iiigonier
Angola
Syracuse
     Total*
bTP Etfluents Tributary to
Flow (rngd)
12.2
4.0
2.9
42.6
18.7
1.6
50.5
35.8
10.39
17.5
4.8
0.9
1.2
0.185
0.434
0.784
0.305
Lake Michigan
[PCB] (ppb)
1.32
0.24
0.23
<0.1
0.1
<0.1
0.38
<0.1
0.13
<0.1
<0.1
<0.1
<0.1
<0.1
<0.1
0.17
0.13
PCB Load
(Ib/day)
0.134
0.008
0.006

0.016

0.159

0.011






0.001
0.0003
99.8
0.335
     PCB load = 0.335  Us/day = 122.3 Ib/yr.
* Total does not include  flows with [PCBl <0.1 ppb.
                                     E-13

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                                    TABLE E-10
                  Lake Michigan Basin Hydrology (7'8'9'10'
Total mean river discharge (1974)  of the 4 states (Michigan,  Illinois,
Wisconsin, and Indiana)  into Lake Michigan = 34,508 cfs
                                           = 1.1 x 1012 cf/yr
Total flow of water in the basin               =9.4 billion gpd
     Flew diverted from Lake to Chicago        = 2 billion gpd
     Flow diverted through Straits of Mackinac = 67,000 cfs
     Other withdrawal's from the Lake          = 11.7 mgd
     Volume of STP effluents entering Lake:
                                from Illinois  =27.6 mgd
                                 from Indiana  = 110.5 mgd
                                from Michigan  = 161.6 mgd
                               from Wisconsin  = 183.4 mgd
                                     E-14

-------
                                  TABLE E-ll
                                                                 (12)
           Estimates of Fish Bicmass  in Lake Michigan  (1972-73)

  Michigan Waters of Lake Michigan - 11.2 x 10  Ib. of lake trout
                                      (age group II & older); 1972
            Northern Lake Michigan  - 55 x 10  Ib. of whitefish
                                      (age groups I-VI); 1972
    From bottom trawls of the Lake  - 220 x 10  Ib. of alewife
                                      (age groups I & over); 1973
                                    - 15 x 106 Ib. of chubs
                                      (age groups I & over); 1973

                   Total  (1972-73)  - 3x 108 Ib.
a.  Lake trout (from Michigan waters of the Lake)       - 11.2 x 106 Ib (1972)
b.  Whitefish (in Northern Lake Michigan)               - 55 x 10s Ib (1972)
c.  Chubs (those available to bottom trawls)            - 15 x 10s Ib (1973)
      (note:  decline in chubs from 139 x 10s Ib
              in 1963-65)
d.  Alewives (those available to bottom trawls +
              estimate of the midwater individuals)     - 2 x 109 Ib (1973)
e.  Coho Salmon (estimate based on the number stocked)  - 7.6 x 10s Ib (1972)
                          Total                         - 2.1 x 109 Ib (1972-73)

    Estimates for the Plankton Biomass:
    a.  Assume 300 kg plankton/hectare of lake
    b.  Area of Lake = 22,400 mi2 = 5.8 x 106 hectares (13)
    c.  Plankton biomass = (5.8 x 106) (300 kg) = 1.74 x 1012 g = 3.8 x 109 Ib

    In addition, the relatively polluted nature of the southernmost portion of
the Lake results in large masses of benthic species, such as tubiflex worms.
In view of this, it is assumed that the benthic biomass is of the order of
4 x 109 Ibs.

                                      E-15

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Vcrsai:
             inc.
                             TABLE E-12
                   Representative PCB Measurement
                               Biota

   a.  PCB in fish  (alewives,  smelt, slimy sculpin)        = 2.35 - 5.13 x 106  ppt
   b.  PCB in water (total cone, dissolved + particulate)  = 55 ppt
   c.  Average PCB in sediments                           = 1.2 x 10s ppt
   d.  Average PCB in wet plankton                        = 7.2 x 106 ppt
   e.  .PCB in the benthos                                = 4.7 x 10s ppt
                                  E-16

-------
APPENDIX E REFERENCES

 1.   Schacht,  P..A.;  Pesticides in the Illinois Waters of Lake Michigan,  EPA
     660/3-74-002, U.S. Environmental Protection Agency, Jan., 1974.

