MANHATTAN COLLEGE
ENVIRONMENTAL ENGINEERING & SCIENCE PROGRAM
WASTELOAD ALLOCATION SEMINAR
US EPA REGION I
LEXINGTON, MASSACHUSSETS JULY 14-16, 1981
TOXIC SUBSTANCES
P.ige
Introduction and Basic Concepts 1
Adsorption-Desorption . 13
Modeling Framework 29
Lakes and Reservoirs 45
Saginaw Bay-Solids and PCB Model 61
Stream and River Models 90
Application to PCB's in the Hudson River 99
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INTRODUCTION AND BASIC CONCEPTS
The presence of toxic substances, such as organic chemicals and heavy
metals, has become a major environmental problem in recent years. The
substances are present in varying degrees in all phases of the environment
— air, water and land. They are transferred between and among these media,
undergo ransformation within each and accumulate in viable and nonviable
constituents. The magnitude and significance of the problem has become
increasingly evident, particularly in the accumulation of toxic substances
in both the terrestrial and aquatic food chains and in the release of
these substances from land and water disposal areas. In this regard, the
impact on the health and activities of man is more direct and significant
than in the case of pollutants which the field has classically addressed.
This concern led to the formulation of the Toxic Substances Control Act,
enacted by Congress in 1976, and, in turn, to the subsequent promulgation
of priority pollutants by the Environmental Protection Agency. The latter
is under continuous review and periodic updating both by EPA and interested
scientific groups in industry, research laboratory and environmental organ-
izations.
A total ban on all organic chemicals is neither desirable nor practical.
The benefits derived from the use of these substances are evident in many
facets of our society — particularly with respect to the increased food
production. The demand for these materials, more specifically the bene-
fits derived from their use, continuously increases. A balance must there-
fore be sought between the extreme positions — complete ban and no control.
Such a balance leads to the use of certain chemicals, which may be safely
assimilated in the environment to such levels as to yield the benefits
without deleterious effects. This goal necessitates the development of
assessment methods which permit an evaluation and ultimately a prediction
of environmental concentrations. The approaches developed herein are,
therefore, directed to two broad areas: an evaluation of the present extent
and dist ution Ltkese ttaiies, with particular regard to their dimi-
nution and removal and secondly, a methodology to assess the potential
impact of proposed chemicals, which may be introduced into the environment.
*D. J. O’CONNOR
—1
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Field surveys undoubtedly provide much insight into the nature of the
first question, but this approach is evidently limited and not applicable
to the analysis of the second, and. potentially more important, question.
In addition, the costliness and time factor of field surveys impose further
disadvantages. Theoretical analysis, in conjunction with controlledlabora-
tory experiments, is the preferred approach. The emphasis in the following
sections is therefore directed to a review of the basic knowledge of the
various phenomena and of the application of laboratory data to the analysis
of the problem. This approach, which is less costly and time—consuming,
lends itself to greater understanding of the problem and broader applica-
tion to a variety of similar problems. Ultimately, however, the equations
developed in this fashion may on.ly be fully validated and tested by proto-
type data. Case histories and data on presently affected water systems
should be fully documented and utilized for this purpose.
In the following sections of these notes, the various phenomena, which
affect the transport, transformation and accumulation of organic chemicals
and heavy me:tals in the various phases of the aquatic environment, are
addressed. Taken into account is the exchange of these materials between
the water and the other phases of the environment, air and land. However,
the primary emphasis is directed to aquatic systems — specifically to the
spatial and temporal distribution of these materials in the various types
of natural water bodies — rivers, lakes, estuaries and the coastal zone.
The approach taken is similar to that defining the distribution of sub-
stances which are natural components of biochemical and ecological cycles
— oxygen, nutrients, minerals, dissolved and suspended solids and the basic
elemerits of the food chain — bacteria and phytoplankton. While these con-
stituents influence water quality and man’s use of water, they do not have
the potentially profound effect of toxic substances, which may impact
directly the health and veil—being of man. The basis of the determination
of the hazardous assessment lies in our ability to define the distribution
of these substances in the aquatic environment. While recognizing distinc-
tion between the effects and fate, it is important to appreciate their
interrelationship in that any reliable hazard assessment is based funda-
mentally on a realistic and valid definition of the fate of toxic substances.
The purpose of this course and these notes is to describe the various pheno—
—2—
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inena which affect the fate and to develop the equations, incorporating these
phenomena, which define the spatial and temporal distribution of toxic sub-
stances. The notes are accordingly divided into two general sections: the
first which describes the various kinetic and transfer phenomena which
affect organic chemicals and heavy metals and the second which precents
various mathematical models of natural water systems, iricorporatin these
kinetic terms with the transport characteristic of each type of natural
system: streams, estuaries, lakes and the coastal zone.
In order to achieve some perspective oVthe overall approach, it is
first appropriate to indicate the basic concepts which are employed in the
development of the various analyses: the principle of mass balance, the
dynamic equilibrium between the dissolved and particulate concentrations,
and the kinetic interaction between these components.
A. BASIC PRINCIPLE - MASS BALANCE
Organic chemicals may exist in all phases of the aquatic environment —
in solution, in suspension, in the bed and air boundaries, and in the vari-
ous levels of the food chain. The interrelationships between and among
these phases, which are shown diagramm tically in Figure A-i, relate to the
transport, reactions and transfer of the substance. The approach taken is
identical, in principle, to that used to define the distribution of water
quality constituents, which are naturally part of biochemical and ecologi-
cal cycles. The equations describing the spatial and temporal distribution
of organic chemicals are developed using the principle of mass conservation,
including the inputs with the transport, transfer and reactions components.
The general expression for the mass balance equation about a specified
volume, V, is:
dc.
V— .=J +ER.+ZT.+Ew (1)
dt i
in which
Cj = concentration of the chemical in compartnent, i.
• J = transport through the system
R = reactions within the system
T = transfer from one phase to another
W = inputs
—3—
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Equation (1) describes the mass rate of change of the substance due to the net
effect of the various fluxes and transformations. The purpose of expressing
the transfer rate CT), distinct from the transport (3) and reaction (B), is
to provide a basis for the development of the equations, which describe more
fully the relevant phenomena.
The general term “compartment” refers to each phase of the physiochemi—
cal regime — the dissolved and particulate in the water, atmosphere and bed
— as well as to each element of the food chain — the phytoplankton, zooplank_
ton, fish and detrita]. material. The transport, reaction and transfer terms
may be positive or negative depending on the direction of kinetic routes
between the chemical in compartment i and its concentration in other compart-
ments with which it reacts or exchanges. The pathways are determined by the
hydrodyna.mic and geophysical features of the natural water systems and by the
physical, chemical and biological characteristics of both the system and the
chemical. The hydrodynamic components transport material from one spatial
location to another by dispersion and advective mechanisms. The physical
factors transfer from one phase to another, such as exchange with the atmos-
phere, adsorption to and desorption from the suspended and bed solids and the
settling and scour of these solids. The chemical factors transform the sub-
stance by processes such as photo—oxidation, hydrolysis and oxidation reduc-
tion reactions. The biological phenomena effect both transference and trans—-
formation: the latter primarily by microorganisms which may metabolize the
chemical and the former by assimilation and excretion by the various aquatic
organisms. Accumulation in the food chain is brought about by both ingestion
of the chemical from the water and by predation on contaminated prey.
Consider the concentration, c, to be the dissolved component of the
chemical in the water. It interacts with the particulate concentration,
p. The interaction may be an adsorption—desorption process with the solids
or an assimilation—depuration process with the aquatic organisms. In either
case the particulate concentration is defined as:
p. = r 1 m (2)
-4—
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p = particulate concentration in I compartment (M/L 3 )
= mass of chemical/unit of interacting mass (M/M)
concentration of the interacting species (M/L 3 )
The mass balance equation for the particulate component, similar to equation
C i), is then:
dp. dm. dr.
= r + m 1 2. = J + ER + ET + EW (3)
It is apparent from equation (3) that an equivalent expression must
be written for the concentration of the interacting compartment, m.. In
principle, the analysis of the problem requires the simultaneous solution
of the three equations: the concentration of the chemical dissolved in
the water, c, the mass concentration of the chemical per unit mass of
interacting species, r, and the concentration of the species itself, m.
Since this compartment may be further subdivided (inorganic and organic
solids, multiple species of fish), equation (2) is more generally expressed
as a summation of the individual components of the interacting substances:
= £ rim R)
The specific conditions for which the analysis Is performed frequently
permit simplifying assumptions to be made. In laboratory batch reactors
and in certain prototype situations, the rate of change of the interacting
species may be zero — i.e. a constant concentration of suspended solids or
bioinass. Thus . = o, from which an equilibrium concentration of solids
or biomass follows, resulting in two simultaneous equations to be solved,
instead of three.
B. DYNAMIC EQUILIBRIUM
As may be evident from the above discussion, one of the essential
propertie of the analysis of this water quality problem is the inter-
action between the dissolved and particulate states of the constituent,
which, in time, leads to a dynamic equilibrium between the two components.
Consider the most simplified conditions of a batch reactor in which the
—5
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mixing is of sufficient magnitude to maintain a uniform concentration
throughout the volume of fluid. Assume the concentration of absorbing
solids, m (M/L 3 ) is constant. Let c and p be the concentrations (Mu 2 ) of
the dissolved and particulate components. If there is nejther transfer
nor decay of the chemical, the total concentration, CT, rt’mains constant
in time and is equal to the sum of the dissolved and particulate:
CTC+P (5)
The latter is related to the concentration of suspended solids, m, as shown
by equation (2):
p = rm
The equilibrium between the dissolved concentration in the water and
the mass concentration of the solids is usually expressed in terms of a
partition coefficient:
- r
c mc C)
or
C
- Equation (6) is the linear portion of the Langmuir isotherm. Although not
always representative of actual conditions, it is a reasonable approximation
when the solid phase concentration, r, is much less than the ultimate ab-
sorbing capacity of the solids. Combining equations (5) and (6), the total
concentration may be expressed as:
cT=c+llmc= +p (7)
The product, ¶m, is a convenient dimensionless parameter, characteristic of
a particular system under equilibrium conditions. For a specified value of
Im, the equilibrium distribution between the dissolved and particulate con-
centrations is established by equation (7), as shown in Figure A-2.
The distribution between the dissolved concentration and the particu-
late concentration in the various levels of the food chain may be expressed
in an identical fa9hion. Accounting for the distribution for various types
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of adsorbing solids and various levels of the food chain, each with its
characteristic partition coefficient, equation (7) may be more generally
expressed:
CT = co. + ElI m.] Ce)
The distribution may thus be categorized in accordance with the adsorbing
solids (orgariics, clays, silts and sands) or the accumu .ating biomass
(phytoplankton, zooplenkton, fish and macrophytes). Si ice the total blo-
mass mass in most natural water systems is usually an order of magnitude
less than that of the non—viable solids, the equations defining each cate-
gory may be decoupled and the former may be solved independently. Under
those conditions in which it may be significant, it may be readily incorpora-
ted as shown in the above equation.
C. KINETIC INTERACTION
The equilibrium, described above, is a result of the kinetic inter-
action between the dissolved and particulate. This property which dis-
tinguishes the analysis from that of purely dissolved substances, leads to
equations of a more complex form. In order to gain an insight into the
nature of these interactions and an understanding of a practical simplifi-
cation, consider the kinetics in a batch reactor, as described above, in
which interaction is taking place between the dissolved and particulate coxn-
ponents and the former is being transferred by volatilization or transformed
by chemical or biological degradation:
K 3
K 2
The reversible reaction (x 1 x 2 ) may represent the adsorption—desorption
between the dissolved component and the particulate in inorganic phase (sus-
pended or bed solids) or the assimilation—depuration in the organic phase
(aquatic organisms). These kinetic coefficients may be functions of the
solids concentrations, as discussed subsequently. In any case, their ratio
is a measure of the distribution or partition coefficient. The non—rever-
sible reaction (K 3 ) describes the decay or volatilization. The kinetic
equations are: -
—7
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= - + K 3 )c + K 1 p (10)
=—K 1 p+K 2 c (ii)
By differentiating (10) and substituting (10) and (ii) into the second-order
differential equation, there results:
+ [ K 1 + 2 + 1(3] - + K 1 K 3 c = o (12)
An identical expression results for p. Assuming the initial concentration,
c 0 , is totally in the dissolved form, the initial condition is
c = C at t = o
Applying the second condition:
dc
—=-Kc att=o
dt 2o
the solution of the differential equation (8) subject to these initial condi-
tions is:
c = c 0 t8e + (l_ 8 )eht) (13)
in which g,h are the positive and negative roots of the quadratic
g,h = — [ 1 + in)
in which K = + K 2 + 1 (3
/ 1 K 1 K 3
in = /1 -
V K
It may be readily shown that g and h are always real anU negative.
In the case of adsorption —desorption, the assumption of instantaneous
equilibrium is frequently made — i.e. the coefficients K 1 and 2 are of
sufficiently large magnitude so that the exchange between particulate and
—8—
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dissolved occurs very rapidly. Furthermore, for organic chemicals, the
decay coefficient is usually of a much smaller magnitude than the adsorp-
tion—desorption. Thus equation (12) simplifies to
[ K 1 + K 2 ) . + K 1 K 3 c =
or
dc — — K 3 (114
- . + K /K 1
in which
K 2
= distribution or equilibrium coefficient
1
An additional insight is gained by developing equation (lie) in an alter-
nate manner by adding equations (10) and (ii) which yields
dc
I = — K c (15)
Assume the interaction between c and p is an adsorption—desorptiofl pro-
cess. The dissolved concentration, c, may therefore be expressed in terms
of the total, CT by equation (7) substitution of which in (15) yields
dcT K 3
_l+i CT (16)
The total concentration decays in accordance with the dissolved coeffi-
cient modified by the parameter ¶m. As a physically realizable example,
consider the transfer represents a volatilization process, in which K 3 is
the gas transfer coefficient. The total concentration cT decreases at a
slower rate than would be the case if there were no partitioning to the par-
ticulate -form, with the total in dissolved form (urn o). In defining the
rate of change of the total, the decay ox- transfer coefficient is simply
modified as shown by equation (16). Conversely, if the decay is associated
—9—
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with the particulate component, the coefficient would be reduced by the
fraction lTrn/(l + ¶zn], in accordance with equation (7).
If both the particulate and dissolved components are subject to decay,
by more than one mechanism, equation (i6) becomes
dc K ITmEK
_.!_ r ci +
dt - Ll+lim l+11m T
in which the subscripts, c and p, refer respectively to the dissolved and
particulate decay coefficients.
The assumption of “instantaneous” equilibrium as expressed by equation
(].i. ) through (17) is a valid representation, or model, of kinetic reactions
provided the time to equilibrium, determined by K 1 and K 2 is rapid relative
to the other phenomena which affect the substance K & K . This condition
C p
is generally applicable to the adsorption—desorption process, since its
equilibrium time is usually much shorter (mm—hours) than that of other
kinetic effects, which may be in the order of days, months or years.
In sun1m ry, the models for the analyses of organic chemicals and heavy
metals are similar to those developed for constituents which are nat .iral
components of ecological cycles. The terms relating to the particulate form
and its interaction with the dissolved component are the additional compo-
nents to be incorporated. These, with the other transform and reactive
terms, cover the various pathways of distribution. Accordingly, each of
these routes and the associated mechanisms are described in the subsequent
sections which comprise the first half of these notes.
The second half is devoted to the development of models, which incor-
porate these reaction mechanisms with transport and inputs, to define the
temporal and. spatial distribution of toxic substances in natural systems.
By virtue of their interactions with the solids in these systems, it is also
necessary to analyze the distribution of the various types of solids. Fur-
thermore, the exchange between the suspended and the bed constituents is
- taken into account. The models, which are developed in the second part of
the notes describe both the physical—chemical effects in the inorganic realm,
in conjunction with the solids, as veil as accumulation and transfer through
the various elements of the aquatic food chain. - Application of these models
to various natural systems are also presented.
