WASTE LOAD ALLOCATION
SEMINAR NOTES
Prepared for
U.S. Environmental Protection Agency
Contract No. 68-01-5918
MANHATTAN COLLEGE
NEW YORK, N.Y.

-------
WASTE LOAD ALLOCATION
SEMINAR NOTES
Prepared for
U.S. Environmental Protection Agency
Contract No. 68-01-5918
MANHATTAN COLLEGE
NEW YORK, N.Y.

-------
TABLE OF CONTENTS
Waste Load Allocation Seminar Notes
Chapter	Title	Page No.
1	Waste Load Allocation Principles.
Principles and Issues of Waste Load Allocations	1-1
Measures of Verification	1-26
2	Water Quality Analysis
One-Dimensional Time Varying Analysis of Streams	2-1
and Rivers
Time Variable Water Quality Models: Estuaries,	2-53
Harbors and Off-Shore Waters
Relationship Between Waste Load Variability and	2-86
Water Quality Response
Example of Time Variable D.O. Modeling: Upper	2-97
Delaware River
The Eutrophication Problem	2-108
A Steady State Eutrophication Model for Lakes	2-155
A Dynamic Model of Phytoplankton Populations*in	2-169
Natural Waters
Simplified Phytoplankton Modeling for Streams	2-219
Effect of Sinusoidal Load Variation on Stream	2-246
Dissolved Oxygen Concentrations
3	Case Studies
The Wicomico Estuary-An Estuarine Eutrophication	3-1
Example
Examples of Sensitivity Analyses	3-36
Rocky Fork Waste Load Allocation	3-61

-------
TABLE OF-CONTENTS (cont'd)
Chapter Title	Page No.
4	Toxic Substances
Introduction and Basic Concepts	4-1
Adsorption-Desorption	4-13
Modeling Framework	4-29
Lakes and Reservoirs	4-45
Saginaw Bay-Solids and PCB Model	4-61
Stream and River Models	4-90
Application to PCBs in the Hudson River	4-99
Applications - Toxic Substances in Streams	4-112
Analysis of Completely Mixed Systems - Toxic	4-135
Substances
Ammonia Toxicity	4-160
Toxics Concentrations in Streams	4-166
Toxics Concentrations in Lakes	4-177
5	Waste Load Allocation Examples
Example Waste Load Allocation Analysis	5-1
WLA Analysis - Initial Deficit, Benthal Demand, P-R	5-28
A Methodology for Estimating Future Benthil' Demands	5-38
in Streams
6	Treatment Considerations
APPENDIX
Simplified Analytical Method for Determining NPDES	A3
Effluent Limitations for POTWs Discharging'into Low-
Flow Streams

-------
PRINCIPLES AND ISSUES OF WASTE LOAD ALLOCATIONS
INTRODUCTION
A) Basic Principles
The central problem of water quality management is the assignment of
allowable discharges to a water body so that a designated water use
and quality standard is met using basic principles of cost benefit
analysis. Figure 1 shows a representation of the overall waste load
allocation (WLA) problem. There are several components to the prob-
lem, including the determination of desirable water use standards,
the relationship between load and quality and projected conditions.
It is generally not sufficient to simply make scientific engineering
analysis of the effect of waste load input on water quality. The
analysis framework must also include the economic impacts as well and
in term must also recognize the socio-political constraints that are
operative in the overall problem context, (see also Thomann, 1980).
The principle steps in the WLA process are summarized in Figure 2 as:
1)	A designation of a desirable water use or uses, e.g. recreation,
water supply, agriculture.
2)	An evaluation of water quality criteria that will permit such
uses,
3)	The synthesis of the desirable water use and water quality
criteria to a water quality standard promulgated by local
State Interstate or Federal Agency,
4)	An analysis of the cause-effect relationship between present
an projected waste load inputs and water quality response
through use of
a)	available field data or data from related areas and
b)	a calibrated and verified mathematical model.
c)	a simplified modeling analysis based on literature, other
studies and engineering judgment
5)	A sensitivity analysis and projection analysis of achieving
water quality standard through various levels of waste load input,
Robert V. Thomann

