United States
Environmental Protection
Agency
Environmental Research
Laboratory
Duluth MN 55804
Research and Development
EPA-600/S3-84-050 May 1984
Project Summary
Physico-Chemical Model of
Toxic Substances in the
Great Lakes
Robert V. Thomann and Dominic M. Di Toro
A physico-chemical model of the fate
of toxic substances in the Great Lakes
is constructed from mass balance prin-
ciples and incorporates principal
mechanisms of particulate sorption-
desorption, sediment-water and atmo-
sphere-water interactions, and chemical
and biochemical decay. Calibration of
the toxic model is through comparison
to plutonium-239 data collected in the
1970's using a 23-year time variable
calculation and indicates that in general,
the sediments are interactive with the
water column in the Great Lakes
through resuspension and/or horizontal
transport. Fifty percent response times
of 239Pu following a cessation of load ex-
tend beyond 10 years with sediment
resuspension.
The calibrated model was applied to
polychlorinated biphenyl (PCB) using a
high and low estimate of contemporary
external load and with and without vola-
tilization. The results of the application
using a 20-year calculation indicate that
a load level ranging from 640 to 1390
kg/yr with volatilization (at an exchange
rate of 0.1 m/d) appears to be represen-
tative of observed surface sediment
data for the open lake waters. Fifty per-
cent response times for PCB following
cessation of load and including vola-
tilization varied from less than 5 years
to 10-20 years for the other lakes without
volatilization. Comparison of these re-
sponse times to decline of concentra-
tions of PCB in Lake Michigan indicates
that at least for that lake volatilization
is occurring at an exchange rate of
about 0.1 m/d.
Calculation using a solids-dependent
partition coefficient for PCB indicate
that the total and dissolved PCB concen-
tration in the water column and sedi-
ment PCB concentration are affected to
less than an order of magnitude. In-
terstitial PCB concentration however in-
creases by about two orders of
magnitude over the case with a solids-
independent partition coefficient.
Higher exposure concentrations to ben-
thic organisms may then result with a
potential route of PCBs to the top
predators in the food chain.
Calibration of the model to data on
benzo(a) pyrene confirms that on a lake-
wide scale the principal external source
in the atmosphere and for the larger
lakes such as Michigan the response
time of the lake to external loads is
about 6-10 years while for Lake Erie
response time is about 2 years.
Application of the model is cadmium
in the lakes, using a solids-dependent
partition coefficient, indicates that the
lakes do not reach equilibrium over a
100-year period. For constant partition-
ing, cadmium concentrations reach
steady state in about 10-25 years. An
estimate of the preceding 50-year aver-
age cadmium input ranges from 200-600
g Cd/km2-yr for the upper lakes to
2000-10,000 g Cd/km2-yr for Lake Erie.
Calculated high concentrations of cad-
mium in interstitial water (e.g. 10/ig/l)
indicate the importance of measuring in-
terstitial cadmium concentrations.
This Project Summary was developed
by EPA's Environmental Research Labo-
ratory, Duluth, MN, to announce key
findings of the research project that is
fully documented in a separate report of
the same title (see Project Report order-
ing information at back).
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Introduction
There is an intense contemporary interest
in the impact of toxic substances on
legitimate water uses in the Great Lakes.
Chemicals such as the PCBs and mirex in
Lakes Michigan and Ontario, have resulted
in the curtailment of recreational fishing ac-
tivities. Furthermore, there is a growing con-
cern for the effect of the presence of
potentially toxic chemicals on the public
health of the Great Lakes basin population.
Because of these concerns, a variety of
questions are raised regarding the possible
recovery times of the Great Lakes following
the reduction or elimination of external in-
puts. In addition, interest in the fate of new
chemicals that may be discharged to the
lakes indicates a need to develop a model-
ing framework that can provide a basis for
projecting the fate of such chemicals in the
water and sediment of Great Lakes.