 2.   State of Michigan Water Resources Commission, Bureau of Water Management,
     Polychlorinated Biphenyl Survey of the Kalamazoo River and Portage  Creek
     in the Vicinity of  the City of Kalamazoo 1972.

 3.   Hesse, J.L.;  Status  Report on Polychlorinated Biphenyls in Michigan
     Waters.  Report to Michigan Water Resources Commission, 1973.

 4.   State of Michigan Water Resources Commission, Bureau of Water Management,
     Monitoring for Polychlorinated Biphenyls in the Aquatic Environment.
     Report to Lake Michigan Toxic Substances Committee, May, 1973.

 5.   Kleinert, Stan; Chief of Water Quality Surveillance Section,  ENR Wisconsin,
     Personal Communication, 1975.

 6.   Winters,  John;  Acting Chief of Water Quality and Standards Branch of
     Illinois EPA, Personal Connunication, 1975.

 7.   United States Geological Survey, Water Resources Data for Michigan.
     Part 1.  Surface Water Records, 1974.

 8.   United States  Geological Survey, Water Resources Data for Wisconsin.
     Part 1.  Surface Water Records, 1974.

 9.   United States Geological Survey, Water Resources Data for Illinois.
     Part 1.  Surface Water Records, 1974.

10.   United States Geological Survey, Water Resources Data for Indiana.
     Part 1.  Surface Water Records, 1974.

11.   Saylor, J.H., P.W. Sloss; Water Volume Transport and Oscillatory Current
     Flow through the Straits of Mackinac.  (Contribution No. 38,  Great  Lakes
     Environmental Research Laboratory),   1957.

12.   Michigan  Department  of Natural Resources  Fisheries  Division, Estimates
     of Biomass of Principal Fish Species in the Great Lakes (first report).
     Fisheries Research Report No. 1813,  1974.

13.   The Lake Michigan Federation, "The Lake Michigan Basin", March, 1975.

14.   National Water Quality Inventory,  "Report to the Congress.  Vol.  II",
     EPA-440/9-74-001. USEPA, 1974
                                      E-17

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REFERENCES

-------
     The literature resulting from analytical measurements on a wide variety of
biological and geological specimens has become very large.  The following list,
while in no sense complete, represents those sources used in this work.
 (1)  Addison, R.F., S.R. Kerr, J. Dale, and D.E. Sergeant, J. Fish Res. Board
     Can., 30, 595, 1973.                                  	
     Anonymous, "Chemicals Found in Lake Fish:  State PCB Ban Urged."  Michigan
     Out-of-Doors, July, 1975.
     Bailey, S., P.J. Buryan, and F.B. Fishwick.  Chemistry and Industry 22:
     705, 1970.	
     Bowes, G.W. and C. Jonkel, in PCS in the Environment, Marcel Dekker Inc.,
     New York, 1974.
     Carey, A.E., G.B. Weirsma, H. Tai, and W.G. Mitchell.  Pesticides
     Monitoring Journal 6  (4):  369-376, 1973.
     Crump-Weisner, H.J., H.R. Feltz, and M.L. Yates.  Pesticides Monitoring
     Journal 8(3);  157-161,1974.
     Doguchi, M., New Methods in Environmental Chemistry and Toxicology.
     Proceedings of the International Symposium, Susono, Japan, 1973;
     Coulston, F., Kbrte, F., and Goto, M., Eds., International Academic
     Printing Co., Tokyo, Japan, 1973.
     Duke, T.W., J.I. Lowe, and A.J. Wilson, Jr.  Bulletin of Environmental
     Contamination and Toxicology; 5(2):  171-180, 1970.
     Edwards, R.  "Polychlorinated Biphenyls, Their Occurence and Significance:
     A Review."  Chemistry and Industry  (No Volume) Issue 47: 1340-8
      (21 November, 71), 1971.
     Fog, M., and I. Kraul, Acta Vet. Scand., 14, 350, 1973.
     Frank, R., K. Ronald, and H.E. Braun, J. Fish Res. Board Can., 30, 1053,
     1973.
     Giam, C.S., M.K. Wong, A.R. Hanks, and W.M. Sackett, Bull. Environ.
     Contam. Toxicol., 9, 376, 1973.
     Greichus, Y.A., A. Greichus, and R.J. Emerick, Bull. Environ. Contam.
     Toxicol., 9, 321, 1973.
     Gustafson, C.G., Environmental Science and Technology 4(10); 814-819, 1970.
     Harvey, G.R., H.P. Mlklas, V.T. Bowen, and W.G. Steinhauer.  Journal of
     Marine Research 32(2); 103-118, 1974.
     Heppleston, P.B., Mar. Pollut. Bull., 4, 44, 1973.
     Hidaka, K., T. Ohe, and K. Fujiwara, Shokuhin Eiseigaku Zasshi, 13, 523,
     1972: C.A., 79, 028100, 1973.
     Huschenbeth, E., Schr. Ver. Wasser-, Boden-, Lufthyg., Berlin-Dahl, 37,
     103, 1972.