-------
6)	Determination of the "factor of safety" to be employed through,
for example, a set aside of reserve waste load capacity,
7)	For the residual load, an evaluation of the
a)	the individual costs to the discharges
b)	the regional cost to achieve the load and the concomitant
benefits of the improved water quality standard
8)	Given all of the above, a complete review of the feasibility
of the designated water use and water quality standard
9).	If both are satisfactory, a promulgation of the waste load
allocation permitted for each discharger
A recent intent by the US EPA to provide guidance for review of advanced
waste treatment illustrates several key points related to the WLA process
(Federal Reg. 1980). The following definitions were offered and are gener-
ally followed throughout these notes:
1)	Secondary treatment: Maximum monthly average BOD,. and suspended
solids = 30 mg/Jl respectively, or 85% removal, if more stringent.
2)	Advanced Waste Treatment (AWT): Maximum monthly average BOD,,
and suspended solids less than 10 mg/Ji, respectively, and/or
total nitrogen greater than 50% removal.
3)	Advanced Secondary Treatment (AST): Intermediate between secon-
dary and AWT.
Several factors are identified that determine the level of review of pro-
jects. The level of review, of course, implies a position on the part of the
US EPA of the important issues that must be considered in a WLA.
The factors that determine the level of review are:
1)	Incremental cost of the project: A capital cost of #3
million is considered as dividing line between
projects requiring detailed analysis.
2)	Local financial impact: The impact is considered signifi-
cant if the total annual cost is greater than 1% for
median income of less than $10,000, 1.5% for median
income between $10,000-17,000 and 1.75 for median
income greater than $17,000.
1-2

-------
3) Inflationary impacts: The impact is considered significant
if the incremental AST/AWT costs are greater than
the delay cost due to an assumed inflation of 12%.
It should be noted that these factors are economic ones and reflect the con-
cern that AST/AWT projects may have a significant economic effect and, as such,
should be carefully evaluated.
The requirements for technical review include
1.	Effluent limitations assessment: This assures the validity of
state adopted, federally approved water quality standards and
represents one level of technical review
2.	Comprehensive evaluation: This evaluation may include
a)	effluent limitations assessment
b)	review of facility planning
c)	additional water quality analysis such as
i) evaluation of established water quality standard
ii) beneficial use designations
iii) evaluation of water quality criteria
These requirements are expressions of the general WLA process shown in Figure 1.
B) Steps in Allocation Computation
In the determination of an allowable discharge,, the principle framework is
given by Figure 2. Within that framework, it is assumed that a calibrated and veri-
fied water quality model is available. At the very least, an assessment of the
given river condition and a choice of modeling framework have been made. The steps
of the WLA process at another level of detail then proceed as shown in Figure 3.
As shown in the steps of this Figure, there are several points at which
iterations are required to provide a defensible WLA. For example, step #4, the
determination of design conditions including flow and parameters should be re-evalu-
ated after a preliminary allocation has been made (step //18). It should also be
noted that the specifications or projections of flow and parameter conditions under
the design event (step it 4} is a most critical step and is a blend of engineering
judgement and sensitivity analysis. In the steps outlined in Figure 3, there is no
specific step included for integrating the cost/benefit factors of the allocation.
1-3