— 10 —
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TRANSPORT KINETIC ROUTES WITHIN THE WATER COLUMN
PHOTOCHEMUCAL DECOMPOSITION
c 711 1
AEROBIC
I - a
I - ’
DIRECT INGESTION
IN VARIOUS LEVELS
OF FOOD CHAIN
AIR
WATER
SUSPENDED
SOLIDS
- W i
[ i 11 j_j F
I ACCUMULATION
— IN FOOD CHAIN
I c,, — — [ c 3 1 j
ANAEROBIC B iODEGRADATION
BEN Wit
WATER
FIGURE At
TRANSPORT - KINETIC ROUTES WITHIN THE
WATER COLUMN
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t4ote :
I.0
0.g
0.
0.4
0. 2.
a
F. re
v( hte of cI:I
F I 4 C 7 g ON
0.01 0.1 1.0 10.0 100.0
FIGURE A2
Equilibrium Concentrations of Dissolved and
Particulate Toxicarit as a Function of ¶m
for cop%Jtaj t
33oLveD FMCTioW
ci .
i
C
- 12
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ADSORPTI ON_DESORPTION*
Adsorption is an important transfer mechanism within
natural water systems, because of the significance of the sub-
stances which are usually involved in this process. The
majority of radionuclides, heavy metal and organic chemicals
are readily susceptible to adsorption. Bacteria and algae also
have a similar tendency. The surfaces to which these consti-
tuents adhere are provided by the solids, either in suspension
or in the bed. The clay, silica and organic content of the
solids are the effective adsorbents by contrast to the sand and
silt components.
The substance, in the complexed form may be then affected
by additional processes such as flocculation and settling. If
the flux due to the latter force is greater than that of the
vertical mixing, the complex species deposit on the bed. In
streams or rivers, they may then be subjected to xesuspension
during periods of high flow or intense winds and be transported
to a reservoir or estuary. Since the hydrodynamic regime of
each of these systems is more conducive to sedimentation than
is that of a flowing stream, the ultimate repository of the
complexed species frequently is in the bed of the reservoir
or estuary. Furthermore, the physiochcriu.cal characteristics
of the estuary tend to promote desorptxon arid the constituent
may be released to be recirculated with the estliarine system
or transported to the ocean. Therefore, in analyzing the
distribution of substances which are subject to adsorption it
may be necessary to take into account a sequence of- events both
with respect to the hydrologic and hydrodynamic transport
through various systems, as well as the kinetic aspects of the
transfer processes of adsorption—desorption and settling-scour
within these systems.
The folluwing sections describe the various factors which
affect the adsorption—desorption processes and, based on
*Donald J. O’Connor
Kevin Farley -
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present the development of the relevant equilibrium relations
and transfer equations.
1. Equilibrium
Adsorption is a process in which a soluble constituent
in the water phase is transferred to and accumulates at the sur-
face of the solids. The adsorptive capacity of a two—phas e
system depends on the degree of solubility of the constituent
and the affinity of the constituent to the surface of the
solid. The greater the degree of solubility the lcss is the
tendency to be adsorbed. A number of organ ’ic compounds have
both hydrophyliC as well as hydrophobic groups — resulting in
the orientation of the molecule at the interface. The hydro-
phylic component tends to remain in solution while the hydro-
phobic part adheres to the surface.
The molecular characteristics of a compound - its size
and weight - are related to adsorption capacity, in a fashion
consistent with solubility. For a given homologous series,
the solubility is inversely proportional to molecuiar weighi
and it has been observed that the adsorption capacity increases
with increasing molecular weight.
The affinity of the solute for the solid may b due to L11
attraction or interaction of an ionic, physical (van der Wails
forces) or chemical nature. Most adsorption phenomena consist
of combinations of the three forms and it is generally diff i-
cult to distinguish between them. The more general term
“sorption” is used to describe the overall process.
In any case, one notable characteristic of the phenomenon
is the dynamic equilibrium which is achieved between the con-
centration of solute remaining in solution and that on the
surface of the adsorbent solid. At equilibrium, the rate of
adsorption equals the rate of desorption. The equ3llbrium
relationship between the concentration of solute aiid the
amount adsorbed per unit mass of adsorbent is known as an
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adsorption isotherm . The amount adsorbed per unit mass
increases with increasing concentration of solute and usually
approaches a limit as the capacity of the solid to accumulate
is reached.
Equilibrium exists when the rates of adsorption and
desorption are equal. The rate of adsorption depends on the
concentration of the solute and the available sites on the
adsorbing solid. The latter is propor.tional to the adsorp-
tive capacity of the solid minus the amount of solute
adsorbed. The rate of desorption is proportional to the
amount of solute adsorbed:
dc
— Kic [ c _c ] - K 2 C (14)
in which
c = dissolved concentration of solute (M/L)
= particulate concentration (M/L)
= capacity of the adsorbent solids (M/L)
= adsorption coefficient
K 2 = desorption coefficient ( )
The overall reaction is second order with respect to adsorption
and first-order with respect to desorption. The particulate
concentration is a product of the concentration of adsorbing
solids in the water, m, and the mass of the solute per unit
mass of the adsorbent, r. Equation (14) may be expressed
= K 1 c m [ r _r] - K 2 rrn (15)
At equilibrium, the rate of change of concentration is zero
and equation (15) becomes after rearranging:
- Is --
-------
cr
r = 1 C (16)
K 1
in which b = —
K 2
Equation (16) is known as the Langmuir isotherm in which the
parameter, b, is related to the energy of adsorption. At
r = r/2, the concentration equals 1/b. Lacking direct exper—
iinerital data on rc its value and that of 1/b may be evaluated
graphically by a linear plot of versus . The intercept
equals l/rc and the slope l/br .
The capacity r depends on the nature, size and charac-
teristics of the adsorbing solids, as shown in Figure 6. The
various types of clays have greater capacities than silts and
sands. The adsorption capacity is, thus, inversely propor-
tional to the size of the particle, specifically to the ratio
of its surface area to volume. Furthermore, the capacity is
directly proportional to the organic content of the solids.
In general solids, composed primarily of organic material,
have greater capacities than the inorganic components. These
materials include detrital matter, and various forms of viable
organic substances, such as bacteria, plankton and macrophytes
in natural systems and biological solids in treatment systems.
The Langmuir isotherm is based on the assumption that
maximum absorption occurs when the surface of the adsorbent is
saturated with a single layer of solute molecules. If one
assumes that a number of adsorbate layers may form, the equili—
briuxn condition, as depicted in Figure B-S, may have various
points of inflection. Essentially an additional degree of
freedom is introduced which reflects a greater degree of real-
ism. The resulting relationships fit certain experimental
data better than the Langmuir, particularly at the higher con—
- 16-
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Figure B-5
Langinuir Adsorption Isotherms
x
0
“.4
4)
L i
4)
C
a,
U
C
0
U
a,
4)
‘-I
U
“ . 4
4)
Li
04
Dissolved Concentration - M/L
-------
centratjons of solute. At lower concentrations the two
isotherms may be approximately equivalent. In addition to
the monolayer assumption, there are other conditions for
which the Langmuir isotherm may not be appropriate. A -
semi-empirical relationship, known as the Fruendljch
isotherm, which has been found to be more satisfactory in
certain cases, is as follows
r = KC 1 /n (17)
The value of the exponent n is usually less than unity. This
isotherm has been widely used in the correlation of experi—
mental data, particularly with respect to the adsorption by
activated carbon in water and wastewater treatment processes.
It is generally accepted that the rates of adsorption
and desorption occur very rapidly. Consequently equilibrium
between the dissolved and particulate species, expressed by
equations 16 or 17 is assumed to be established instantaneously.
The above isotherms appear to be Particularly appropriate
for the analysis of a singular adsorbate or those cases where
one is predominant, such as PCB in the Hudson and kepone in
the James River. When there are a number of compounds present,
preferential adsorption and displacement may occur. Present
research efforts are directed to the analysis of this problem.
A competitive Langmuir isotherm and ideal solution theory are
being applied in these cases.
2. Partition Coefficient
The partition coefficient is the ratio of the mass of
substance adsorbed per unit mass of absorbent solids and the
dissolved concentration of solute in the linear range of the
Langmuir and Fruendlich isotherms. For very low concentra-
tions of solute, c < 1/b, the Langmuir isotherm is linear:
r = i c (18)
-------
inwhich 1T=
The parameter, ii, is a partition coefficient. At high concen-
trations of solute c >> 1/b, the adsorbent is saturated at its
capacity r . These characteristics are more dramatically
borne out when logarithmetic coordinates are used for various
values of the partition coefficient.
The constant K in the Fruendlich isotherm is comparable
to the partition coefficient. As the exponent n approaches
unity, the isotherms are identical. Since the concentrations
of organic chemicals in natural systems are generally low and,
thus, well below the capacity of solids in these systems, the
linear assumption is a reasonable approximation in many cases.
The partition coefficient incorporates the capacity para-
meter, r. Therefore, the same factors which influence its
magnitude has a comparable effect on the partition coefficient.
Large values are characteristic of organic material and clays,
by contrast to silts and sands. Examples are shown in Figure
B-6.
3. Dissolved — Particulate Distribution
Under equilibrium conditions, the distribution be-
tween the dissolved and particulate fraction is established
not only by the partition coefficient as described above, but
also by the concentration of the adsorbing solids. The solids
may be suspended in the flowing water or relatively fixed in
the bed of the system. Under extremely high flow in rivers or
winds in lakes, the bed may be scoured and the solids are
introduced into the overlying water for a brief period of time,
after which they settle to the bed. In any case, assuming
sufficient time has elapsed to establish adsorption equili-
brium, the total concentration of organic chemical or metal,
-------
Figure 3-6
Equilibrium Concentrations of Kepone
p .,
0
0
4 J
C
U
C
0
U
a’
4 J
I -I
U
..4
4. ,
Ii
04
LEGEND;
• RANGE POINT (ZO%ORGANIC)
O T ALA$5Ik ( O % ORGAIIIC)
- A JAJIES SEbIMENT (44%’
o JAHL SEDIMENT 1(1.5%
• BENTON IT C
£ K*OLINITE
0 SAND
EF GULF’ BRE.EW
I —
Dissolved Concentrations — ig/I.
-------
CTV is the sum of the dissolved and particulate:
CTC+CP (19)
The dissolved component may be expressed in terms c the par-
ticulate fraction, r, and the partition coefficient, while the
particulate concentration as a product of the concentration of -
adsorbing solids, m, and the particulate fraction:
cT= +rm (20)
The particulate fraction as a function of solids concentration
for various values of the partition coefficient is shown in
Figure B-7.
Given a chemical or metal, with a large partition coef-
ficient, whose major source is the bed solids, which is of
uniform and constant concentration, this equation provides an
approximate means of correlation. A linear plot of total con-
centration of chemical versus suspended solids concentration
yields a straight line whose slope is r and intercept is r/ir.
An example is shown in Figure B-B for mercury in the Mississippi
and Mobile Rivers.
4. Transfer Rates
The discussion above concerned equilibrium condi-
tions. The time required to achieve this condition involves
the transfer and kinetic mechanisms between adsorbate and
adsorbent. The sequence of processes, which characterize the
transfer of a substance from solution to a material which has
an adsorptive capacity, may be grouped in the following three
steps: The first is the transfer of adsorbate through a liquid
film to the surface of the adsorbent; the second is the diffu-
sion of the adsorbate within the pores of the adsorbent; and
the third is the fixation of the adsorbate on the interior pore
or capillary surfaces of the adsorbent. The last step is
usually assumed to be very rapid and equilibrium exists at this
location. In some cases, the transfer of solute through the
surface film or boundary layer is the rate-limiting step. If
- tip-
-------
1
J0
44
62
1
N0f4 -
WATER ERODIbJ > £RODIN T&BLE
r1o i J HOVI 4G ‘k bEb M
______- M0i4 -
_________________ —
5P A . - —
—
/
/ ,/ /,/ /
/
I J I
/
/
4/
/
/ I
ALLUVIAL
I /‘ 5TRL*J1( /
/ /
/ /
___ I J I —
I’,’
Solids Concentration — mg/L
Figure B-7
Relationship — Particulate Fraction — Solids Concentration
0
. 1 -I
U
1.4
0
0
U
—4
4)
1.1
0
, ,/ ,,
_ —— .—
/
I —--
-2t-
-------
p.
Figure B—8
Total Mercury - Suspended Solids Correlation
0
- -I
14
a)
C.)
0
0
>‘
1 .4
C)
a)
0
Suspended Solids - mg/L
-U-
-------
there is sufficient mixing due to the turbulence of the flowing
water, the second step, that of diffusion within the porous
material controls the rate. -
In very dilute solution of both species, the frequency
with which the solute comes in contact with the absorbent may
determine the rate—limiting step. In some cases, adsorption
may be occurring on contact of the solute with the bed mater-
ial and the control may then localize in transfer through
surface film on the exterior surface of the bed solids. The
situation is comparable to the biological oxidation ‘of organic
matter, which takes place in the flowing water by the plank-
tonic bacteria and in the channel bed by the benthic organisms.
Both reactions occur simultaneously in natural systems, but in
many cases, one or the other controls depending on the depth of
the flow, the nature of bed and materials contained in each.
Given the steps described above, the reaction sequence
may proceed in accordance with steps 1—2—3 or steps 1-3-2
depending on the nature of diffusion within the solid. In the
latter case the diffusion is referred to as solid-phase inter-
nal diffusion. In the former sequence, it is fluid-phase pool
diffusion. Various models have been constructed, incorpora-
ting these concepts and additional refinements. Most approaches
include the three mechanisms: film transfer, diffusion in the
particle and an interfacial equilibrium between liquid and
solid phase concentrations.
The equilibrium coefficient, as previously discussed, may
be readily determined in the laboratory for the various types
of solids which may be encountered in natural systems.
The fluid phase film transfer coefficient appears to
conform to general mass transfer correlations developed in the
field of chemical engineering. In a simplified form the
transfer coefficient is approximately:
D U 12
(21)
- 4-
-------
in which DL = diffusivity in liquid
U = flow velocity
d = effective particle diameter
The diffusivity in the above expression is that in
liquid. The diffusivity within the pores is reduced by
virtue of the size, porosity and tortuosity of the pore
structure. A common correlation is of the form
DLC
in which c = internal porosity of the solid particle
The model is structured with transfer in two phases:
liquid and pore. A flux balance is applied at the interface
and the concentration equilibrium applied at the appropriate
interface. A typical analysis is shown in Figure B-9.
-
-------
DNOCNP
24 -
DINITRO
-
0
-
DNO
SP
2,4 -
DINITRO - o - SEC -
Figure B-9
Example - Adsorption Kinetics
LO
00
03
44
0
4J
U
0
U
a,
‘-4
0
U)
.-I
C
0
I -i
a,
U
0
U
a,
-4
0
U,
U,
‘ -I
C
-I
.4
4- I
OhCØ
Time - Minutes
-------
ADSORPTION-DESORPTION REFERENCES
DiGianO, F.A. and W.J. Weber, Jr. December, 1972. “Sorption
KinetiCS in Finite-Bath Systems.” Journal of The Sanitary
Engineering Division, ASCE, Vol. 98, No. 5A6, Proc. Paper
9430, pp. 1021—1036.
Keinath, T.M. et al. April, 1976. “Mathematical Modeling of
HeteroCJefleOUS Sorption in Continuous ContactOrS for Wastewater
Decontamination.” Final Report, U.S. Army Medical Res. Command.
Keinath, T.M. 1975. “Modeling and Simulation of the Perfo-
mance of Adsorption ContactOrS,” in Mathematical Modeling for
Water Pollution Control Processes, ed. Thomas M. Keinath and
Martin P. Wanie].ista, Ann Arbor, Mich . Ann Arbor Science Pubi.