-------
    Horn, W.,  R.W.  Risebrough,  A.  Soutar,  and D.R.  Young.   Science  184  (4142).
    Interdepartmental Task Force on PCBs.  "Polychlorinated Biphenyls  and the
    Environment."   COM-72-10419.   1-192.   National Technical Information
    Service,  Springfield,  Virginia (U.S.  Dept.  of  Agriculture, Comerce,  Health-
    Education and  Welfare, EPA,  and other agencies),  1972.
    Lunde,  G., J.  Gerber,  and B.  Josefsson.   Bulletin of Environmental
    Oontamination  and Toxicolcgy 13 (6):  656-661, 1975.
    Law, L.M., and D.P.  Oberlitz.  Pesticides Monitoring Journal 8(1): 33-36,
    1974.                           	
    Martell,  J.M., D. A. Rickert, and F.R. Siegel. Environmental  Science and
    Technology, 9: 872-75, 1974.
    Oloffs, P.C.,  L.J. Albright,  and S.Y. Szeto.   Canadian Journal of
    Microbiology 18(9);  1393-1398, 1972.
    Oloffs, P.C.,  L.J. Albright,  S.Y. Szeto, and J. Lau.   Journal  of Fisheries
    Research  Board of Canada,  30(11): 1619-1623.
    Panel on  Hazardous Trace Substances.   "Polychlorinated Biphenyls-;
    Environmental  Impact."  Environmental Research 5(3); 249-362.  1972.
    Peel, D.A., Nature,  254: 324-325, 1975.
    Risebrough, R.W., P. Reiche,  D.B. Peakall,  S.G. Harraan, and M.N. Kirven,
    Nature  (12/14): 1098-1102, 1968.
    Risebrough, R.W., and B. deLappe. Environmental  Health Perspectives
    Exp 1:  39-45,  1972.
    Saschenbrecker, P.W.,  Can. J. Comp.  Med., 37,  203, 1973.
    Smith,  W.E., K. Funk,  and M.E. Zabik, J. Fish. Res. Board Can.,  30, 702,
    1973.
    Walker, W.H.,  "Where Have All the Toxic Chemicals Gone?" Ground Water
    11(2):  11-20,  1973.
(2)  Annan., World  Almanac, Washington Star News, Washington, B.C., 1975.
    National  Water Quality Inventory. Report to the  Congress.  Vol. II.
    EPA-440/9-74-001. Office  of  Water Planning and Standards.  Appendices
    C-l to  C-69, D-l  to  D-55,  E-l to E-76.,  1974.
(3)  Bevenue,  A., J.M. Ogata, and J.W. Hylin. Bulletin of  Environmental Con-
    tamination and Toxicology 8(4): 238-241, 1972.
    Bidleman, T.F., and  C.E. Olney.  Science 183  (4142): 516-518.   2nd Copy,
    1974.
                                     F-2

-------
             T.F., and C.E.  Olney.   Bulletin of Environmental Contamination
   and Toxicology 11 (5):  442-450, 19W.	