-------
Aside from the broad guidance mentioned earlier and aside from more elaborate
optimization schemes, it is assumed in Figure 3 that the final WLA is worth
accomplishing in the light of the promulgated water quality standard.
From a broad perspective, there are several classes of issues resident
in the WLA process as follows:
1)	Water Quality Issues
2)	Cost-Benefit Issues
3)	Issues of evaluation of alternate control options
Some of the principal aspects of these issues are discussed below.
II. WATER QUALITY ISSUES
A. Introduction
Although Figure 1 shows schematically the WLA problem, there are
several other issues that must be addressed. The basic question in WLA is
"What is the permissible equitable discharge of residuals that will not exceed
a water quality standard." Additional relevant questions then are:
1)	What does "permissible" mean? Is "permissible" in terms of maxi-
mum daily load, 7 day average load or 30 day average load?
2)	What does "exceed" mean? Does it mean "never" or 95% of the time
and for all locations?
3)	What are the design conditions to be used for the analysis?
4)	How credible is the water quality model projection of expected
responses due to the WLA, i.e. what is the "accuracy" of the model
calculations and how should the level of the analysis be reflected,
if at all, in the WLA?
From a water quality point of view, the basic relationship between waste load
input and resulting response is given by a mathematical model of the water system.
The development and applications of such a water quality model in the specific con-
text of a waste load allocation involves a variety of considerations including the
specifications of parameters and model conditions. However, the preceding ques-
tions raise some additional issues that are discussed below.
The water quality issued raised by these questions involve the following con-
siderations :
1-4

-------
1)	Magnitude and temporal variations in waste loads
2)	Specification of design hydrological conditions for the water system
including considerations of the temporal variations in river flows
3)	Water quality standard specifications including the temporal varia-
bility of water quality
4)	Modeling relationships between temporal variations in waste load,
flow and quality
5)	Measures of credibility and performance of the water quality model
B. Waste Loads and Variability
1.	Introduction. It should be recognized in any WLA analysis that
effluents from waste treatment plants can vary significantly over time. Although
average values of various constituents can be specified and can often be used in
a WLA, the temporal variability of the load needs to be incorporated either
directly or indirectly into the analysis. A variety of sources provide estimates
of the average concentrations of sewage and the expected concentrations after
various treatment steps (e.g. Metcalf and Eddy, 1972; Thomann, 1972; Mueller and
Anderson, 1979). Some examples of temporal variations in effluent quality are
shown in Figure 4.
As indicated in Figure 4(a) and Cb), there may be significant diurnal varia-
tion in both flow and quality constituent, in this case, ammonia. In streams that
are dominated by the effluent, these variations may be reflected in downstream
water quality. Figure 4(c) shows the variation in BOD loading CLb/day) from a
primary effluent. Inspection and also analysis of this time series indicates a
significant seven day oscillation or periodicity in the effluent. Figure 4(d)
shows the variation in the final effluent BOD loading from an activated sludge
plant and indicates a strong seasonal increase in load. In this particular case,
the marked increase in the late summer is due to an additional load from a seasonal
canning industry that discharges to the municipal system. These examples indicate
the variability that is normally present in all effluents and that should be rec-
ognized in a WLA.
2.	Analysis of Variations in Load
a. Basic statistics - Several simple measures can be used to
qualtify temporal load variations. These -measures include
1-5

-------
i) Central tendency measures - e.g. mean, median,
geometric mean
ii) Dispersion measures - e.g. standard deviation,
variance, coefficient of variation
The mean concentration c if given by
lc.
C = ~N~	(1)
where c^ is the individual concentration values and N is the number of
data points. The geometric mean, representing the mean of the logarithms of the
data is sometimes useful where the underlying distribution of the data is log nor-
mal. The geometric mean is given by
nc.
:8 * -r	<2>
2
The estimate of the variance of the concentration s is
c
2 
-------
TABLE 1. STATISTICAL VARIATION FOR EIGHT PLANTS
	(From Thomann, 1970)	





Mean

Mean
CV


Mean flow,

Mean

primary
CV
secondary
secondary

Plant
in mil-
CV
influent
CV
effluent
primary
effluent
effluent
Remarks
Number
lions of
flow3
BOD, in
influent
BOD, In
effluent
BOD, in
BOD, in