Matthews, A.?. and W.3. Weber, Jr. November 1975. “Effects of
External Mass Transfer and Intraparticle Diffusion Ofl Adsorp-
tion Rates in Slurry Reactors.” Presented at the 68th Annual
Meeting, American Institute of Chemical Engineering, Los Angeles,
Calif.
Mattson, J.A. et al. July 1974. “Surface Chemistry of Active
Carbon: Specific Adsorption of Phenols.” Journal of Colloid
and Interface Science, Vol. 48, No. 1.
Vermeulen, T. 1958. “Separation by Adsorption Methods.” in
Advances in Chemical Engineering . T.B. Dren and J.W. Hoopes,
Jr., ed., Vol. 2, P. 147, Academic Press, New York.
Weber, T.W. and R.K. ChakravOrti. March 1974. “Pore and
Solid Diffusion Models for Fixed-Bed Adsorbers.” AIChE Jour.,
Vol. 20, No. 2.
Weber, W.J. Jr. 1972. Physiochemical Processes for Water
Quality Control . Wi1ey-Iflter5c eflCe. New York.
Weber, W.J. Jr. and J.C. Morris. April 1964. “Adsorption in
Heterogeneous Aqueous Systems.” Journal Amer. Water Works
Assoc., Vol. 56, No. 4, pp. 447—456.
Weber, W.J. Jr. and R.R. Rurner Jr. Third Quarter 1965.
“Intraparticle Transport of Sulfonated Alky]benzenes in a
Porous Solid: Diffusion With Nonlinear Adsorption.” Water
Resources Research. Vol. 1, No. 3.
Proceedings of The Kepone Seminar II. U.S. EPA Region III,
Philadelphia, Pa., Sept. 1977.
- v i-
-------
SUMMARY OF REACTION RATE COEFFICIENTS
Carbaryl
Propham
Chioropropham
Malathion
Parathion
Diazi.nori
2,4-D Butoxy
ethyl ester
Ca pta n
Methocychlor
Toxaphene
DDT
Atrazine
*
pH, Temp
S
6
7
8
9
7
7
6
8,0°C
8,270
8,40°
7,200
7,20°
6,28°
9,280
8,28
7,27°
7
7,27
3
11
Chemical
Hydrolysis
day
4.6 x
5.3 x
0.046
0.53
4.6
6.9 x
6.9 x
s low
0.058
0.46
17.3
2.8 x
0.023
0.63
27.7
1. 39
1.9 x
slow
2.4 x l0
0.011
8.6 x
10
Direct
Photolysis
day 1
0.11
0.11
2.7 x
5.7 x l0
s low
0. 017
0. 022
0.049
slow
0.053
*
0.1—0.3
slow
1.3 x
0.017
Biolysis
day
2.3 x 10
0.22
0. 24
6.1
sensitized photolysis in natural waters
-------
MODELING FRAMEWORK
This section of the notes presents the development and application of
various mathematical models which define the spatial and temporal distribu-
tion of toxic substances in natural water systems. The previous sections
discussed the various transfer and kinetic factors which affect the concen-
tration of such substances. These factors are now combined with the trans-
port regimes characteristic of the different types of natural water systems,
both freshwater and marine. The former include reservoirs/lakes and
streams/tidal rivers, and the latter estuarjes/emba ents and the coastal
zone.
The purposes of the modeling framework are twofold: the first relates
to the general hazard assessment of proposed or existing chemicals which,
in turn, may lead to waste—load allocation procedures. Such analyses may
usually be accomplished by means of the spatial steady—state distributions.
The second general purpose relates to the time-variable aspects of the
problem. Such analyses apply to the effects of a short—term release of a
toxic, such as an accidental spill or a storm overflow discharge. An
equally important application in this regard is directed to the time re-
quired to build up to the steady and perhaps more significant the time
required to cleanse a system from existing contamination.
As discussed in the previous sections, one of the most distinguishing
characteristics of toxic substances is the partitioning between the dis-
solved and particulate components. Thus equations are developed for each
of these components and in addition for those solids which provide sites
for the adsorption of the substance. The analysis involves therefore, the
solution of at least three simultaneous equations, describing the concen-
tration of the various components in the water column. Furthermore, for
those water systems which interact with the bed, additional sets of equa-
tions are developed to account for distribution in the benthal layer and
its effect on water column concentrations. Given these concentrations,
the dissolved and the particulate in the water column and in the bed, the
distribution through the food chain is then considered.
* Donald J. O’Connor -
-8-
-------
In order to provide a perspective of the overall approach, the basic
concepts which are employed in the analysis are first presented, followed
by the development of the equations defining the dissolved, particulate
and solids components. Certain sections which are contained in the first
part of the notes are therefore repeated in the following in order to pro-
vide continuity of development.
A. BASIC PRINCIPLES
1. Mass Balance
Organic chemicals may exist in all phases of the aquatic environment —
in solution, in suspension, in the bed and air boundaries, and in the vari-
ous levels of the food chain. The interrelationships between and among
these phases, which are shown diagrammatically in Figure 1, relate to the
transport, reactions and transfer of the substance. The approach taken is
identical, in principle, to that used to define the distribution of water
quality consitutents, which are naturally part of biochemical and ecologi-
cal cycles. The equations describing the spatial and temporal distribution
of organic chemicals are developed using the principle of mass conservation,
including the inputs with the transport, transfer and reactions components.
The general expression for the mass balance equation about a specified
volume, V, is:
dc.
V— 2 -=J.+ER.+ET.+zw ( 1)
dt 1 1 1
in which
c = concentration of the chemical in compartment, i.
J = transport through the system
P = reactions within the system
T = transfer from one phase to another
W = inputs
Equation (1) describes the mass rate of change of the substance due to the
net effect of the various fluxes and transformations. The purpose of ex-
pressing the transfer rate CT), distinct from the transport (J) and reaction
-------
(R), is to provide a basis for the development of the equations, which des-
cribe more fully the relevant phenomena.
The general term “compartment” refers to each phaBe of the physiochemi-
cal regime — the dissolved and particulate in the water, atmosphere and bed
— as well as to each element of the food chain — the phytoplankton, zooplank-
ton, fish and detrital material. The transport, reaction and transfer terms
may be positive or negative depending on the direction of kinetic routes
between the chemical in compartment i and its concentration in other compart-
ments with which it reacts or exchanges. The pathways are determined by the
hydrodyna.mic and geophysical features of the natural water systems and by the
physical, chemical and biological characteristics of both the system and the
chemical. The hydrodynamic components transport material from one spatial
location to another by dispersion and advective mechanisms. The physical
factors transfer from one phase to another, such as exchange with the atmos-
phere, adsorption to and desorption from the suspended and bed solids and the
settling and scour of these solids. The chemical factors transform the sub-
stance by processes such as photo—oxidation, hydrolysis and oxidation reduc-
tion reactions. The biological phenomena effect both transference and trans-
formation: the latter primarily by microorganisms which may metabolize the
chemical and the former by assimilation and excretion by the various aquatic
organisms. Accumulation in the food chain is brought about by both ingestion
of the chemical from the water and by predation on contaminated prey.
2. General Equations for Various Components
Consider the concentration, c, to be the dissolved component of the
chemical in the water. It interacts with the particulate concentration, p.
The interaction may be an adsorption—desorption process with the solids or
an assimilation—depuration process with the aquatic organisms. In either
case the particulate concentration is defined as:
p r m (2)
p particulate concentration in i compartment M/L 3
• r 1 = mass of chemical/unit of interacting mass M/M
concentration of the interacting species M/L 3 -
- 3 1 -
-------
The mass balance equation for the particulate component, similar to equation
(1), is then:
dp. dm. dr
1 1 i
— = r. + m. — = J + ER + ET + LW (3)
dt idt idt
It is apparent from equation (3) that an equivalent expression must
be written for the concentration of the interacting compartment, m.. In
principle, the analysis of the problem requires the simultaneous solution
of the three equations: the concentration of the chemical dissolved in
the water, c, the mass concentration of the chemical per unit mass of
interacting species, r, and the concentration of the species itself, m.
Since this compartment may be further subdivided (inorganic and organic
solids, multiple species of fish), equation (2) is more generally expressed
as a sununation of the individual components of the interacting substances:
11
p. = E r.m (14)
1
The specific conditions for which the analysis is performed frequently
permit simplifying assumptions to be made. In laboratory batch reactors
and in certain prototype situations, the rate of change of the interacting
species may be zero — i.e. a constant concentration of suspended solids or
biomass. Thus = o, from which an equilibrium concentration of solids
or bioznass follows, resulting in two simultaneous equations to be solved,
instead of three.
3. Dynamic Equilibrium
As may be evident from the above discussion, one of the essential
properties of the analysis of this water quality problem is the inter...
action between the dissolved and particulate states of the constituent,
which, in time, leads to a dynamic equilibrium between the two components.
Consider the most simplified conditions of a batch reactor in which the
mixing is of sufficient magnitude to maintain a uniform concentration
throughout the volume of fluid. Assume the concentration of absorbing
solids, m (M/L 3 ) is constant. Let c and p be the concentrations (M/L 3 ) of
-32
-------
the dissolved and particulate components. If there is neither transfer
nor decay of the chemical, the total concentration, CT remains constant
in time and is equal to the sum of the dissolved and particulate:
(5)
The latter is related to the concentration of suspended solids, m, as shown
by equation (2):
p = rm
The equilibrium between the dissolved concentration in the water and
the mass concentration of the solids is usually expressed in terms of a
partition coefficient:
r
c mc C)
or
Equation (6) is the linear portion of the Langmuir isotherm. Although not
always representative of actual conditions, it is a reasonable approximation
when the solid phase concentration, r, is much less than the ultimate ab-
sorbing capacity of the solids. Combining equations (5) and (6), the total
concentration may be expressed as:
c =c+11mc= —+p (7)
T urn
The product, im, is a convenient dimensionless parameter, characteristic of
a particular system under equilibrium conditions. For a specified value of
¶m, the equilibrium distribution between the dissolved and particulate con—
centrations is established by equation (7), as shown in Figure A-2 ChQp.X.
The distribution between the dissolved concentration and the particu-
late concentration in the various levels of the food chain may be expressed
in an identical fashion. Accounting for the distribution for various types
of adsorbing solids and various levels of the food chain, each with its
characteristic partition coefficient, equation (7) may be more generally
expressed:
-.33-
-------
CT = c [ l + ElJ mj] (8)
The distribution may thus be categorized in accordance with the adsorbing
solids (organics, clays, silts and sands) or the accumulating biomass
(phytoplarikton, zooplankton, fish and macrophytes). Since the total bio-
mass mass in most natural water Systems is usually an order of magnitude
less than that of the non—viable Solids, the equations defining each cate-
gory may be decoupled and the former may be solved independently. Under
those conditions in which it may be significant, it may be readily incorpora-
ted as sho m in the above equation.
4. Kinetic Interaction
The equilibrium, described above, is a result of the kinetic inter-
action between the dissolved and particulate. This property which dis-
tinguishes the analysis from that of purely dissolved substances, leads to
equations of a more complex form. In order to gain an insight into the
nature of these interactions and an understanding of a practical simplifi-
cation, consider the kinetics in a batch reactor, as described above, in
which interaction is taking place between the dissolved and particulate com-
ponents and the former is being transferred by volatilization or transformed
by chemical or biological degradation:
K 1 K 3
p c - (9)
The reversible reaction (K 1 K 2 ) may represent the adsorption_aesorptjon
between the dissolved component and the particulate in inorganic phase (sus-
pended or bed solids) or the assimilation_depuration in the organic phase
(aquatic organisms). These kinetic coefficients may be functions of the
solids concentrations, as discussed subsequently. In any case, their ratio
is a measure of the distribution or partition coefficient. The non-rever
sible reaction (5) describes the decay or volatilization. The kinetic
equations are:
(10)
-31--
-------
—K 1 p+K 2 c (II)
Addition of equations 10 and 11 yield
dC
(12)
If equilibrium is rapidly achieved by contrast to the other time con-
stants, specifically identified as K 5 in this-example, the dissolved compo-
nent, c, may be expressed in terms of the total Concentration, CT, by equa-
tion (7), substitution of which in (12) yields
c = c [ Be9t + (l_B)ehtj (13)
in which g,h are the positive and negative roots of the quadratic
g,b = — [ 1 + m)
in vhichK=K 1 +1 (2 +1(3
/ L K 1 ’
It may be readily showii that g and h are always real and negative.
In the case of adsorption_desorptjon, the assumption of instantaneous
equilibrium is frequently made — i.e. the coefficients K 1 and K 2 are of
sufficiently large magnitude so that the exchange between particulate and
dissolved occurs very rapidly. Furthermore, for organic chemicals, the
decay coefficient is usually of a much smaller magnitude than the adsorp—
tion—desorption. Thus
dc
+ K 1 K 3 c 0
dc - — K 3
—— c (1)
-------
in which
K 2
= distribution or equilibrium coefficient
1
An a ditioria]. insight is gained by developing equation (114) in an alter-
nate manner by adding equations (10) and (ii) which yields
dc
- K 3 c (15)
Assurie the interaction between c and p is an adsorption...desorption pro-
cess. The dissolved concentration, C, may therefore be expressed in terms
of the total, CT, by equation (7) substitution of which in (is) yields
dc K
dt _l+IImCT 1
The total concentration decays in accordance with the dissolved coeffi-
cient modified by the parameter ¶zn. As a physically realizable example,
consider the transfer represents a volatilization process, in which K 3 is
the gas transfer coefficient. The total concentration CT decreases at a
slower rate than would be the case if there were no partitioning to the par-
ticulate form, with the total in dissolved form (lTm = o). In defining the
rate of change of the total, the decay or transfer coefficient is simply
modified as shown by equation (16). Conversely, if the decay is associated
with the particulate component, the coefficient would be reduced by the
fraction ¶m/ [ l + urn], in accordance with equation (7).
If both the particulate and dissolved components are subject to decay,
by more than one mechanism, equation (16) becomes
dcr, . ITmZK
dt = + 1 + ] CT (17)
in which the subscripts, c and p, refer respectively to the dissolved and
particulate decay coefficients.
—3G. -
-------
The assumption of “instantaneous” equilibrium as expressed by equation
(i4) through (17) is a valid representation, Or model, of kinetic reactions
provided the time to-equilibrium, determined by K 1 and K 2 is rapid relative
to the other phenomena which affect the substance,; K & K • This condition
is generally applicable to the adsorption—desorption process, since its
equilibrium time is usually much shorter (mm-hours) than that of other
kinetic effects, which may be in the order of days, months or years.
In sum ry, the models for the analyses of organic chemicals and heavy
metals are similar to those developed for constituents which are natural
components of ecological cycles. The terms relating to the particulate form
and its interaction with the dissolved component are the additional compo-
nents to be incorporated. These, with the othe’r transfer and reactive
terms, cover the various pathways of distribution. Accordingly, each of
these routes and the associated mechanisms are described in the subsequent
sections which comprise the first half of these notes.
The second half is devoted to the development of models, which incor-
porate these reaction mechanisms with transport and inputs, to define the
temporal and spatial distribution of toxic substances in natural systems.
By virtue of their interactions with the solids in these systems, it is also
necessary to analyze the distribution of the various types of solids. Fur-
thermore, the exchange between the suspended and the bed constituents is
taken into account. The models, which are developed in the second part of
the notes describe both the physical—chemical effects in the inorganic realm,
in conjunction with the solids, as well as accumulation and transfer through
the various elements of the aquatic food chain. Application of these models
to various natural systems are also presented.
-------
OSoPiio )
0 I’o*PiO.J
I” .
I.ID PI$ 3Ø
• .ceLJ D
I(%WE TIC 4
s :E cTo! .S
LSTRI B iTio i
OL%DS *
D si g
Le ]
0 tisisV
L-J P tIcAN,b*
DI&A1
‘-I-
tlb
I
4
I . — -
IThflOtJ A A
O .Lo5 *
OF
To,c t C.