This report presents the results of the
development and calibration of a physico-
chemical model for the Great Lakes. The
report begins with the basic theory of the
model, the associated model equations and
useful simplifications of the model. A steady
state version of the model is then applied to
a two-dimensional representation of Sagi-
naw Bay PCB distribution. Plutonium-239 is
used as a calibrating variable for the Great
Lakes time variable model. Further applica-
tion is then made to the PCBs in the Lake
system and the importance of solids depen-
dent partition coefficient and resulting sedi-
ment diffusion is then explored. Finally,
application of the model is also made to ben-
zoia) pyrene and cadmium in the Great
Lakes.
Theory
Suspended Solids Model
Since many chemicals, such as PCBs,
sorb to suspended particulate matter, the
first step in the development of the overall
model is the mass balance of suspended
solids. In this work, a single class of solids
is considered and is intended to incorporate
inorganic solids and organic particulates. The
solids are considered at steady state in the
water column and sediment. The model does
not directly include horizontal transport of
the bed sediment. At steady state, the water
column solids for a completely mixed lake
is given by
WMa
Wn =
Wa Ws
m =
q +wn
(1)
where m is solids concentration (mg/£), WMo
is the areai loading rate of solids (g/m2-yr),
q is the ratio of lake flow Q(m3/s) to volume
V(m3) (m/yr), and wn is the net loss of solids
from the water column (m/yr) given by
Wrs+Ws
where wa is the settling velocity (m/yr), wrs
is the resuspension velocity (cm/yr) which
parametizes sediment/water interactions,
and ws is the net effective sedimentation
velocity (m/yr), given by
wn M
ws = ,„,
PS (1-0) (3)
forf, as the density of the solids (g/cm3) and
the porosity of the sediment. All of the
above relationships apply in principle to a
multi-dimensional model where additional
terms for dispersion and advection must be
included. The model incorporates these
terms.
Toxic Substances Model
The theoretical construct for the physical-
chemical fate of a toxic substance in the
Great Lakes includes the following features:
1. sorption-desorption mechanism of the
chemical with the suspended particulates in
the water column and sediment,
2. loss of the chemical due to mechanisms
such as biodegradation, volatilization,
chemical and biochemical reactions, and
photolysis,
3. transport of the toxicant due to advec-
tive flow transport, dispersion and mixing,
4. settling and resuspension of particulates
and diffusive exchange between sediment
and water column, and
5. direct inclusion of external inputs that
may be subject to environmental control.
Although the computational framework is
multi-dimensional, the basic equations can
be readily seen for a single completely mixed
lake, where the mass balance for the total
toxicant is given by
V dc-r/dt = WT - Q CT - Wa fp CT
+ wrs fps CTS + KLA (fds CTS/^S - fd CT/)
-KVcr+k,, A(cg/He-fdCT/) (4)
This equation is derived on the assumption
that all sorption-desorption kinetics are
"fast," linear and reversible. In Equation (4),
the subscript "s" indicates the sediment, the
total toxicant is CT (^g/^(bulk)) given by
cT = Cp + cd (5)
where cd is the porosity corrected dissolved
concentration (^g/C(bulk)) and cp is the par-
ticulate form of the toxicant (jug/Hbulk)) and
is given by
cp= rm (6)
for r as the toxicant sorbed to the solids
(^g/g(d); g(d) = grams dry weight).
Also in Equation (4), WT is the external
input of the chemical (kg/yr), A is the sur-
face (sediment) area (km2), KL is the sedi-
ment water diffusive transfer coefficient
(m/d), k( is the volatilization transfer coef-
ficient (m/d), cg is the toxicant concentra-
tion in the atmosphere overlying the water
(ng/m3), H« is the Henry's constant, i.e., the
partitioning between the gaseous and
aqueous phase, K is an overall loss rate (d"1)
given by
K = Kd fd + Kp fp (7)
and fd and fp are the fraction of the total in
the dissolved and particulate forms respec-
tively and are determined from
fd = (1 - TT-'Mf (8a)
TT'M
fp -
1+TT'M
(8b)
In these latter equations, n' is the porosity
corrected partition coefficient (I /kg) given
by
IT' = r/cd . (9)
The equation for the total toxicant in the sur-
face sediment segment is
dcrs . , . ,
Vs ^— = Wa A fp CT - Wrs A fps CTs
+ KLA(fd CT/0 - fds CTs/*s)
- Ws A CTS - Ks Vs CTs
(10)
where
KS = Kds fds "*" Kps fps- (11)
Similar equations are written for sediment
segments below the surface sediment layer.