   Harvey, G.R.,  and W.F.  Steinhauer.  Atmospheric Environment 8(8); 777-782,
   J..7/4*

   Holden, A.V.   Nature 228(12/19);  1220-1221, 1970.

   Sodergren, A.  Nature 236:  395-397, 1972.

   Tarrant, K.R., and  J.O.G. Tatton. Nature 219: 725-727, 1968.

(4) Panel on Hazardous Trace Substances.  Environ. Res., 5, 1972.

(5) Bengston, S.A., Ambio, 3_ No. 2,  p. 84, 1974.

(6) Ruttner, F.,  1952.  Fundamentals of Limnology.  University of Toronto
    Press.  295 p., 1952.

(7) Mackay, D., and A.W. Wolkoff.  Environmental Science and Technology
    7(7):  611-614, 1973.          	

(8) Saylor, J.H., and  P.W. Sloss.  Water Volume Transport and Oscillatory
    Current Flow  Through the Straits of Mackinac.  (Contribution No. 38,
    Great Lakes Environmental  Research Laboratory), 1975.

(9) State of Michigan  Water  Resources Carrmission, Bureau of Water Management.
    Polychlorinated Biphenyl Survey  of the Kalamazoo River and Portage Creek
    in the Vicinity of the City of Kalamazoo, 1972.
    State of Michigan  Water  Resources Commission, Bureau of Water Management.
    Monitoring for Polychlorinated Biphenyls in the Aquatic Environment«.
    Report to Lake Michigan  Toxic Substance Committee, May, 1973.
    Haile, C.L.,  G.D.  Veith, G.F. Lee, and W.C. Boyle, Chlorinated Hydrocarbons
    in the Lake Ontario Ecosystem, 1975.

(10) Follows from  Mean  Value  Theorum; See for example,  "Advanced Calculus,"
    I.S. Sokolnikoff,  McGraw,  1939,  pp. 113ff.

(11) U.S. Dept. Interior, Federal Water Pollution Control Administration, Water
    Pollution Problems of  Lake Michigan and Its Tributaries, January 1968.

(12) Neely, Brock. Personal  oommunication^

(13) Handbook of Physics, E.U.  Condon & H. Odishaw, McGraw-Hill, New York,  1967.
    Section 5-15ff.

(14) Nisbet, Ian.  Personal conntunication.

(15) American Physical  Society  Handbook, 2nd Edition; D.E.  Grey, Ed., McGraw
    Hill, New York, 1963,  Table 2r-3, pp.  2-208.
                                      F-3

-------
(16) Fulk, R.,  D.  Gruber and R.  Wullschleger,  "Laboratory Study of the  Release
    of Pesticide  and PCB Materials to the Water Column During Dredging and
    Disposal Operations/1 under Contract DACW 39-74-C-0142, December 1975.

(17) See Reference (6).

(18) Annon., World Almanac, Washington Star News, Washington,  D.C.,  1975.

    National Water Quality Inventory.  Report to the Congress.  Vol II.
    EPA-440/9-74-001.  Office of Water Planning and Standards.  Appendices
    C-l to C-69,  D-l to D-55, E-l to E-76, 1974.

    Great Lakes Basin Framework Study, Great Lakes Basin Commission, April 11,
    1975.

  (19)  (a)  Dept. of the  Interior and New York Dept. of Health.  "Water Pollution
      Problems  and Improvement  Needs  - lake Ontario and St. Lawrence River Basins,"
      June, 1968.