FIGURE j
-------
B. CLASSIFICATIOI OF AI ALYSIS AIiD MODELS*
Equation (1) is the most general expression to define the distribution
of a toxic substance in a natural water body. Given the characteristics of
the drainage area and water system and the nature of the substance, it takes
on a more definitive form. As described previously, the distribution bet ’ ‘P-n
the dissolved arid particulate components of the toxic material and the ki: .-r. c
interactions are the essential factors, which are common to all types of
models. What distinguishes the various models, discussed in the subsequent
sections of the notes, are the transport components of a specific water
system and the characteristics of the bed, with which it interacts. Thus,
the basis of the classification lies, to some degree, in the transport
regimes of the general types of water systems — lakes, streams and estu-
aries, but more significantly rests on the transport characteristics of the
bed itself, and the magnitude of the water—bed interaction. The kinetic
and transfer routes are common to all types. Each of these factors are
discLlssed in this section, concluding with the proposed classification.
1. Kinetic and Transfer Routes
The cornponents and their Interactions are shown diagrammatically in
Figure 1. The concentrations of the toxic substances are presented in both
the water column and the bed. The distribution between the dissolved, C,
and particulate, p, components is determined by the magnitude of the adsorp-
tion and desorption coefficients, K 1 and K 2 , and the concentration of the
adsorbing solids, m. Each of these components may be susceptible to decay
and exchange, as shown. For conservative, non—volatile toxics these trans-
forrn routes are negligible but the settling—resuspension transfers are
potentially important for any substance, regardless of its other character-
istics. These are the characteristics of the system and the substance which
essentially determine the complexity of the analysis.
2. Transport Regimes
Each of the general types of natural water systems may be classified
in accordance with characteristic fluid transport regime and the interaction
of the water with the bed. The components of the transport field are the
advective Cu) and dispersive CE) elements which, in general, are expressed in
three—dimensional space. Each of the systems to be considered — streams, estu-
aries, lakes and coastal waters — are usually characterized by a predomi-
*
Donald J. O’Connor
—3’—
-------
riating component, in one of more dimensions. The transport in streams may
be frequently approximated by a one—dimensional longitudinal analysis (A),
in lakes by one or two dimensions (B), in which the vertical is the major
component and in estuaries by a two—dimensional scheme (C) (longitudinal
and vertical, as shown in Figure 2A. A spatially uniform condition- (com-
pletely mixed) is type D whose transport coefficient is the detention time,t.
3. Bed Conditions
The bed conditions, which are relevant to the analysis are shown in
Figure 2B. They may be classified as inactive, or stationary, and active;
or nixed. The latter may be further subdivided: without and with horizon-
tal transport. A further characteristic of bed conditions relates to the
phenomenon of sedimentation. All natural water bodies accumulate, in
varying degrees, materials which settle from the water column above. In
freshwater systems, reservoirs and lakes are repositories of much of the
suspended solids which are discharged by the tributary streams and direct
drainage. In marine systems, estuaries and embayments accumulate solids
in similar fashion and the coastal zones to a lesser degree. In flowing
freshwater streams and tidal rivers, suspended solids may settle or scour
depending on thea magnitude of the velocity and shear associated with the
flow. Bed conditions in these systems are therefore subject to seasonal and
daily variations, while the beds of estuaries and lakes which are also sub-
ject to such variations, tend to accumulate material over long time scales.
The increase in bed depth and concentration is expressed in terms of a sed-
imentation velocity 1 measured in terms of months or years 1 by contrast to
the settling velocity of the various solids in suspension, measured in
terms of hours or days.
1 . Classification of Models
The classification, suggested in these notes, is essentially based on
the types of bed conditions shown in Figure 2B, in conjunction with one of
the three types of fluid transport shown in Figure 2A. The three general
types are enumerated in a progressive fashion from the simpler to the more
complex, as presented in Table 1 and described below. The final form of
the equations is based essentially on one of the three types, in conjunc-
tion with the kinetic interactions shown in Figure 1.
—40-
-------
TYPE I - STATIONARY BED
A stationary bed is basically characterized by zero to negilgible
horizontal motion. This condition is most commonly encountered in lakes
and reservoirs of relatively great depth, with minimal winds. It also occurs
in freshwater streams under low flow conditions and in marine systems with
little tidal ri xing. It may therefore be associated with any one of the t}.ree
trar sport systems shown in Figure 2A.
The essential characteristic of this type of system is relatively low
degree of vertical mixing in the fluid. The bydrodynamic environment is one
which permits the gravitational force to predominate and suspended particles
of density greater than that of water settle. The accumulation of this mater-
ial in the bed causes an increase in the thickness of the benthal layer, the
rate of increase being referred to as a sedimentation velocity. The bed is
also characterized by minimal or zero mixing in the layer in contact with the
water.
TYPE II - ! D LAYER
This condition, which is probably more common, is characterized by some
degree of r ixing in the contact layer of the bed. The mixing may be due to
either Dhysical or biological factors — increased levels of shear, associatci
with horizontal or vertical velocities and gradients or bioturbation, attri-
butable to the movement of benthal organisms. It exists, therefore, in lakes
where the wind effects extend to the bottom and in streams and rivers under
moderate flow conditions.
In each of these cases, the shear exerted on the bed is sufficient to
bring about mixing in interfacial layer, but not sufficient to cause signifi-
cant erosion and bed motion. The net flux of material to the bed is the
difference between the settling flux and that returned by the exchange due to
the mixing. Thus, the bed thickness may increase or decrease and the sedi-
mentation velocity may be positive or negative. The mixed layer interacts
with a stationary bed beneath, as shown. This type of bed condition may
also be associated with any of the three fluid transport types, but is
more usually associated with type B and in the littoral zone of lakes,
where the yater depths are sufficiently shallow to permit wind effects to be
transmitted to the bed.
-4 - , -
-------
TYPE III - BED TRANSPORT
This bed condition possesses both mixing and advective characteristics.
The shearing stress exerted by the fluid is of sufficient intensity to cause
erosion and resuspension of the bed and the fluid velocity of sufficient
magnitude to induce horizontal motion of either or both the resuspended
material and the interfacial bed layer. This phenomenon involves the com-
plex field of sediment transport, which has been greatly developed in streams,
but much less in estuaries and lakes. The bed system may now be envisioned
as three distinct segments: a moving interfacial layer, a mixed zone and a
stationary bed beneath. There is vertical exchange between the moving
and mixed layers and the vertical transport in the bed is characterized by the
sedimentation velocity.
This type of bed regime is associated only with types B and C fluid
transport system. The direction of horizontal motion of the bed in accord-
ance with velocity vector of the fluid in contact with the bed surface. In
fresh water streams and rivers, the bed transport is downstream in the
direction of flow. While in estuaries, the net bed transport is upstream
in the saline zone due to the tidally averaged motion as shown in Figure 2B.
- 42—
-------
C
A B
C 4 rc .i &j
7, .c p
F E- FLU ’J%IJ
c.Te ,Ms( i#Et.3
U- ‘ *et% trjec
V ie.i-4ico ieAOC’ %j
e wwtU 9
LA gES AeJD
Co mL ‘JItTh t Q- colt
V- VoI ’ s
ts ‘YCj -
rusE &I
tA -
U
Cernp ’-4e
%e.
- - T t S?o T C-GtPiES
I
W &T
5ID 4£ i r .JG
BeD
—-
bt4 ,i %; IP%Qu
DEFI’)%TtO OF
ft ThTs° J OC rc’4
c
— -----
N__
__________ -
C.
FD
? ID,4E.arisjG BED
OV _____
U 1 -
It rLspe 3 ..vv .
I • ) ct t tQ”
$ C e -
f1c uP.. E 2 - BED CQfl sO S
-E
vi 1 N
% w r
i. 4
ii
• LI
u -.43-.
-------
TABLE 1
BED CONDITION
I II III
STATIONARY MIY D SEDI!€NT
BED LAYER TP NSPORT
WITH WITH LAYER
___________ BED & BED
Ub 0 0 >0
eb >0 >0
DEEP, MODERATE LITTORAL
A LAKES
MINIMAL DEPTH, ZONES
RESERVOIRS
WINDS WINDS
COASTAL ZONE
B STREAMS
& RIVERS
LOW
FLOW
MODERATE
FLOW
HIGH
FLOW
C ESTUARIES
EMBAYMENTS
ENCLOSED
BAYS
MINIMAL
TIDES
LITTORAL
ZONES
MAIN
CHANNEL
LOW FLOW
MAIN
CHANNEL
MODERATE
FLOWS
D CO LETELY
MIXED
APPLICABLE TO ALL TYPES,
PARTICULANLY TO LAKES
RESERVOIRS & EMBAYI€NTS
.44.,
-------
LAKES Ai D RESERVOIRS
A. I1 TRODUCTI0N’
The analyses of wa r quality in lakes and reservoirs are consi ered
in this section. Because of certain similarities which exist between lakes
and oceans, many of the models described in this chapter are appropriate
for problems in the coastal and off—shore regions of the oceans. The spec-
trum of time—space scales which characterize the analysis in these water
bodies is much broader than that encountered in streams and estuaries.
This difference is attributable not only to the geornorphology and dimen-
sionality of the respective systems but also to the driving forces and com-
ponents of the transport terms. Thus, many water quality analyses in
rivers, tidal and non—tidal, are one—dimensional within the relatively
def:ned bcundary of channel cross section. Furthermore, this uni-dimen—
sionality, which applies both to flow and quality frequently exists under
steady—state conditions.
By contrast to the one—dimensional steady-state analysis, many water
quality problems in lakes and oceans are time variable in two or three
dimensions. The deep, relatively slow moving, hydraulic regime, over wide
horizontal scales, is en important factor in this regard. Because of the
greater depths, thermal differences and density structures are seasonally
er.countered. The vertical distribution of many constituents associated
with these regimes is a significant water quality problem, which has a
counterpart in the toxic problem.
A large scale analysis may frequently be used on the assumption of a
spatially uniformity of concentration over the time unit of analysis.
Since large scale problems (10—100 miles) are usually associated with equi-
valently long time scales, the incremental time step of the analysis
may be of sufficient duration to justify the assumption of spatially uni-
formity. For example, if the concern is the long term build up of conser-
vative toxic substances which may occur over years or decades, an appro-
priate time step of such an analysis is the year. Over this period many
lakes and reservoirs, with their characteristic spring and fall over urn
* Donald J. OtConnor
‘13
-------
and mixing due to winds and seiches, reflect a spatially uniform condition.
More specifically, the variations which occur over the year are small by
contrast to the increase in concentration anticipated in future years. At
this relatively large time-space scale, the typical time variable problem
is the long term build_up of a toxic constituent. The steady—state relates
to the equilibrium concentration, resulting from a constant input, and the
time required to establish equilibrium, if indeed one is possible.
The following sections of this chapter describe the toxic distributions
in comoletely mixed systems of lakes and reservoirs and secondly, address
the analysis of the vertical distribution of toxic substances in these water
bodies. The completely mixed analysis is coupled with Type I and II bed
conditions with various applications. it is unlikely that a Type II con-
dition would be encountered in lakes under this scale assumption. The
vertical analysis is presented with a Type I bed condition with a specific
example of quarry with lindane and DDE inputs. A final application is dis-
cussed with respect to Toxic Substances in the Great Lakes. In each case,
the distribution of suspended solids is first developed, followed by the
analysis of toxic substances, which receives input from the solids analys .s.
-------
B. A! ALYSIS OF CO LETELY Mi) D SYSTEMS*
1. Type I Analysis — Stationary Bed — No esuspension — Sedimentation
a) Sus ended Solids
The concentration of suspended solids in a reservoir or la ’.e d —
penis on the physical characteristics of the incoming sediment and the
hydraulic features of the system and inflow. The important characteristics
of the sol ds are the grain size and settling velocity distributions and the
behavior of the finer fractions with respect to aggregation and coa&uation.
The detention time and the depth of the water body are the significan: :r.ydrau_
lic and gec iorphological features. The following analysis assumes steady-
state conditions in a completely mixed system, in which the concentration of
solids is spatially uniform.
These assumptions are obviously crude, but of sufficient practicality
to a it at least an order of magnitude analysis of the problem. They are
prec:sely the assumption, implicit in the analysis of the “Trap Efficiency”
of reservoirs in which the efficiency of removal of solids has been corre-
lated to the ratio of the reservoir capacity to the tributary drainage area(l).
Consider a body of water whose concentration is spatially uniforn through-
out its volume, V, receiving an inflow, Q, as shown in Figure B-l. Under
steady state conditions, hydraulic inflow and outflow are equal. The mass
balance of the solids takes into account the mass inputted by the inflow,
that discharged in the outflow and that removed by settling. The mass rate
of change of solids in the reservoirs is the net of these flu .xes:
V = - — vAin 1 (1)
in which
in. = concentration of solids in inflow
1
rn 1 = concentration of solids in water body
v = settling veloc’ity of the solids
A = horizontal area thru which settling occurs
The flu ,c Qm., equals the rate of mass input, W. Dividing through by the
volume, V, the above equation becomes
d i n 1 V 3.
= v — m ( — + K) (2)
*
Donald J. O’Connor
- -4v7-.
-------
in which
t = detention time = — CT)
0
S
= settling coefficient
= mean depth = CL)
Under the steady state condition, equation (2) may be expressed as,
W/Q
1 + ‘ t 0 (3a)
Division by W/Q yields
Zn 1 - 1
3b
so
which is the fraction of the incoming solids rertaining in suspension and,
with the assui ption of complete mixing, is also the concentration in the
outflow. The fraction removed is simply
f — 1+Kt R)
The dimensionless parameter, Kt, represents the combined effects of the
settling characteristics of the solids and the average detention time of
the system. The coefficient, K 5 , may be replaced by its equivalent, v/H,
and the dimensionless parameter is v /v 0 , in which V = — = , the overflow
rate of the system. o
It is apparent from the above development that conditions in the bed
have no effect on the concentration in the water body, because there is no
resuspension of the bed material. The benthal concentration, on the other
hand, is due directly to the influ.x of the settling solids. The rate of
change of mass of solids in the bed is therefore
dM 2
= + A 1 vm 1
The mass, 142, equals the product of the bed volume V 2 , and bed concentration,
Zn2. Thus
2d 2In 2)_m 2 dV 2 +V 2 2
dt dt — dt dt — s 5 l .5a)
-4,—
-------
Dividing through the A 5 , and expressing the resulting as V., th final
result is
V V
S d
= I — U )
at steady-state — i.e. when the mass settling rate equals the accur.uJ. tiori
rate:
= m 1 —a. (5c)
b) Toxic Substances
The distribution of toxic substances, such as organic chemicals and
heavy metals in reservoirs and lakes is established by application of the
principle of continuity or mass balance, in a manner sir.ilar to that employed
in the case of the suspended solids. Each phase, the dissolved and particu-
late, is analyzed separately, taking into account the adsorptive—desorptive
irteraction with the other. For the dissolved component, the mass balance
includes decay and transfer terms(2) ) in addition to the inflow and outflow.
The basic differential equation
w
dc 1 c c
= - i—. — K c 1 - K 0 m 1 c 1 + K2p1 C )
in which
V = reservoir volume (L 3 )
= rate of mass input of the dissolved component. (I /T)
c i = dissolved concentration in water body (r’ /L 3 )
= overall first order rate coefficients (T ) which may include b±olo-
ical degradation, hydrolysis, direct photolysis & volatilizatior..