The report explores these equations and
also the simplifying case of the steady state
condition where basic relationships between
external chemical loading and resulting
chemical concentrations in the lake can be
derived as a basis for allocation of chemical
loading.
Model Calibration
The time scale of the model is considered
to be long term, i.e., year to year. The
physical segmentation of the model con-
siders the Lakes to be completely mixed with
the exception of Lake Erie (Figure 1). This
Lake is divided into three basins; west, cen-
tral, and east to reflect varying regions of
solids deposition and water column solids
concentrations. In addition, Saginaw Bay is
included as a separate embayment from Lake
Huron to represent a more local region in-
teracting with a large lake. Three sediment
segments of 2 cm each in depth are included
under each of the lakes or region of lake.
This results in a model with eight water col-
umn segments and 24 sediment segments
totaling 32 segments.
The calibration procedure was as follows:
(a) From a review of data on fine grain solids
loading to the Lakes, net depositional flux
of solids, and water column suspended
solids concentrations. Equation (1) was used
to provide first estimates of wn, the net loss
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N
Sediment
Segmentation
Lake Michigan
Lake Erie
0 50 100
Statute Miles
Figure 1. Great Lakes and Sagmaw Bay and sediment segmentation used in model.
rate of solids from the water column. From
assigned porosity in the surface sediment
layer, particle density and net flux of solids
to the sediment, the net sedimentation rate
is computed from Equation (3); (b) With the
estimate of the net loss of solids, wn, a range
of particle settling velocities were assigned
and the resuspension velocity necessary to
maintain the solids balance was computed
from Equation (2) as
wr, = w. ( — - 1) .
Wn
(c) Since there are an infinite number of
combinations of settling and resuspension
velocities that will result in the same solids
balance, the time variable plutonium-239
model was numerically solved to provide the
tracer calibration. All decay mechanisms and
sediment diffusion were assumed to be zero
and a sensitivity analysis using three values
of plutonium solids partitioning was con-
ducted.
Figure 2 shows the results of the plu-
tonium calibration under different conditions
on particulate settling (for w0 = w,«,,
resuspension is zero). The calibration is not
favorable for the case of no resuspension
and is improved by including the resuspen-
sion parameter. No significant difference was
noted between 2.5 and 5 m/d. Additional
sensitivity analysis discussed in the full report
supported the conclusion that some interac-
tion of the sediment with the water column
is occurring in the Lake system.
PCB Mass Balance
The range of contemporary (i.e., approxi-
mately within the past 5-10 years) external
total PCB loads to the Great Lakes was
estimated at a high and low load level. The
estimated ranges of PCB loads incorporate
three components: the atmospheric input,
tributary loads and direct point source inputs
from municipal and industrial sources.
Rather than attempt to describe each of
these components in detail and recognizing
the wide variability in some of the reported
data, a range of concentrations or loading
rates was applied. The computations were
then made at two load levels (high and low)
and with and without volatilization. A con-
stant partition coefficient of 100,000 t /kg
was used throughout and a volatilization ex-
change coefficient of 0.1 m/d was
estimated.
The results of the four conditions (high
and low load levels, with and without
volatilization) after running the preceding
calibrated model with zero initial conditions
for 20 years to approximate steady state, are
shown in Figures 3 and 4. Comparison to the
limited water column and sediment data in-
dicates that the upper load level without
volatilization overestimates the data in the
open lake waters. The effect of volatilization
of PCB as indicated in Figure 3 is to reduce
the steady state water column concentration
by 50-70% except for Lake Erie where the
reduction due to volatilization is about 30%.