      (b)  Great Lakes Water Quality Board,  "Great Lakes Water Quality, 1973
      Annual Report  to  the International  Commission," April, 1974.

      (c)  International Lake Erie Water Pollution Board, and the International
      Lake Ontario-St.  Lawrence River Water Pollution Board, "Pollution of Lake
      Erie, Lake Ontario and the International  Section of the St. Lawrence River,"
      Vol. 1,  2, 3 (1969).
      (d)  U.S.  Dept. of Interior, Federal Water Pollution Control Admin., "Water
      Pollution Problems of Lake Michigan and Tributaries," January, 1968.

      (e)  Sly,  P.G.  J.  Fish. Res.  Bd. Cair.,  33_, pp.  335-369, 1976.

      (f)  Kemp, A.,  T.R.  Dell & J.  Jaquet.  J.  Fish. Res. Bd. Cair., 33y 440-
      462, 1976.
      (g)  Gresswell, R.  & A.  Hupler.   "Standard Encyclopedia of World's Rivers and
      Lakes," Putman, New York, 1965.
      (h)  Kemp, A.L., T.W.  Anderson,  R.C. Thomas and A. Mudrochova.  J. of
      SediiTEntary  Rheology,  4£, 207-218 (1972).

  (20) Hague, R., D.W. Schmedding,  and V.H.  Freed.  Environmental Science and
      Technology 8(2);   139-142,1974.

  (21) "Background  to the Regulation of PCBs in Canada,"  Environmental  Contaminants
      Committee of Canada,  April 1, 1976.  Tech. Report 76-1.

  (22) Monsanto, Tech. Bull. 0/PL-306A.

  (23) Obtained from integration of the Clausius - Clapeyron equation assuring
      that the heat of  vaporization is constant.  See,  for example, "Physical
      Chemistry,"  S.  Glasstone, Van Nostrand,  New York,  1946,  pp. 138ff.
                                        F-4

-------
(24)  Hutzixiger, O., S. Safe, and V. Zikto.  "The Chemistry of PCBs."  CRC Press,
     Cleveland, Ohio, 1974.

(25)  Hutzijiger, 0., S. Safe, and V. Zikto.  "The Chemistry of PCBs."  CRC Press,
     Cleveland, Ohio, 1974.

(26)  Hague, R., and D.W. Schmedding.  Bulletin of Environmental Contamination
     and Toxicology 14:  13-18, 1975. ~~~	

(27)  Kennard, E.H.  "Kinetic Theory of Gases," McGraw-Hill, N.Y.,  1938.

(28)  Langmuir, "Phenomena, Atoms and Molecules," Philosophical Library,  N.Y.
     Chapt. 15, 1950.

(29)  Handbook of Physics, E.U. Condon & H. Odishaw, McGraw-Hill, New York, 1967.
     Section 5-15ff.

 (30) American Physical  Society Handbook,  2nd Edition, D.E. Grey, Ed., McGraw-Hill,
     New York,  1963,  Table 2r-3, pp.  2-208.

 (31) Parker,  B. and G.  Barscm.  Bioscience, No.  87  (1970).

 (32) Hutzinger, 0., S.  Safe,  and V.  Zikto.  "The Chemistry of PCBs."  CRC Press,
     Cleveland, Ohio, 1974.

 (33) Bidleman, T.F.,  and C.E.  Olney.  Bulletin of Environmental Contamination
     and Toxicology 11(5) ;  442-450,  19747                                  "

 (34) Zandler, M.E. &  Mu Shik  Jhon.  Ann. Rev. Phys. Cham., 17,373  (1969).

 (35) Branson, D.R., Blau,  G.E., Alexander, H.D., and Neely, W.B.   "Bipconcentration
     of 2,2l4,4l-Tetrachlorobiphenyl in Rainbow Trout as Measured by an Accelerated
     Test," Trans. Anerican Fisheries Society, CIV  (1975), pp.  785-792.