K = the adsorption coefficient (L 3 /M—T)
in = suspended solids concentration (M/L 3 )
K 2 = the desorption coefficient (T )
pi = particulate chemical concentration (M/L 3 )
For the pal-ticulate concentration:
- A. - K 5 p - K2p + K 0 m c i (7)
-------
in which
W = rate of mass input of the particulate adsorbed chemical (MIT)
K = settling coefficient (T’)
Adding equations (6) and (7) cancels the adsorption and desorption terms
and yields the rate of change of the total concentration CT in terms of the
dissolved and particulate:
dCTl W
= v - - Kc 1 — K 8 p 1 (8)
The sorption coefficients, K and K 2 are usually orders of magnitude
greater than the decay and transfer coefficients of thc dissolved and par-
ticulate. The rate at which equilibrium is achieved between the two phases
is very rapid by contrast to the rates of transfer and decay. Thus liquid...
solid phase equilibrium is assumed to occur instantaneously. The dissolved
and particulate concentrations, C and p, may therefore be expressed in
terms of CT by equation 14, substitution of which in equation (8) yields:
dc c K K ¶m 1
T 1 - W T 1 c 1 _____
at — V 1 - t 0 - 1 + cTl - 1+llm 1 CT
Under steady-state conditions, the above may be expressed, after multi-
plying through by t:
- W/Q
t
1+ ° [ K +lTni 1 K
l+lJmi Ci Si
For those substances, whose dissolved components are not susceptible to trans-
fer/decay, such as heavy metals, equation (9) reduces to
(10)
Ti l+K t [ ml ]
S1 0 l+lImi
Note that equation (io) is identical to equation (3a) with the exception t t
the dimensionless settling parameter Kt is multiplied by the fraction
—so—
-------
The latter terz extresses the fractj of t:.e t;tal co c r- w :: : 5 ir.
the ;articu:ate fo=. For values of ¶r. >> 2, :t is aptare t t:tat ect.c.tj
fl) is ideinica: to (3a,. Witn refer r ce to eqtatio z 9 ) :c;, t:.e
fraction rezo-,ed i s
— n
:. re:t ::. :f ectatic C .,) indicates that the rtr.: 1 .: cff:2:et:;-
i:Lii. : :e’.e ent ort t e aete:t:;. titr :r i E ttjj.c coeff:...
:s the ratic, of t e setti z.: Vel:2:ty :f : e s:fl . art. t:c
c: ::.t re!-rv:.ir cr 2.a-:e. Fr :- a-r.’ r. t: ar. .c:.str-; t:-.
::.e-.i:a:; the aa. :ti-za: tar.re:er re .nrei :s t- — .rti:: ::e:f:c:..:-
::). ttc :ase of arrant: c: er.:cLi 0 1.... ar-c s :e;t_ .:. t_.
. Lt’.fl.tj ’ -e transfer, y:rc.;’t:: Cr t:.:t;:.- —ce re :t_:.:.,
:tLflj:: of ;:- ree-:L:.t re ct ,, coefnc;e ts is n cersa:y e;st:c:. t
::-. :ete::t::z. t...rt avera: , i :tL, Cnct ar rraifl--
e.:- .aze.. c:. tr avera:- :ras r:L or ..rnt.C :::.±:tj,:.; tvez the t:- -
srrLes :f the anal: s:z. stttflr: e o::ty settit; Cc :f::_E -
-e c : - ±i:- :t :-- er a :i : :‘r..- :rtfn. _ c. fj -,. c:n entr:t-:’-
• - . : - . , ,• •.‘ . -— •.. — . c ---4 • - — - — ‘-:- - -, $ .. .
—. __ a.._. — I .. ,. • • _ -. -s . -
J..Lte: C...i wfl_y, w i:L, w_th t:e s:fli: co::c . ttrat:c:., .-: Ci! t1t.
: anettr ¶::. ;L:e:. tc::; nt - e n r.t :..rezertr :f tL tota. &r.
:i .t i ::::er.trat_ :.s cf the heavy ret /c:- s::i : ::.ec.i:c, ten- ‘n
CLc..Lr.t _. L- . :t.:t infcrtati t.: rtr a;-.L: ef: :c: rt: -
far tzt:. !t t:2 and ci-.ezj:a: vLL.n arr :c:..r ,ti--c
: ted a cv , cert fr cher.:nl: nt :; z- st.t ’- ;:en t:
- • •• - - t—- — J ’ ., .4 - - —a ’ — .
-r _z e .rat_ t... ..
t n :L±:: t:--.., of ?o:enti : t&nttt of these rc te: — e.g. th Vat::
rcL: r &: : E :flt:r arc :ro;ertic- wnicl. terni- CSEe&srt-rtt of t:- —
cr n-Jca tra:; tr C - . ) 5). L cratcrv er -c-rjner ts na- e :ecessar-.- to
n nt the cnezic : an: L1ol: cai ro ca — e.c. tht io cn ad ja:_:. of
s:ance (6 )4 ; ;. In arty particu lar case, an assessment, eIther a.:.’t:
ca l Cr ezperjrAenta! sha zld be nade t establjs- the degree to whi:]. tr
fornatjon or tran:fcr aay be £icnificarjt. Solutions of the above are
i:. F igure E—e.
-------
The bed concentration may be described by constructing its mass balance.
Infliax is due to the toxic substance associated vith the settling solids and
the volumetric accumulation is accouLted for by the sedimentation velocity
as in the bed solids analysis (equation 5)
dc
K c,., -t K c (2.2)
dt P1 5 1 P2 d 2 T 2
at steady state
f v
1 S
C (1.,
T 2 f v T
P2 d
in which
f = the fractions dissolved and partjculat
1 1
v = settling veiocity
= sedi ientatjo velocity
Since the bed solids concentration in 2 >>> and :s u ua12 .y >>>
as a reasonable approxj tjon
1’ “landf O
P2 a 2
V V
S
Cm =P2=f Cm —p
P IVd i V
substituting for p =
V
S
r 2 m 2 = — r im i
Vd
since v n 2 = v:n 1 under steady state, then
P2 r 1 ( )
The above analysis does not take into account the Possibility of the
exchange of the dissolved component between the bed and the water. This is
discussed in the folloving section, which considers solids resuspensjor. —
condition more likely to enhance exchange of the dissolved component.
-------
2. 2y e fl AnCysis — Mixed Bed —
The tyte of ara.yns describe. Sr. thiE secti3r iz :ienjc_: t t:-.r. of
tte previous, -wits the adLt:icn of a. reEtstensic tent i b th the sc: z:
&.:.c toxic e;-aa::;:.s. The ;h:-zica: strtcttre of tze zy te is s :w:.
raiz tica::-,- 5: ?2.:..re E—, :ro vr.ich it is atp&re:: a ze:s a:a:c
iet- c;ea fcr .t3th tnt water cc t - -a i t:e .ei, sn:
. , E...e:ie Z.flds
rEcte :f ::.ar.re of scfl s it. :ze c :
= * 7. - *7’ — +
= r .:;cs: 7cc:ity — : /:
= c::cen:ra::D: of s : r in the :ed —
rtan5 r t rt arc as rren; s:y _efi e tic::
- -- - - e.n
r;- f.... :f sc _c C- as a-..
-“‘‘tV Vt..fls
— . • 1
— E_ - J.. - +
-. S .’ - • - —
• 1 ‘- 1 —
= avc:-L:e dc:tL of :- vater cc z:
. -sss £ isYCe of the be SOiIdE it.cu5e 5 the ir.f :-: :f trc
ccfli: ::-:r :r.c wi .ter (ar as c:tflow frct. tr.e t dte tc the re:
L:fl::±LtLt ’::.
— _ _ _ .r ’ a ”’
Ct
i:. which
— averLc dctth of the bed
At steady —state conditions, = C, the concentrctjor. in the bed Zr.:.- h
exn-essed In tens of the concentratior , in the water fron ( 18):
a53w4.
-------
m 2 — (19)
in which -
V
=— s _
V +V
u d
Sub tjt tj 0 of which in equation (17) under steady state yields
V V V
W 1 s u d
0 v_mj r —— —mi
0 u d
Ex ressj . = K and solving for m 1 , after simplification gives:
— W/Q ,
1+8K t
Si 0
in w .ich
Vd
u d
The vaiue of fails between zero and unity. The latter repre ents
the ease of no resuspension v = 0 and 8 = i, reducing (20) to (3) and e
former of no sedimentation Vd = 0, reducing (20) to
m l = W/ li
, ‘
In this case the settling flux is exactly balanced by the resuspensicn
fl x resulting in zero net change and the concentration of solids is s iy
that of a conservative substance, as indicated by (21).
The bed concentration follows from substitution of (20) in (19):
- W/Q
m2_ + 8 K
so
Algebraic Simplification yields
m 2 = — W Q to (23)
For lakes or reservoirs of shallow or moderate depth (E 1OM), oder_
ate high settling velocities (V 5 ‘ ‘ 3M/DAY) and low resuspension ve1ocitj
-------
l M/Th), the 8 tent is more than an order less than the sedi! r tatjon
term and (22) reduces to
m2=FV (2k)
:r. which
K Vd
— H 1
b) Toxic Substances
The equations for the toxic substance are developed in an identical
fashion as in the T rpe I Analysis. Each phase in the water column, the dis-
solved, c, and the particulate, p, is analyzed separ - ely with adsorption and
desorption kinetics in addition to the input, outflow and settling tents.
urthermore, allowance is made for the exchange of the dissolved co- ponent
between the water and the bed, expressed in terms of the differer.ce -. t: e
dissolved concentrations. Addition of the two equations cancels the ai—
sorption —desorption terms and yields:
dc , ., W C,.,
= vj- — — + ‘ u 1 P2 + Kb (C2 — ci) (25)
.r. wnich
the subscript 1 refers to the water column and 2 to the bed
cT = concentration of toxic in the water column
K = = selling coe.ficient (lIT)
S £21
V.
K = = resuspension coefficient (lIT)
UI ill
K
= -j . = dissolved exchange coefficient (lIT)
K = transfer coefficient of the dissolved between water and bed (a.)
Expressing p and c as fractions of the total concentration (equation of
the previous chapter) and combining similar terms yields:
dcT I = - + f K 1 + d 1 CT I + + d 2 CT 2 (26)
the bed equation is developed in a similar fashion
-------
T 2 = [ r K 52 + d 1 Kb] CT — [ r (K + Kd) + d 2 Kb 2 CT (27)
in which
f = particulate fraction in each segment, 1 arid. 2
P1,2
= dissolved fraction in each segment, 1 and 2 -
1,2
The working equations for the steady—state condition are developed in a
ianner similar to that of the solids. Under steady state conditions, the
total concentration in the bed is expressed in terms of the total concen-
tration in the water with equation (27). Substitution of (27) in (26)
yields the water concentration as a function of the input load, W, and
the parameters of the system. Since m2>>>ml and ¶m2 >> 1, f “ land
d 2 “ 0. For this simplification, which is realistic for IT>i000, the water
and bed concentrations are respectively
W/Q
C 1 — 1 + 8 d. [ lIm 1 K + Kb (28)
fK +fK
- pS2 4D2 ()
2
U2 2
in which
V
0 _____
p
u d
1
— l+l!mj
— ¶mj
p — l+l 1 m 1
V
K = —
s H
Kb=
V
K= o
U
K =Vd
d H
For the condition of negligible exchange of the dissolved between water
and bed (K o), the above equations reduce to -
-------
W/Q
CT = 1+ f K t (30)
P1 i 0
c = c (31)
in which, in accordance with equation 1
V
S
=
V +V
u d
Fo - toxics of high partition coefficient and systerns of high solids (1
, , 5), the above respectively reduce to equations (21) and (19), the
equivalent solids equations.
-------
T’IP .
r
3I
LIcE
w
V
‘4
1
E Su P E 3 S%OU
• a
0
era
I4&ISS IMF Ug
V OL. U
I-% bE T%4
4 4 SoUDS
CT To’ t%C.T ThL
4 DlS t b TQ cT O13
1 j C.T%0,J
ETTLWG V Loci ’f
E5USPF, sto VEtOClt’f
4&Po . 1 oi cotrI Ic% 4i1
t ( D%s o .g b
Tn u eoE FFIcuLI r
*&Q.1 cuL&T , C6.’4
w.1 ‘Is
L’ 4
I
M/Ll
‘ -IT
‘I
I ,
‘I
It
5Ub3 1% PT !
I WArtt
‘I’
ScL%O
“Jet
C,’
TOXIC .
FIG. B—i Schematic of rpe I & pe II Solids Parameters
-------
ANALYSIS
0.0 flr ’c.
=
AJ € JH
to
0.0
0.03
0. I
1.0 ¶ rndc
FIG. B—2 Fraction Remaining for Various Detention Times
and Kinetic Parameters
-.5’ . .
0
2.
-------
TYPE I ANALYSIS —
fp o.o7.
cp=o.t
, sto
8 10
r,. B—2 ( unt,’d)
0 4 6
1
. ‘
I)
2.
4
I0
Fraction Remaining for Various Detention Times and Kjnptjc Parameters
-------
*
Saginaw Bay - Solids and PCB Model
Steady S”tate Toxicant Model -_Theo
In order to understand the interactions Ltwcen s. d-
irnents, water column solids and a given toxicant, several time
variable models have been employed. These models attempt to
incorporate the mechanisms of solids settling, sediment resus-
pension, net sedimentation and transfer to the deep sed mer.ts,
interstitial diffusion of dissolved toxicant and other decay
and transfer mechanisms. The difficulty with the more complex
interactive time variable toxicant models is that the specifi-
cation of the various parameters (e.g. resuspension velocity
and surface sediment solids concentration) is not unique and
var .ous combinations of the parameters, within reported ranges,
yield a similar calibration.
Consequently, it is desirable that a procedure be
developed that utilizes available field data for calibration
and that minimizes the number of parameters that must be
specified. A simplified steady state approach provides a
direction. Since the analysis framework is steady state,
questions related to the time it would take to reach a new
equilibrium state cannot be answered. Furthermore, the time
for the entire system of water column and sediment to reach
steady state may be long. On the other hand, as noted above,
complex time variable models sometimes tend to obscure the
principle mechanisms of net settling and water column-sediment
exchanges. A steady state framework, therefore, is a simplified
*
Robert V. Thoznann and 7ohn A. Mueller
-------
first approximation to chemical fate that does not address issues
related to temporal questions but does provide a useful model
for estimating chemical concentrations in a simpler way.
Suspended Solids Model
Consider first the steady state model for suspended
solids in a multi—dimensional system. It is assumed that the
bed sediment that is coupled to the water column is stationary.
Figure 10 shows a definition sketch. The mass balance equation
for the solids in segments l, and is, using backward finite
differences is
o = — Q 12 M 1 + £12 (M 2 -M 1 ) — V 1 AM 1 + v 1 AM 1 (10)
0=v AM -v AM -v AM (11)
si 1 ul is sdi is
where N 1 and M 2 = solids concentration in water column segment 1,2
EMIL 3 ; L = volume of water plus solids)
M 1 = solids concentration in sediment segment, is
S [ M/L 3 )
W 1 = input solids loading [ MIT; M=xnass of solids)
Q = flow from segment 1 to 2 (L 3 /T]; A=sediment
12 2 W
area CL 3
= bulk dispersion between 1 and 2 [ L 3 /T]
v 1 = settling velocity (LIT]
v = resuspension velocity (LIT]
ul
Vdl = sedimentation velocity [ LIT]
A similar set of equations can be written for segments 2 and 2s.
Equation (11) can be solved for the sediment concentration
as:
V
si
M 1 5 = +v 3M 1 = a 1 M 1 (12)
ul sdl
- Vs 1
where =
1
-------
Substituting eq. (12) into eq. (10) and simplifying
gives:
0 = W 1 — Q 12 M 1 + E’ (M 2 —M 1 ) — WAM - (13)
where w is the net loss of solids from water column segment
#1 and is given by
= V 1 Vdl (14
si V +V
ul sdi
Note that eq. (13) essentially states that for a multi-
dimensional system such as Saginaw Bay, the sediment interaction
can be substituted out of the equation set and incorporated in
the net loss parameter, w 1 . A mass balance around the sediment
segment then yields
v AM = w AM (15)
sdl is sl 1
which simply states that the solids flux into the sediment
layer from the water column is balanced by the solids flux
leaving the sediment segment due to net sedimentation. In
principle, the net sedimentation velocity can be measured so
that the solids concentration in the sediment can be calculated
from eq. (15). In practice, however, the spatial variability
in the sedimentation velocity and the uncertainty in the
sediment solids concentration that interact with the water
column make it difficult to separate the two quantities. This
is a reflection of the occurrence of nepholoid layers or
“fluff” layers that are at the boundary between the water column
and the bed sediment. As a consequence, in the absence of
detailed data on v or N , only the net flux to the sediment
sd l is
from the water column can be estimated. This assumes, of
course, that all terms in the water column equation (13) are
known with more certainty than the sedimentation velocity or
the sediment solids.