This reflects the higher fraction of PCB in the
particulate phase for Lake Erie due to the
higher solids concentration. The inclusion of
volatilization also has a significant effect on
the time to reach equilibrium. For example,
for Lake Michigan at the upper level of
loading without volatilization, the time to
equilibrium in the water column is greater
than 20 years in contrast to less than 10 years
when volatilization is included.
Plutonium and PCB
Response Times
Simulations were made of the response of
the Great Lakes system to an instantaneous
elimination of the external load using the
preceding model. For plutonium, the results
indicated that the time to reduce the con-
centration by 50% is less than 5 years when
resuspension is not included but increase by
about an order of magnitude under resus-
pension is incorporated. For PCB, the effect
of volatilization in the 50% response time (in-
cluding resuspension) was investigated and,
as an example, it was calculated that for
Lake Michigan the response time varies from
15-20 years without volatilization to 1-2 years
with volatilization.
Effect of Solids Dependent
Partitioning and Sediment
Diffusion
An evaluation was made of the sensitivi-
ty of the model to a hypothesized depen-
dence of the partition coefficient on the
solids concentration. For plutonium, the
results showed that settling velocities of
2.5-5.0 m/d with or without solids-depen-
dent partitioning provide an approximately
equal representation of the observed data.
For PCB, a compilation of published data in-
dicated that the PCB partition coefficient did
exhibit a marked dependence on the solids
concentration at levels of less than 1 ng/£
to sediment solids concentrations.
Two cases of solids dependent partition-
ing of PCBs were therefore examined:
a) 7i = 73,990 M- 435, and
b) n = 25,120 M-' 2 for solids < 10 ng/f
n = 73,900 M- 435 for solids > 10 ng/f.
The calculations indicated that the total
and dissolved water PCB concentrations are
not sensitive in a significant way to the
assumption on partitioning. The principal ef-
fect on the dissolved component is in
Western Lake Erie where the dissolved con-
centration increases by a factor of three. In
all other lakes, however, for practical pur-
poses, the total and dissolved concentrations
are unaffected by the partitioning assump-
tion including the case of a constant solids-
independent partition coefficient. The sur-
-------
j n
1 .U
is
<3
3
f
1 0.5
n
\ Superior
\
\
\ ?
^^ \ ^
•">* . 4 « "v, a
T o"
I rt n K
J. N U.o
\ Michigan
\
\
_ \
\
^^"M^ AT ii 'jj* ^
T T T T
III
1 1 1 1 1 1
1971 72 73 74 75 76 77 1971 72 73 74 75 76 77
Year Year
1.0
0.5
Huron
M
-*-
^ = IVne,
-2.5 m/d
= 5.0 m/rf
_J I 1 1
1971 72 73 74 75 76 77
Year
Ontario
s = Sept.
A = Aug.
1971 72 73 74 75 76 77 1971 72 73 74 75 76 77
Figure 2. Comparison of calculated 239'240pt/ concentration {fC, /I) in the water column for all
lakes to 1971-1977 data for three conditions of the paniculate settling velocity.
n = 400,000 I/kg.
face sediment concentration was also not
markedly affected (to order of magnitude)
by the partitioning assumption, although a
decline of about 50% is evident in the lake
sediment and a decline of about 70% is
calculated for the surface sediment of
Saginaw Bay.
These reductions in sediment PCB par-
ticulate concentration reflect the assumed
reduced partitioning at the high solids con-
centrations and are, therefore, subsequently
reflected in the PCB concentration of the in-
terstitial water of the surface sediment. It is
in the interstitial water that the effect of the
solids-dependent partitioning was most pro-
nounced. Increases in the dissolved PCB
concentration of about two orders of magni-
tude were calculated.
For Lake Michigan, as an example, the in-
terstitial concentration of PCB as calculated
for a constant partition coefficient is about
0.25 ng/l. For a variable partition coefficient
(Relationship (b) above), the concentration
increases to about 30 r\g/(. Values of pore
water PCB at three stations in southern Lake
Michigan have been reported at levels of 159,
214, and 342 ng/l which is about one order
of magnitude higher than that calculated.