 (36) Willford, Wayne  A., Hesselberg,  Robert J., and Nicholson, Lawrence W.  "Trends
     of Polychlorinated Biphenyls  in Three Lake Michigan Fishes," Conference
     Proceedings  - National Conference on Polychlorinated Biphenyls  (Nov. 19-21,
     1975), Washington, D.C.:EPA, March 1970.


 (37) Hansen,  D.J., Parrish, P.R.,  Lowe, J.I., Wilson, A.J. Jr., and Wilson, P.O.
     "Chronic Toxicity, Uptake, and Retention of Aroclor(R) 1254 in Two Estuarine
     Fishes," Bulletin  of  Environmental Contamination' and Toxicology, VI  (1971) ,
     pp. 113-119.
     Neely, W. Brock.   A Material  Balance Study of Polychlorinated Biphenyls in
     Lake Michigan.   Midland,  Michigan:  Environmental Sciences Research, The
     Dew Chemical Co.
                                      F-5

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(38) Veith,  G.D.   Transcriptions of Hearings, Wisconsin Dept. Natural Resources,
    Madison, Wise.,  August 28,  1975.

(39) Versar, Inc., PCBs in the United States;   Industrial Use and Environmental
    Distribution NTIS PB-252 402/3WP. February 1976. Appendix D.
                                         F-6

-------
BIBLIOGRAPHIC DATA
SHEET
  Tid
                     1. Kcpon No.
                         560/6-77-006
                A First Order Mass Bali
                and Fate of PC
2.
                                              Model for the Sources
7. Author(s)
          Frank C. Whitnore,  Ph.D.
9. Performing Organization Name and Address
          Versar, Inc.
          6621 Electronic Drive
          Springfield, Va.   22151
12. Sponsoring Organization Name and Address
          Office of Toxic  Substances
          U.S.  Environmental Protection Agency
          Washington, D.C.   20460
 15. Supplementary Notes
                                                                       3. Recipient's Accession No
                                                                       5. Report Uutc
                                                                         July 27,  1977
                                                                       6.
                                                                       8. Performing Organization Kept
                                                                         No- 474-5G	
                                                                       10. Projecr/Task/Work Unit No.
                                                                         Task  5
                                                                       11. Contract/Grant No

                                                                         68-01-3259
                                                                       13. Type of Report & Period
                                                                          Covered
                                                                       Final Task Report
                                                                       14.
          Project Officer:  Thomas Kopp
16. Abstracts
           A first order model for the sources, distribution and fate of PCBs  n an
                           is described.  The model  is then applied to Lake Michigan
           and to the Great Lakes Systems.  The results obtained from the model
           indicate that atmospheric sources are a  major PCB input to the Great
           Lakes.  Because of the great water mass  of the lakes, the PCB concentrat
           appears to be storage controlled rather  than loss controlled.  The
           major loss laechanisms are found to be co-evaporation from the air-
           water interface and entrapment with sediments.  If is estimated that  if
           all inputs or PCBs rate lake Michigan were eliminated,  it would take  mon
           than 70 years for the concentration of PCBs in the water to decrease  by
           50
17. Key 'iords and Document Analysis.  I7a. Descriptors

   Polychlorinated  Biphenyls
                                                     Environmental Transport
   Water Chemistry
   Sediment Water Interactions
   Bioaccumulation
   Adsorption
   Air Pollution
   Atmospheric Models
                                                     Precipitation Washout
   Water Pollution
I7b, Identifiers/Open-Ended Terms
I7c. COSATI Field/Group
18. Availability Statement
           Pel
                   Unlimited
FORM NTis-39 (Rev. 10-73)  ENDORSED BY ANSI AND UNESCO.
                                                           19.. Security Class (This
                                                             Report)
                                                           	UNCLASSIFIED
                                                           20. Security Class (This
                                                              Page
                                                                UNCLASSIFIED
                                                    THIS FOKM MAY UK R EIJ ROD U C E D
                           21. No. of Pages

                               180
                                                                                 22. Price
                                                                                  U3COMM-OC

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