-------
If now suspended solids data are available for the
water column then the equation set represented by eq. (13)
can be used to obtain spatially varying estimates of w for
any segment i. Note that the sediment segments are not in-
cluded directly in the model but are incorporated in the net
loss term.
Preliminary estimates of w. may be obtained from
eq. (15) or from solving eq. (13) directly for w 1 with given
water column solids concentrations. These estimates, however,
may be subject to wide variations, including inconsistency in
net sedimentation as a result of small changes in water column
concentrations. The procedure finally adopted in this research
was to obtain estimates of w from trial and error calculations
S I.
of the water column model to calibrate to the observed suspended
solids concentrations, A single set of net loss rates is then
obtained that balances mass in the water column and sediment
but does not require specification of the settling or resus-
pension velocities.
For the case of net gain from sediment, that is a steady
state erosion zone, the water column equation is:
0 = - + E 2 (M 2 —M 1 ) + V BAN 1 B (16)
where v is scour velocity and N is sediment solids concen-
uB lsB
tratiora available for scour.
Let — Q 12 M 1 + E 2 (M 2 —M 1 ) m (17)
where m [ N/T) is the net production (loss) of solids.
A useful procedure for this case is then:
1) Compute it, the net mass production or loss of solids
for each segment
2) If in positive, then
in = W 1 AM 1 and -
w
si AM
-------
3) If m negative, then
m = v AM
uB lsB
and if desired, VB the net scour velocity can be
cal culated.
Toxicant Model
The basic objective of the steady state toxicant model
is to obtain a modeling framework that utilizes available
field data for calibration, and eliminates the need for directly
spec .fying sediment—water interactions. The approach then is
not from first principles of detailed mechanisms of settling,
resuspension and interstitial diffusion, but rather from an
analysis of field data. It is assumed that laboratory data
are available for the following:
1) water column rates of degradation, photolysis,
vaporization, hydrolysis
2) sediment microbial degradation rates
3) partition coefficients at water column and sediment
solids concentrations.
The available field data are combined with these labora-
tory data in such a way that overall loss and transfer coefficients
are obtained.
The analysis begins from the point where the dissolved
and particulate fractions of the chemical have been assumed
in local equilibrium, and the total toxicant mass balance
equation for a given segment has been obtained. The equation
for segment 1 is then:
o = — i2 CT1 + Ej 2 (cT 2 cTl) — vlAflcTl
+v Af c +E’ F c —E’ f c
ul pis Tis is Dis Tis is Dl Ti
— xli V 1 CT 1 ::3)
—‘5.-
-------
The equation for the sediment segment, ls is
0—v Af c -v Af c +E’f c
ci p1 TI. uI. pie Tis is Dl Ti
_EjsfDlscTis — vsdlfplsA cTls_Kll,sfDisviscTls (19)
where W,ri = input toxicant loading (MT/TI
CT1,CT2,CT 15 =total toxicant concentration in segments 1, 2
and is respectively [ MT/LI
K 11 1 overail loss rate of dissolved form (e.g. vaporiza-
tion, decay) (1/Ti
K decay of dissolved toxicant in sediment [ i/Ti
vi, DS=voiumes of segments 1 and is respectively (L 3 +)
E’ iriterstitiai water sediment - water column diffusion
is 3
coefficient (LIT]
The fraction of toxicant in the particulate form is given by
iT M
= 1 1
p 1 1 + 7T 1 M 1 (20)
anö the fraction dissolved is
1 (21)
Dl 1 + 1T 1 14 1
where 7T is the partition coefficient [ MT/N MT/L 3 + ]
at ambient water column solids concentrations.
Similar expressions are used for f and f , the
plc Dis
fraction particulate and dissolved respectively in the sedi-
ment segment, is, that is,
iT N
is is
- is is
and Dls 1/1 + iT 1 N 1 - 23)
where iT 1 is the partition coefficient at ambient sediment
solids concentrations.
-------
If now equations (9) and (10) are added, one obtains
an interesting result:
0 = — Q 12 + E’ (cT2_cTl) - K1 1 fD 1 %rlcTl
-y f Ac - f V c (24)
sdi pis Tis us Dis is Tis
It can be noted that all of the sediment interaction
terms are eliminated through the addition of the equations.
This is a result of taking the mass balance around the water
column and sediment so that the only loss terms are those that
are net from the entire System. These net loss terms are fluxes
out due to transport and dispersion, decay in water column and
sediment and net sedimentation of mass out of the sediment
segment. Of course, equation (24) still, includes the sediment
total, toxjcant concentration -
Therefore, let
c M
= _ Tls = 11 — - - (25)
Ti c f
Ti pis
r [ M/14]sed
is T S
where 11 = 3 — (26)
CT 1 [ + L ] water
T w+s
where r is the toxjcant concentration on a Solids basis
is
in the sediment.
The variable 11 represents an overall Partitioning
between the Solids toxicant concentration in the sediment and
the total, toxicant concentration in the water column. Note
also from the Solids balance discussed Previously
c i = ( !i) ( PJ. _ ) (iS) (27)
sdl pis 1
where r 1 is the water column toxjcant concentration on a Solids
basis (MT/MI. Substituting eq. (25) into (24) and simplifyj -.
gives:
0 = WT], — Q 1 c + E 2 (CT2_CT 1 - w ACT 1 (28)
-------
where wTl [ L/TJ is the net loss of toxicant and is given by
v K f H +a [ v f +j f H )
Ti ii Dl 1 Ti sdl pis us Dis is
where H 1 and H 15 are the depths of the water column and sediment
resT rtiveiy.
Equation (28) is a mass balance on the water column
toxicant only and all sediment interactions are embedded in
the net loss of tOXicant WTi The estimate of this net loss
rate can be obtained from the water column field data and a
finite segment water quality model without sediment segments.
The procedure then is -
1) From estimate for each segment using a
water column model
2) From and laboratory data on decay rates in
water column and sediment, and partition coefficients, and
estimates of net sedimentation from field data and the solids
balance model, compute from eq. (29) as
aT l = wTl - KllfDl H 1 (30)
where = vdlfl + )CllsfDlRl
3) Calculate the sediment toxicant concentration from
eq. (27) as
f v
= ,_ pls sdl. , 31
Ti ‘f ‘ ‘V ,
p1
The latter calculation can be used as an additional
calibration for the model if data on r , the sediment toxicant
is
concentration are available. Such is the usual case.
A very useful special case is obtained for those toxi-
cants that are highly sorbed to solids and for which sediment
decay nd diffusion processes are negligible. PCBs are an
example. If then it is assumed that K 11 and E are zero,
then it can be shown that
= x 11 Dl H 1 + f 1 w 1 (32)
-------
and r r (3
is 1
This xesu].t indicates that for PCB, if the net solids
loss to the sediment, w can be obtained and information is
si -
available on the partition coefficient, then the entire steady
state PCB problem can be approached through the simple equations
(32) and (33). For the case of no net sedimentation, then
w = Oand
si
WT1 ll D1 H 1
andr =r
is 1
These special case models for K 11 =O were applied to the
PCB distribution in Saginaw Bay.
Application: Saginaw Bay Solids & PCB Model
After a considerable amount of time variable modeling
on Saginaw Bay, including long—term calculations for the Great
Lakes of Cesium—].37, it was determined that the initial thrust
on Saginaw Bay could best be accomplished via the steady-state
model previously discussed that incorporates horizontal trans-
port, net solids settling and resuspension and sedimentation,
and the interaction of the solids with PCBs. Accordingly, the
5 segment Saginaw Bay model was prepared for a steady—state
computation.
Segmentation & Transport Coefficients
The segmentation was obtained from the Grosse Ile Labora—
tory of the EPA under this cooperative agreement, including segment
volumes, areas and depths. The dispersive exchange coefficients
and the flows between each of the segments and Lake Huron were
also obtained from hydrodynamic modeling conducted by the Grosse
Ile Laboratory. That work, however, concentrated on the time
variable aspects of 1977 and 1979 and, as a result, the coeffi- -
cients of turbulent exchange and flow have to be modified to
represent a long—term steady—state condition. The temporally
averaged flows and exchange coefficients that were used in the
—“I—
-------
steady-state computation for the five segments in the water
column are as shown in figure ii together with the segmentation.
A chloride calibration was then performed using these
flows and bulk dispersion values. Chloride data were obtained
from STORET for the years 1974 through 1977 and all data
found in a segment were averaged for each annual period for
that segment. Loadings consisted of the Saginaw River dis-
charge and atmospheric sources (6670 kg/day), the latter values
obtained from data in IJC (1977). Saginaw River chloride
loadings for 1974 were estimated to be from 1.04 to 1.15
million kg/day according to Grosse lie and Canale, and the
1977 discharge was 0.8 million kg/day as per Grosse lie. For
the simulation, the 1977 value was used. Boundary conditions
were selected to be 6.3 mg/i for both segment 4 and 5 on the
basis of available STORET data nearest the open lake boundary
of the model. The comparison of calculated concentrations
of chlorides with the 1974—1977 data in figure 12 indicates
good agreement and, therefore, confirms the transport and
dispersion regime as representative of steady state conditions.
Suspended Solids Calibration
The Saginaw River and smaller tributaries to the Bay,
s re1ine erosion, atmospheric fallout and phytoplankton
b.omass are the components of solids loads used to calibrate
the solids in Saginaw Bay. Grosse lie provided a long-term
estimate of the Saginaw River load, whereas the contributions
of other tributary drainage areas were estimated from average
flows and a long—term average suspended solids concentration
estimated for the Saginaw River. Bank erosion values were
derived from county by county erosion volumes in Monteith
and Sonzogni (1976) and proportioned to Saginaw Bay on the
basis of shoreline length. Volumes of eroded material were
converted to mass loadings by assuming a porosity of approxi—
mately6O% and a specific gravity of 2.65. To account for
immediate settling of heavier fractions, a 50% reduction was
used to obtain the final estimates. Atmospheric sources were
obtained from the II C report cited previously. Phytoplanktcn
biomass was obtained from a algal model simulation performed
— ‘tb—
-------
by the Grosse lie Laboratory. A summary of all, segment loads
by class is contained in Table 2. The predominance of the
Saginaw River and phytoplankton loadings is apparent.
Boundary conditions, consistent with limited available
data, were selected primarily on the basis of trial and error.
Preliminary computations indicated that initial estimates
of approximately 2 mg/I. solids at the open lake boundary were
too low since calculated solids concentrations in segments
4 and 5 were well below observed values and mass balances of
these segments indicated that the boundary fluxes dominated
these segments. Final values of 4.3 mg/i for segment 4 and
5.5 mg/i for segment 5 were selected. The former value is
thought to be more associated with advective flow entering
the Bay from Lake Huron and the latter value more representa-
tive of observed segment 5 concentrations leaving the Bay with
the net advective flow (see net circulation, figure 11).
Net removal rates of the suspended solids were then
assigned to segments 2,4, and 5 where solids deposition
zones are either documented to occur (segment 2) or estimated
to occur (segments 4 and 5) . No net removal rates were
assigned to segments 1 and 3 since sedimentation appeared
to be minimal there on the basis of sediment solids and PCB
data in sediment cores. Initial values of the net removal
rates were made from mass balances of each segment using ob-
served water column solids concentrations. There were then
input to the 5 segment Saginaw Bay model, using the transport
coefficients previously calibrated, and adjusted until the
calculated and observed suspended solids concentrations were
in agreement. As seen in figure 13, the calculated values
in the water column are in good agreement with the observed
data of 1976 through 1979, when values of the net removal rate
of 12.7, 13.8 and 9.7 meters/year are used for segments 2,4 and
5 respectively. Sensitivity analyses indicate that the differences
in the net loss rates in segments 2,4 and 5 are not signifi ’ ant.
Equally acceptable calibrations are obtained for values betw
10 and 20 rn/yr. for segments 2,4 and 5.
‘ii
-------
With the estimated net removal rate of solids w
S
from the water column, the flux of solids into the bed is
calculated as.w AM EM IT]. This is equal to the sedimentation
sI 1 s
flux which is calculated as v AM . Since both v and
sdl is sdl
M 1 vary with sediment depth, no single value can be specified.
Howe r:., from eq. (15) the relationship between v 1 and
is unique. If Vdl is selected, then M 1 is a predetermined
value. Log-log plots of the relationships between the sedimenta-
tion rate and the bed solids concentration are included in the
bottom of figure 13. -
A considerable amount of effort was expended in
determining the sediment concentrations of solids drawing on
the work of Robbins (1980). From sediment cores located primarily
in segment 2 of the Saginaw Bay model, a selected number of
cores were examined for the sediment solids concentration at
the midpoints of a 10 cm well—mixed layer and at the mid-
points of two deeper 5 cm layers. The results are summarized
in Table 3. For the well—mixed surface sediment layer,
sediment concentrations average approximately 390,000 mg/i
for nine cores with a range of approximately 230,000 to 900,000
mg/i. This range is shown in figure 13 for segment 2. If the
lower value of the range is used, the corresponding sedimentation
rate for the 10 cm well-mixed layer would be approximately
0.8 mm/yr., somewhat less than a previously reported value of
3 mm/yr. (Robbins, 1980).
These results indicate the utility of the simple
steady state solids balance. The water column data are known
with some accuracy and donot exhibit marked spatial gradients.
Note that the maximum spatial differences in the average water
column suspended solids is about a factor of four. In contrast,
the spatial heterogenerity of the sediment is quite marked with
regions of deposition, scour and no apparent net deposition.
Suspended solids may then vary markedly in a given segment
horizontally , but, most importantly, vertically. Boundary
layer sediment solids ufluffw layers may be available for
interaction with the surface water column at concentrations
less than sediment data from cores. Conversely, estimated net
-------
sedimentation velocities are often cited only for those regions
of deposition and not over an area equivalent to a model segment
of Saginaw Bay. The calculation discussed above provides a
good estimate of the net flux to the sediment over the segment
area. The trade off between net sedimentation over the segment
area and sediment solids concentrations is shown in the lower
figures of figure 13. If, as noted above, the solids data from
the sediment cores are used, then the net sedimentation velocity
varies from 0.25 to 0.8 mm/yr. or almost one order of magnitude
less than the 3mm/yr. previously cited. If on the other hand,
an average net sedimentation over the entire area of segment
2 is fixed at say 3 mm/yr., then the sediment solids concentra-
tion that is consistent with that sedimentation velocity is
about 45,000 mg/i or one order of magnitude less than the
average sediment solids in the top 5 cm of the cores. The
results indicate, therefore, that with only the net flux of
solids to the sediment as known with some confidence, then it
is not possible to uniquely specify the net sedimentation
or boundary layer sediment solids. Additional tracers (of
which the radionuclides or PCBs are examples) would provide
additional information that could aid in specifying the net
sedim iitation and sediment solids concentrations.
A mass balance of suspended solids for the entire model
is presented in figure 14 for three flux categories: the
external and internal loads, the net flux removed from the
water column and the boundary transport. In the lower right
panel, it is seen that 2,970,000 lb/day of solids enter the
model, 40% (1,190,00 lb/day) is incorporated into the sediments,
and the remaining 60% (1,780,000 lb/day)leaves the Bay and
enters Lake Huron. -
PCB Calibration
With the horizontal transport and net loss rate of
suspended solids calibrated, analysis of the PCB concentrations -
can proceed. Total PCB loadings were obtained from the Gro -e
lie Laboratory for 1979, the first year for which total PCB
field data were available. As noted in Table 4. the Saginaw
River load is approximately 75% of the total load and atmospheric
-------
sources contribute an additional 25%. Although open lake con-
centrations are reported to be in the 1 ng/l range, the
boundary condition was selected as 10 ng/l —. the value needed
to calibrate observed data in segments 4 and 5.