However, the estimate of 30 ng/7 represents
a lake-wide average including regions of
nondeposition. One would, therefore, expect
an observed lake-wide average to be less
than individual core samples.
The calculation on the sensitivity of the
PCB distribution in the Great Lakes to a
sediment-dependent partition coefficient in-
dicated that since the increased interstitial
PCB concentration in the sediment is about
two orders of magnitude higher than the
overlying water dissolved PCB concentra-
tion, one would expect benthic organisms
to carry a significantly higher body burden
than organisms exposed solely to the water
column and as a result would be a potential
significant source of PCBs to top predators
in the food chain.
Since the interstitial PCB component is
potentially significant and since the issue of
solids-dependent partitioning is of contem-
porary interest on constructing mass
balances of PCB, it is recommended that ad-
ditional sampling of pore water PCB and
PCB concentration in benthic organisms be
conducted in various Great Lakes regions.
Application of Model to
Benzo(a) Pyrene and Cadmium
The physico-chemical model was further
applied to two other chemicals: (a) benzo(a)
pyrene, a polycyclic aromatic hydrocarbon
and b) cadmium, a representative metal.
Figure 5 summarizes the results for the BaP
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(4J
Superior
Huron
5 10\
fflm
1(2}
External Load
Condition
Upper Level
Lower Level
Volatilization Rate
(m/d)
0.0
1
fl
0.1
n
0
I ) = Ret. No.
Michigan Saginaw Bay Ontario
figure 3. Calculated water column total PCB concentration (ng/lj for conditions on external load and volatilization rate.
calculations and indicates that a more
avorable (but not totally desirable) com-
parison to observed data is obtained at the
higher BaP partition coefficient of 100,000
7 /kg. On the basis of this application of the
physico-chemical model to BaP in the Great
Lakes, it was concluded that the estimate of
the BaP partition coefficient obtained from
published empirical relationships is probably
low by about an order of magnitude for the
Great Lakes system, and with an increased
BaP partition coefficient and assuming loss
due to volatilization, the physico-chemical
toxic substances model of the Great Lakes
approximate observed BaP water column
and sediment data to order of magnitude.
The application of the model to cadmium
in the Great Lakes indicated that the degree
of any dependence of the cadmium partition
coefficient with solids has a marked effect
on time to steady state and interstitial cad-
mium concentration. Under a solids-depen-
dent cadmium partition assumption, the
Great Lakes, especially the upper Lakes, do
t reach a steady state condition after 100
years of constant loading while under a con-
stant partition coefficient for cadmium, the
Lakes do reach an equilibrium condition
varying from about 25 years for Lake
Michigan to 10 years for Lake Erie. Also the
concentration of cadmium in the Lakes
would be expected to increase by about 60%
over the next 50 years if the average cad-
mium loading for the preceding 50 years
continues.
Based on assumed sediment cadmium
concentrations for Lake Erie, it is estimated
that the cadmium concentration in the water
column is about an order of magnitude
higher than the other Lakes. Finally, the
results indicate that if loads are projected to
increase, then cadmium concentrations in
the Lake system may increase to levels of
concern.
References
1. Swain, W.R. 1978. Chlorinated organic
residues in fish, water and precipita-
tion from the visinit of Isle Royale,
Lake Superior. J. Great Lakes Res.
4(3-4):398-407.
2. Rice, C.P., B.J. Eadie and K.M. Erstfeld,
1982. Enrichment of PCBs in Lake
Michigan surface films. J. Great Lakes
Res. 8(2):265-270.
3. Richardson, W.L., V.E. Smith, and R.
Wethington, 1983. Dynamic mass bal-
ance of PCB and suspended solids in
Saginaw Bay — A case study. In D.
Mackay, S. Paterson, S.J. Eisenreich,
M.S. Simmons (Eds.). Proc. Physical
Behavior of PCBs in the Great Lakes.
Ann Arbor, Mich. pp. 329-366.
4. Eisenreich, S.J., P.O. Capel, B.B.
Looney, 1983. PCB dynamics in Lake
Superior water. In D. Mackay, et al.
(Eds.) Physical Behavior of PCBs in the
Great Lakes, Ann Arbor Science Press,
Ann Arbor, Michigan, pp. 181-211.
5. Frank, R., R.L. Thomas, H.E. Braun, J.
Rasper and R. Dawson, 1980. Organo-
chlorine insecticides and PCB in the sur-
ficial sediments of Lake Superior (1973).
J. Great Lakes Res. 6(21:113-120.
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Eisenreich, S.J., G.J. Hollod, and T.C.
Johnson. 1979. Accumulation of poly-
chlorinated biphenyls (PCBs) in Surficial
Lake Superior Sediments. Atmospheric
Deposition - Em. Sci. & Tech., Vol. 13,
pp. 569-573.
Frank, R., R.L. Thomas, H.E. Braun,
D.L. Gross, and T.T. Davies, 1981. Or-
ganochlorine insecticides and PCB in
surficial sediments of Lake Michigan
(1975). J. Great Lakes Res. 7(1):42-50.
Eadie, B.J., M.J. McCormick, C. Rice,
P. Le Von and M. Simmons, 1981. An
equilibrium model for the partitioning of
synthetic organic compounds incor-
porating first-order decomposition.
NOAA, Great Lakes Environmental Re-
search Lab., NOAA Tech. Memo. ERL,
GLERL-37, 34 pp.
Armstrong, D.E. and D.L. Swackhamer,
1983. PCB accumulation in southern
Lake Michigan sediments: Evaluation
from core analysis. In D. Mackay, et al.
(Eds.), Physical Behavior of PCBs in the
Great Lakes, Ann Arbor Science Press,
Ann Arbor, Michigan, pp. 229-244.
10. Frank, R., R.L. Thomas, M. Holdrinet,
A.L.W. Kemp, N.E. Braun, and R. Dow-
son, 1979a. Organochlorine insecticides
and PCB in the sediments of Lake Huron
(1969) and Georgian Bay and North
Chennel (1973). Science of Tot. Env.,
13:101-117.
11. Richardson, W.L. (Personal com-
munication).
12. Frank, R. 1977. Anthropogenic in-
fluences of sediment quality at a source.
Particles and PCBs. In Shear, H. and
A.E.P. Watson (Eds.), Proc. Workshop
on the Fluvial Transport of Sediment-
Associated Nutrients and Contaminants.
International Joint Commission, Wind-
sor, Ontario, 309 pp.
13. Frank, R., R.L. Thomas, M. Holdrinet,
A.L.W. Kemp, and H.E. Braun. 1979b.
Organochlorine insecticides and PCB in
surficial sediments (1968) and sediment
cores (1976) from Lake Ontario. J. Great
Lakes Res. 5(1):18-27.
14. Eadie, B.J., 1983. Polycyclic aromatic
hydrocarbons in the Great Lakes. GLERL
Cont. No. XX. NOAA, GLERL, Ann Ar-
bor, Mich., 23 pp.
8001-
800 I
SOOp
Extended Load
Condition
Upper Level
Lower Level
Volatilization Rate
(m/d)
0,0
1
R
0.1
n
0
- Mean & Range; ( ) = Ref. No.
Michigan
Saginaw Bay
Ontario
Figure 4. Calculated surface sediment PCB concentration (ng/g) for conditions on external load and volatilization rate and comparison to observed
data
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woo
c
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R. V. Thomann and D. M. DiToro are with Manhattan College, Environmental
Engineering and Science, Bronx, NY.
W. L. Richardson is the EPA Project Officer (see below).
The complete report, entitled "Physico-Chemical Model of Toxic Substances in
the Great Lakes," {Order No. PB 84-170 828; Cost: $17.50, subject to change)
will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Large Lakes Research Station
Environmental Research Laboratory—Du/uth
U.S. Environmental Protection Agency
Grosselle, Ml 48138
United States
Environmental Protection
Agency
Center for Environmental Research
Information
Cincinnati OH 45268
Official Business
Penalty for Private Use $300
"
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