Partition coefficients were selected on the basis of
obs rved dissolved and particulate fractions and values of
10,000, 50,000 and 100,000 pg/kg per pg/i were selected for
segments 1, 2 and 3, and 4 and 5, respectively. These are
in accord with values calculated from field measurements,
as seen in Table 5. With the partition coefficients selected,
the removal rates of total PCB are then calculated as the
particulate fraction of the suspended solids net settling
rate (see eq. (32) for X 11 0). For segment 2, for example,
the net removal rate WT2 is:
w w x f
T2 s2 p2
2 M 2 ( .05) (11.2 )
where f 2 = 1+ 2 N 2 = 1+(.05) (11.7) = 0.37
and then WT2 = (12.7) (.37)=4.7 rn/yr.
Similarly, the net total PCB removal rates for segments 4 and
5 are 4.8 and 3.5 rn/yr., respectively.
With the loads, boundary conditions and net removal
rates described above, together with the horizontal transport,
the steady state model is used to calculate total PCB concentra-
tions in the water column. The top panel of figure 15 shows
the agreement between calculated values and data observed in
1979. Dissolved and particulate fractions also agree well
with observed data, as noted in the next two panels of the
figure. The bottom panel displays the particulate PCB per
unit weight of solids and, again, agreement between observed
means-and calculated values is good for the water column.
In the previous theoretical section of this report,
it was shown that, for depositional areas, and areas whc.re
settling and resuspension were equal, the PCB per unit weight
of solids in the water column Cr 1 ) — a reproduction of the
-------
bottom panel of figure 15. Directly below, is a plot of the
PCB in the sediment Cr ), where the solid line is the calculated
is
value of r 1 assuming r 1 =r 1 . The data are segment averaged
sediment concentrations for 1979, provided by the Grosse lie
Laboratory. Agreement between calculated and observed means
is good for segments 1 and 2. It is hypothesized that segment
3 may be a net erosion zone (see suspended solids calibration,
figure 12) in which case the assumption that r 1 = r 1 is not
appropriate.
A mass balance of total PCB is shown in figure 17 for the
Saginaw River and atmospheric loads, net settling fluxes and
boundary fluxes. As noted in the lower right panel, approximately
30% of the total PCB entering Saginaw Bay from external loads
is incorporated into the sediments of the Bay and approximately
70% is exchanged with Lake Huron.
The separate effects of the external PCB loads
(Saginaw River and atmospheric) and the boundary conditions
are illustrated in figure 18. The total PCB due to both
external loads and boundary conditions is compared with ob-
served data in the top panel of the figure, where the peak
concentration in segment 1 is seen to be approximately 24 ng/l.
Of the 24 ng/l, approximately 6 ng/1 is due to the boundary
condition (center panel) and the remaining 18 ng/l is the
effect of the loads. Thus, complete removal of the Saginaw
River loads and maintenance of the boundary at 10 ng/l would
result in at least a 75% reduction in the segment 1 PCB
concentration under this new steady—state condition. Addi-
tional reduction would occur since some significant fraction
of the’ boundary concentration is probably caused by the loads.
Therefore, reducing the boundary concentration to lower open
Lake Huron levels would reduce the concentration in segment 1.
If, for example, the boundary decreased to a value of 5 ng/1,
the concentration in segment 1,under the no—load situation,
would be approximately 3 ng/1.
A mass balance of PCB for the external loads aloy.e
(figure 19) shows that approximately 2o% of the load entering
the Bay is incorporated in the sediment and 90% enters Lake -
—75
-------
1 ;uron — the bulk of it from segment 5. A similar balance
for the boundary condition reveals a net Source from Lake
Huron into segment 4, and a net sink into the Bay sediments
before the remaining mass returns to Lake Huron from segment
5 (figure 20).
Con ci U s ion
A simplified procedure for estimating the concentra-
tions of PCB in the water column and sediment of a water body
due to external sources of PCB has been applied to Saginaw
Bay. Due to its simplicity, many insights can be gained with
respect to the factors governing the distribution of toxicant
in a natural water system, including the net pathways of the
material.
Further work is proceeding on testing the sensitivity of
the results to the net removal rates and the impact of the PCB
boundary conditio 5 The PCB simulation will be redone using
1979 flow and dispersion coefficients in order that transport
and loading information would be synchronous.
-------
TABLE 2
ESTIMATED LONG—TERM AVERAGE SUSPENDED SOLIDS INPUTS
Tributary
Model Loads
Segment (lb/day)
Bank
Eros ion
(lb/day)
Atmospheric
Loads
(lb/day)
Phytop].ank ton
Mass
(lb/day)
Total
Loading
(lb/day)
Mean
Std. Dev.
390, 000
200, 000
670, 000
320, 000
720,000
240, 000
WData from Robbins (1980)
1 Stations all in Saginaw Day model segment 2.
— “7 -
1
1,232,000*
28,200
10,100
132,200
1,402,500
2
3
123,900
34,900
92,600
63,900
31,400
15,100
341,600
143,300
589,500
257,200
4
21,900
124,100
23,700
176,300
346,000
5
43,700
50,700
24,700
251,300
370,400
Total
1,456,400
359,500
105,000
1,044,700
2,965,600
*Saginaw River
1, 208,000
TABLE 3
SEDIMENT SOLIDS CONCENTRATIONS (1)
Core Solids Concentrations(mg/1 (Bulk))
at Following Depths
(2)
Station - 5 cm 12.5cm
17.5 c
1A
510,000
1,350,000
1,130,000
6A
250,000
700,000
730,000
hA
230,000
560,000
620,000
24—1
280,000
390,000
507,000
37—1
900,000
1,040,000
730,000
43—1
340,000
420,000
450,000
46—1
280,000
450,000
850,000
50—A
250,000
340,000
420,000
28—A
450,000
790,000
1,070,000
-------
TABLE 4
ESTIMATED TOTAL PCB LOADING FOR 1979(1)
Tributary
Loads
(1 b / d iJ.
1.61 (2)
Atmospheric
Loads
(lb/day)
Total
Loading
(lb/day)
2 saginaw River
TABLE 5
Total PCB PARTITION COEFFICIENTSW
Segment
1
2
3
4
5
Approx. Range
700- 30,000
7,000—190,000
20, 000—160, 000
10,000—250,000
10,000—920,000
10, 000
50,000
50,000
100,000
100,000
(1) All values 3.n )ig/3g per pg/i
Data from Grosse Ile Laboratory (1979)
Segment -
1.
0.05
1.66
2
—
0.16
0.16
3
—
0.07
0.07
4
—
0.12
0.12
5
—
0.12
Totals
1 .61
Source: USEPA ERL Grosse
0.52
lie
2.13
Partition Coefficient(11)from Observed
Concentrations
Ilean
10, 000
80, 000
60, 000
90,000
280, 000
71 Used in Model
—‘7:-
-------
—— 9
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—‘19
-------
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FLOW
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(cFs)
FIG .
II SEGM NTATIOP4 4 I sTIMAreb L.N -Ttp
Av p ce TRANSPORT toEF fcI T3 I 4
SAGINAW BAY
I
-------
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-------
STREAM & RIVER MODELS
A. INTRODUCTION* -
This chapter of the notes describes the distribution of toxic substances
in fresh water streams & rivers. The characteristic feature of these water
bodies is the longitudinal advective motion induced by gravity due to the
slope of the natural channel or by a head differential due to a backwater
effect of a dam. In either case, the transport is due primarily to the
advective component, rather than the dispersive component. In a steady—
state analysis of the systems, the latter can frequently be neglected without
introducing significant error. For those cases in which the dispersive
component may be significant, reference is made to the following chapter
of these notes. This section deals exclusively with streams and rivers,
in which the advective translation is the significant transport mechanism
of the water column.
The water flow and the various substances contained therein interact
in varying degrees with the bed, which are classified in accordance with the
three general types of bed conditions, as described previously. Type I
is a stationary non—interacting bed receiving settling solids, with no
resuspension. rpe II treats a mixed bed with a net zero horizontal motion,
but which is interacting with the water column. The shear produced by
the flowing water causes mixing and resuspension of the interfacial bed
layer, but is insufficient to induce bed motion. rpe III covers the
case in which the shear is of sufficient magnitude to induce both scour
and bed transport. The following sections of this chapter cover T ’pes I &
II and jpe III is dealt with in the estuary chapter.
bonald J. O’Connor
-------
B. LONGITUDINAL ANALYSIS*
The advective transport component, which is simply the flow velocity
in fresh water streams and rivers, is common to the various types of analysis
described above. Consequently, the discussion is first focused on this aspect,
which is best considered in light of the concentration of a dissolved tracer,
such as total dissolved solids or chlorides. The source of ions, such as
these, is invariably the ground water inflow and possibly the waste—water
input, itself, which in addition to containing the toxic substance also
may have an appreciable concentration of dissolved solids.
1. TRANSPORT
Consider. the case of an upstream tributary, in which the ground
water inflow is an appreciable fraction of the river flow. An inflow of
this nature produces a spatially increasing flow in the downstream direction.
Consider further a variable cross sectional area, which in general also
increases in the downstream direction. The mass balance takes into account
inflow, ground water input and outflow. Assuming lateral homogeneity of con-
centration, the balance is taken about an elemental volume of cross sectional
area A(x) and length &. The basic differential equation for the dissolved
solids is
3Q
A - — ( ) + s A + s
3t g dx s dx (1)
in which
s = concentration of a dissolved tracer
Q = flow
and the subscripts g and s refer to the ground water and surface runoff
components, respectively.
Under steady state low flow conditions, the surface runoff is zero
and the above equation, after expanding the first term on the right—hand
side, reduces to:
ds sdQ 5 gdQ
q [ Sg_S) (2)
in which
q = S. = exponential flow increment
The subscript is dropped from the flow since the only source of flow is
the ground water. The solution is
*r c nald J. O’Connor
-qi—
-------
()
g 0
in which
w
£
0 Q
W = mass input of dissolved solids at x = 0
flowatx=o
Depending on the relative magnitudes of the ground water concentration
and the concentration due to the vaste input, the spatial distribution of
dissolved solids increases or decreases to an equilibrium value, Sg•
-it-
-------
2. TYPE I AI ALYSIS - STATIONARY NON-INTERACTIVE BED
The condition of a stationary, zion—interactive bed occurs under
low flow conditions in streams and rivers. The vertical mixing of the
flowing water is sufficiently low to permit the settling of the suspended
solids and to preclude motion and scour of the bed material. It is recog-
nized that some fraction of the solids is probably maintained in suspension —
e.g. the sm.aller clay sizes and/or the flocculent organic particles of low
specific gravity. However the majority of the solids are susceptible to
settling and accumulation in the bed.
a. Suspended Solids
As in the case of the dissolved solids, discussed above, consider an
upstream tributary in which the ground water inflow is the source of water
for the stream flow. However, in this instance, the concentration of suspended
solids in the ground water is negligible. The basic differential equation,
allowing for settling is therefore,
(Qm) -Km R)
iii which
in = concentration of suspended solids
K = settling coefficient = V 5
H
v= settling velocity
H = average depth of the stream
Expanding the first term on the right hand side of the above equation arid
simplifying, the steady state form is
= — + q) in ( )
in which
U = velocity =
q = exponential flow increment =
the solution is
K
+ q)x
mm e U
0
-.q3...
-------
in which
= boundary concentration at x = o.
It is assumed that the incremental flow is balanced by the increasing area
resulting in a constant velocity, U. The boundary concentration may be due
to the input of suspended solids from a point source — e.g. a treatment plant
or tributary — or to an input from the upstream river segment of different
hydraulic characteristics. The concentration approaches zero for large x.
In the subsequent development the effect of incremental flow due to
ground water is not included. It may be readily introduced in the final
working equations as an additional exponent as shown in the above equation.
An example of this effect is discussed subsequently.
b. Toxic Substances
The equation for toxic substance are developed in a similiar
fashion, using the mass balance principle. The dissolved component includes
the transport with adsorption - desorption interaction with the particulate
and allowance is made for a reaction or transfer effect. In this case, assume
the transfer term is an evaporation loss:
o = - U - K m c + 1C 2 p - K c (7)
in which
K = evaporation coefficient
a
The particulate form is described in a simi].iar fashion with a settling term
o = - U dx + K 0 m c — K 2 p — K 5 p (8)
Addition of these equations yields
dc
0=_U _KaC_KsP
Substitution of the dissolved and particulate fractions for c and p gives
de
0=—U T
— CT [ fdKa + t K 5 ] (10)
in which
1.
1+lIm
- l+lIni
Assuming the river stretch is segmented such that each element may be
approximated by a constant concentration of suspended solids; the solution
-------
of the above is straightforward.
CT = CT e fdKa + fK (ii)
in which
WT
CT Q
WT = mass discharge Of total toxic ( )
3
Q = river flow (; —)
Knowing the total concentration, the dissolved and particulate may be readily
determined from the f and f equations.
d p
If the effect of incremental flow is significant, the above equation
is written in the following form:
— [ Cf K + f K + q]x (12)
CTCTe da PS
—qs-
-------
3. rpe II Analysis — Mixed—Interactive Bed
This case describes a bed which is receiving solids due to the settling
flux from the water column and returning solids by resuspension. The toxic
substance in particulate form is transported by similar routes. The water
column concentration is designated by subscript 1 and the bed by subscript 2.
The analysis of each is discussed separately.
a) Suspended Solids
The basic equation for the solids is similar to that previously de-
veloped and in addition, includes a source term due to resuspension. The
steady—state equation is:
O= —U --—-K 1 m 1 +K 1 m 2 - (13)
in which
v
K i = resuspension coefficient =
1
= concentration of solids in the bed
= resuspension velocity
The solution of this equation is:
x x
— — x
Km —K u —
u12 si —K u
= K [ 2. — e ] + zn 0 e sl
si
If the ground water flow is significant, the above is expressed as
K K
K m si Si
= ul 2 [ i — e iF + q)x) + m e U + q)x (15)
K 1 +qU °
The first term describes the build—up to spatial equilibrium of solids and
the second term the decay by settling of the boundary solids. The spatial
equilibrium concentration is
m Kum vm
el 12 — u2
K - v
Si 5
The spatial distribution of solids will either build—up or decrease to the
equilibrium values depending on the relative magnitudes of me and m 0 .
The equation for the concentration of the solids in the bed includes a
sedimentation term. Under steady—state: -
0 = K 1 - K 2 m 2 + Kd 2 m 2 (a6)
-------
in which
K = sedimentation coefficient =
d2 2
H 2 = depth of the bed.
It is apparent that the sedimentation term, which reflects the thickness of
the bed, may be either positive or negative, depending on the magnitudes of
the settling and resuspension terms. Thus, the bed increases or decreases
along the length of the river in accordance with the decrease or increase in
the spatial distribution of suspended solids. At spatial equilibrium the
bed thickness is constant and the equilibrium concentrations in water
and bed are maintained in accordance with the above equation defining m 1 .
b) Toxic Substances
The basic equation for the toxic substance follows from the above
considerations. The dissolved component is identical to that for the
Type I analysis:
dc
o = - - Km 1 c 1 + K 2 p - Kaci (17)
in which, as in the previous case, allowance is made for a decay or transfer.
A volatilization transfer is assumed in the above.
The particulate component has an additional term due to the resuspension
effect:
dp 1
o = - + KaiCi — K 2 p 1 — K 51 p 1 + K 1 p 2 (18)
Mdition of the dissolved and particulate components yields the equation for
the total concentration.
dc
o = - U dx — Ka 1 CT — K 1 p 1 + K 1 p 2 (19)
Substitution of the dissolved and particulate fractions for c and p are re-
placing p 2 =
dcT
+K rn
dx T• ul22
inwhich fK +fK
da ps
For the condition of spatial equilibrium of solids for which m 1 = me l and
-------
K 1 m 2 = K 1 m the solution
________ _a .
CT a [ 1 - e uJ + cTe u (21j
Simplification of the first term yields
K 3 r 2 m 1 — r 2 m 1
— K (22)
f +f L
p d—.-.
in which KL = evaporationStransfer coefficient KH 1 (LIT)
V = settling velocity of solids = K 51 R 1 (LIT)
For the case of spatially varying solids, the above equation may be used as
an approximation by segmenting the system into a number of elements, such
that the solids are approximately Uniform in each, but varying from one to
the other in accordance with the solids equation.
If the ground water flow is significant the appropriate equation is
CT = K 51 r 2 me 1 i — + q) Xj + cTeu + q)x (23)
It is to be noted that a direct simple anal rtjcal solution results for
the condition of spatial equilibrj of the solids. For the case of
Spatially varying Solids, however, the differential equation is
dcT K +K 1 (x )
0 = - — [ al + • (x) CT + K 1 r 2 m (214)
-K x
in which q x) = ¶m 1 (]. — e U—
Finite difference forms of the equation may be used to calculate the
distribution of toxic chemical, in which the necessary solids concentrations
both in the bed and water column are inputs to each segment of the system.
The solids equations are solved for the appropriate concentrations, which
are introduced into the toxic distribution.
-------
Application to PCBs in the Hudson River
INTRODUCTION AND GENERAL PROBLEM FRA WORK
The focus of this review is the description of the distribution and
fate of polychlorjnated biphenyls (PCBs) in the Hudson River and Estuary
using a simplified model of the physical_chemical system. (An analysis of
the fate of PCBs in the food chain is given in Chapter 10 of the Notes).
A settlement between the New York State Department of Environmental Conser-
vation (NYSDEC) and the General Electric Company (GE) concerning the con-
tarination of the Hudson River by PCBs discharged by GE’s facilities at
Fort Edward, New York, called for an overall study of the Hudson. A more
complete treatment of the model discussed here is given in (i). This model
treats the entire river estuarine and harbor regions of the Hudson system
in a simplified manner and does not address the details of estuarine sedi —
merit transport and exchange. The model is intended to provide some guidance
on the order of magnitude response that may be anticipated under different
envirorinjental controls. Considerable research in this area is continuing
and the results of that research may influence the conclusions drawn herein.
Figure 3. is a schematic of the Hudson River which indicates the mile
points (NP) of key locations and also shows the divj jons of the Hudson into
reaches for the physical transport analysis and reaches for the biological
analysis. From the Federal Dam at Troy to the Ocean, the Lower Hudson is
tidal and depending on the average freshwater flow, the end of the salt
water intrusion oscillates approximately between the Tappan Zee Bridge
(rip 25) and Poughkeepsie (NP 75) and under severe drought conditions, it May
reach as far north as NP 80. The long term monthly average discharge and
the 1976 monthly average discharije from the Upper Hudson to the Lover Hudson
are 13,270 cfs and 22,100 cfb respectively.
ANALYSIS OF WATER COLU? Th AND SEDI!i NT PCB DATA
The principle of the conservation of mass permits a first approximation
to describing the spatial distribution of the various components of PCBs.
The following assumptions are made: a) the mass of PCB in the food chain
*
Robert V. Thomann
—9g ..
-------
is small relative to that in the water column; b) a local equilibrium pre-
vails between the particulate and dissolved phases of the PCBs; c) the ad-
sorption phenomena is linear; d) the river system is in temporal steady
state (although longer term trends may be present); and e) losses from the
water column are principally through sedimentation, although some evalua-
tions of losses due to evaporation and biodegradation has been made.
The general equation for the total PCB concentration, c (lJg/l) in a dimen-
sional system can be written as:
dc d 2 c K+K+K
UT - E dX 2 + + an d ] CT = [ wTB+wTA+wTE] (1)
where x is distance downstream, u is the river or estuary velocity (cm/sec),
E is the tidal dispersion (m 2 /day), m is the mass of suspended solids (mg/l),
“a” is a partition coefficient between the particulate and dissolved phases
(ug/g ÷ g/1), K 5 , Ka K, Kd are coefficients [ day ] representing sedimen-
tation, evaporation, photooxidation, and biodegradation, respectively; and
W , WTA and WTE are total input loads (kg/l_day) of PCB from bottom sedi-
merit interactions, atmospheric sources and other external sources, respec-
tively. For the Upper Hudson area, WTA can be assumed close to zero and
Wr., can be given from the resuspended bed sediment load as Wr, r W
B b ss
where rb is the concentration of PCBs in the resuspended sediment (i.ig PCB/g
sediment a measurable quantity) and W is the sediment input ( kg sediment )
SS liter—day
A mass balance on the suspended solids is therefore also required and is
giverL by
udmEdmKW (2)
With m from (2) and estimates of the coefficients for Cl), CT can be calcu-
lated. Since the total concentration is the sum of the particulate and
dissolved, the dissolved concentration, CD, can be calculated from:
C = cT/(l+lTm) (3)
—‘Do-.
-------
The concentration then provides an estimate of the dissolved form of PCB
which may be available for uptake and bioconcentratjon by the aquatic food
chain. The approach to analyzing the PCB column data was to first fit the
suspended solids data usiri Equation (2) which provides an estimate of K
and W (but not uniquely). Then using field data of TB and the determth d
distribution of in and K 5 , the PCB data are calibrated using Equation (i).
In using this latter equation, a knowledge of the partition coefficient ¶1
is needed. The limited available data for the Upper Hudson River show a
large variation from 20—500 pg/g per pg/i. Dexter 2 in his work examined
the partitioning of PCB in the two phases and reported values from 13-75 ug/g
per pg/i. A value of 100 pg/g per pg/i was chosen for this work. The reaches
for the physical analysis of PCBs are shown in Figure 1.
For the Upper Hudson (north of Federal m), the model was applied to
PCB surveys of March 18 and March 29—31, 1976. The resulting profiles and
the survey data are shown in Figure 2 and as shown, the agreement between
the observed data and the calculation is good. However, background and
tributary PCBs had to be assigned based on rather meager data.
Figure 3 shows the calculation profile for the entire length of the
Hudson to the Battery. In the lower Hudson, data on total PCBs were
available only for the reach for 65 — 90. In the top graph of Fig-
ure 3 are shown two profiles resulting from different asswnptions on
bottom PCB concentration as shown in the bottom graph. The dashed line
therefore in the water column PCB calculation corresponds to an assump-
tion of 1 pg PCB/g sediment for the lower Hudson. It is estimated based
on Figure 3 that the total PCB concentration from I 0 to Iv 110 ranges
from 0.1 - 0.5 pg/i. The average dissolved PCB concentration (not meas-
ured) is estimated at about 0.1 pg/i (100 ng/1).
ANALYSIS OF DREDGING OF UPSTREAM SEDI?’ENTS
Various schemes have been suggested for reducing the effect of the
upstream PCB sediments, including the removal of the contaminated sedi-
ment by dredging. Therefore, two dredging alternatives were considered
and their impacts on the water column PCB were calculated.
Under the first alternative, only the Thompson Island pool at Fort
-------
Edward is dredged to a bottom sediment PCB concentration of 1 lJg/g. Under
the second dredging alternative all pools of the Upper Hudson are dredged
to a bottom sediment PCB concentration of 1 pg/g.
Figurrs L 1 howz the results oC the aiculatjon undcr the two dredj jrir
alternatives and as3ulning that the bed sediment PCB concentration remains
the same as at present. The average PCB concentration for the Upper Hudson
is calculated to be appreciably reduced from approximate present levels of
0.5 1 .zg/l to 0.28 ugh and 0.114 ug/l under the two alternatives. This repre-
sents an approximate 20% and 70% reduction of level from the Upper Hudson
to the Lower Hudson. These results assume no change in the estuary PCB
sediment concentration. However, at the mean annual flow, the estuarine
sediment PCBs are the primary source of estuarine water column PCBs. There-
fore, if the contaminated sediment of the Upper Hudson were not partially or
totally removed or inactivated, such sediment would continue to add to the
conta ination of estuarine sediments via the naturally occurring sediment
d:scharged over the Troy Dam.
Recognizing this indirect effect and an approximate range of 20_70%
reduction in load at Troy depending on the degree of dredging, it has been
assu.rned that the bed sediment_bed load input may drop by 50%. The results
of the calculation under this assumption are shown in Figure 1 4B. In this
case the calculated total PCB concentration is almost halved and in the
biologically active region, the average dissolved PCB concentration is esti-
mated at 0.05 .ig/l.
ThE NO—ACTION LTE NATIVE - UPPER HUDSON
If no action were taken, some notion of the time span required for the
reduction of the PCB load to the estuary from the Upper Hudson may be gained
by means of a mass balance. The mass balance is considered around the water
column of the Upper Hudson for the Mi.rch 18, 1976 survey, as shown in Fig.
5A. From the inputs to the calculated profile the load to the Upper Hudson
due to the upstream conditions is 5 lb/day, due to the tributaries 2 lb/day,
and at the flow of 12,700 cfs the load to the Estuary is 17 lb/day. This
causes a net loss of 10 lb PCB/day from the bottom sediment. From a similar
—I Dt-
-------
mass balance at 148,700 cfs from the calculated profiles, for the March 29—31,
1976 profile, there is a net loss of 225 lb PCB/day from the bottom sediment.
Using these net losses at the given flows (Fig. 6) and the long term monthly
hydrograph, an approximate average daily net bottom PCB loss can be computed
for the typical year. Following this procedure the approximate daily net
bottom PCB loss is 15 lb/day on a yearly average. Then, for the estimated
1450,000 lb of PCB in the entire volume of sediments of the upper Hudson, it
would take at least several decades for these sediments to be “flushed out”.
This assumes the entire sediment volume would be flushed out. If only a
fraction of the mass were “available” for scouring, then the response time
would be reduced accordingly. In addition, other effects such as evapora-
tive losses and biodegradation may reduce this time.
Evaporative losses can be computed by assuming that (1) the soluble cozr-
ponent only will be depleted by means of gas transfer process and (2) that
the PCB in the air is negligible when compared to the soluble component.
Assuming that this gas transfer is liquid film controlled, the evaporative
loss will be:
N = KLAc
where
N = evaporative loss in (MIT)
KL = liquid film coefficient in (L/T)
c = The dissolved PCB concentration in (M/L 3 )
A = The surface area through which the transfer occurs CL 2 )
the liquid—film coefficient was taken as 0.07 rn/h, and the dissolved compo-
nent for the March 18, 1976 survey is 0.2 pg/l averaged over the entire
Upper Hudson. With this parameter, the evaporative loss is estimated at
15 lb/day.
If biodegradation is included at an assumed rate of Kd = .25 (dayY 1 ,
then there is an additional loss of 5 lb/day. It is also assumed in these
calculations that the biodegradation process depletes only the dissolved
component, but this is not known. A biodegradation process depleting the
particulate component could also be postulated with, perhaps, different
-103—
-------
rate. Thus if these processes for the dissolved component are included in
the mass balance, the total net bottom loss is increased to 30 lb/day (Fig.
5B). Since these additional losses are depleting the dissolved component,
it is of interest to consider the dissolved input. Assuming that the
interstitial water is saturated with PCB, then the soluble input can ba ince
approximately 40 of the PCB loss due to evaporation and biodegradation.
Fig. 5C. The response time to “flush out” the Upper Hudson sediments is
therefore reduced by a factor of about 2 when evaporative and biodcgrada_
tlOfl losses are included. Sediment burial and subsequent interstitial d..f-
fusion rates may also markedly reduce the time to flush out the Upper Hudson.
Such a calculation would require a detailed model of the bed sediment PCB
arij iriteractors with the overlyiri water.
ACKI CWLEDGE? ENT
Special thanks are due to Messrs. John St. John, Thomas Gallagher and
Michael Kontaxis of Hydro Qual, Inc. (formerly Hydroscience, Inc.) for their
valuable assistance and input into the work described herein. This project
was part of a contract between Hydroscience, Inc. and the New York State
Department of Environmental Conservation.
— 1.0*-
-------
REFE HEN CES
1. hYDF 0SCIENCE, INC. 1978. Estimation of PCB reduction by remedial
- - n on the Hudson River ecosystem. Prepared for New York State
Department of Environ. Conservation by Hydroscience, Inc., Westwood,
N.J.: 107.
2. DEXTER, R.N. 1976. An application of equilibriwn adsorption theory
to the chemical dynamics of organic coMpounds in marine ecosystems,
Ph.D. Diss. Univ. of Wash. Seattle, Washington: 181.
—los -
-------
TRFBUT4RFIS
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FIGURE I
SCHEMATIC OF THE HUDSON RIVER AND SEGMENTATION
USED it4 PCB ANALYSIS (e 1OLOGICAL AND PIIYSICAL)
—I0 -•
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3
.(J91 •(331
(80 ITO
MILEPOINT
180 (70
MILE POINT
160
(60
I 50
(50
0 ’
0
a.
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0
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w
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z
tLI
a.
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D
U,
2
200
80
60
40
20
200
(90
(90
180 17Q
MILEPOINT
FIGURE 2.
TOTAL PCB AND SUSPENDED SOLIDS CALCULATED PROFILES.
(UPPER HUDSON RIVER)
MARCH (9, (976
OGI: (2,700 CFS
2
a
0’
U
a.
PAARCM 29,1976
48,7CC C 3
S
S
‘I
200
I
(90
0
. 5
MARCH 19, 1976
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4
I
60
(80 (70
MILEPOINT
MARCH
a
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0
‘U
0
z
‘U
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(60
40
29, 1976
(50
20
200
190
S
I.
160
150
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FIGURE
I
a
I
BATTERY
3
BATTERY
TOTAL PCB CALCULATED PROFILE AND BOTTOM PCB DISTRIBUTION
-------
a
z
0
I-
4
I-
z
U i
UI
z
0
U
U
a..
-I
4
0
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a
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z
0
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4
4
I-
z
‘U
z
0
U
U
a-
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4
I-
0
I-
0.6
04
0.6
A
FIGURE 4
EFFECT OF REMEDIAL ACTION
ON PRESENT AND POSSI9LE FUTURE ESTUARINE CONDITIONS
BATTERY
0
OATTERY
:12,700 CFS
1.2
I0
0.0
LEGENO
0-PRESENT CONDITIONS
0-DREDGING TI10 PS0N ISLAND POOL TO I q/gm
®-DREDGING ALL POOLS TO I q/gm
02
0.8
(B)
04
MI LEPOINT
-------
TRIBUTARY PC
AT.2 1 LQ/S
0
0
TRIBUTARY PCB
(B) AT
UPSTRE AM
BOUNDARY
AT
0i
r
/2,700 CFS
EVAPORATION AND
BIODEGRADATION LOSSES
LOAD TO
ESTUARY
NET BOTTOM PCB LOSS
TRIBUTARY PCB
(C) AT 2 g/I
00
/2,700 CPS
SEDIMENT PCB DIFFUSION PCB
LOSS LOSS
EVAPORATION AND
BIODEGRADATION LOSSE%
I LOAD TO
J ESTUARY
LEGEND
C) PCB LBS/-DAY
FfGURE
S
PCB MASS BALANCE
(UPPER HUDSON RIVER)
(A)
0
®
UPS TRE AM
BOUNDARY
AT.2 9/I
©
LOAD TO
ESTUARY
NET BOTTOM PCB LOSS
UPSTREAM
BOUNDARY
AT.2 ,ig/I
— hO—
-------
FRESH WATER FLOW (CFS)
NET PCB
FIGURE
6
LOSS FROM BOTTOM SEDIMENTS
(UPPER HUDSON RIVER)
‘0,000
‘0,000
‘00,000
.—llI—
------- |