gallons

milli-
BOD
milli-
BOD
milligrams
milligrams


per day

grams per

grams per

per liter
per liter




literb

liter




1
2.5
0.21
183
0.26
128
0.21
23
0.50
N.J. Sec. Pit.-Little









industrial waste
2
6.5
0.32
125
0.27
100
0.23
14
0.82
Conn. Sec. Pit.-Lit-









tle industrial waste
3
17.5
0.17
275
0.27
205
0.27
35
1.07
111. Sec. Pit.-Moder-









ate industry; opera-









ting problems
4
60.6
0.19
453
0.26
319
0.39
59
0.79
Cal. Sec. Pit.-Heavy









industry; seasonal









canning load
5
100.7
0.15
180
0.25
94
0.28

-
Penn. Pri. Pit.-Mod-









erate to heavy









industrial waste
6
102.2
0.21
260
0.33
202
0.34
_
-
Ohio Pri, Pit.-Moder-









ate to heavy indus-









trial waste
7
107.1
0.27
163
0.30
116
0.27
-
-
Penn. Pri. Pit.-Mod-









erate industrial









waste
8
140.2
0.14
215
0.17
-
-
57
0.22
Penn. Sec. Pit.-Mod-









erate to heavy









industrial waste
a	
CV = coefficient of variation = s/x.
All BOD values for 5-day period.
- __

-------
b. Frequency distributions of effluent quality - Another repre-
sentation of the variation in effluent quality can be obtained
by plotting a frequency distribution of the concentration or
flow. This is obtained by simply arranging the data in ascen-
ding order and assigning an estimated frequency of m/N + 1
where m is the number representing the position of the ranked
concentration and N is the total number of data points. A dis-
tribution plot of concentration vs frequency scaled to a normal
density function can then be prepared. Figure 5(a) shows a
typical distribution, in this case for the Westernport Treat-
ment Plant located in the North Branch of the Potomac River at
Luke, Md. The data are for one month of daily composited sam-
ples. From the frequency distribution, one can determine the
median effluent concentration C50%) as well as the 5% exceed -
ance level. As shown, 95% of the time, the effluent concentra-
tion is equal to or less than about 70 mg BOD/il for this plant.
Therefore, 5% of the time the concentration is expected to be
greater than 70 mg B0D/.
Figure 5(b) shows frequency distributions for different averaging of the efflu-
ent BOD i.e., 7 day average and 30 day average. These averaging periods are often
of use in assigning load allocations for systems that are not responsive to daily
oscillations in load. Estuaries, large deep rivers and iakes would be such water
bodies.
If the 95th percentile is used as a measure of the upper bound or maximum con-
centration, then relationships can be derived between this upper bound and the mean
values. This has been done by Roper et al. (1979) for 12 months of operational
data gathered from 10 secondary and 9 AWT plants. Only secondary plants that had
mean effluent BOD^ of 30 mg/i. or less were included in order to provide an analysis
consistent with "typical" secondary effluent. Figure 6 from their work is particu-
larly useful. This Figure relates the effluent arithmetic mean BOD,, or total sus-
pended solids (TSS) to the equivalent 95th percentile levels. Therefore, if the
long term design concentration of BOD,, is 10 tng/A then
a)	monthly average 95th percentile concentration is 17 mg/Jl
b)	weekly average 95th percentile concentration is 19 mg/
and c) daily average 95th percentile concentration is 22.5 mg/i
I-?

-------
Note that the 95th percentile daily level is more than twice the long term
average.
In a WLA, one would work backward from the water quality analysis of the
stream to obtain the 95% concentration level. A typical requirement might then
be "the effluent concentration shall not exceed 20 mg/Jl BOD^ more than 5% of the
time based on a monthly average" (Roper et al. 1979 provides a procedure for esti-
mating other percentile concentrations). This would make the notion of a "maxi-
mum" monthly average as previously defined more rigorous. In this case, "maximum"
is considered to be defined by the 95% level. Waste load variability must be rec-
ognized and incorporated in a WLA analysis in order to properly incorporate stream
quality variability around given water quality standards.
2. Intermittent Loads
Loading for intermittent sources depends on a number of factors
that may influence both the flow and the concentration. The flow from urban run-
off is usually highly transient resulting from variable precipitation, so at
times there is no load being discharged. For discharges from combined sewers,
therefore, several input loads can be estimated:
1.	Equivalent annual (or other interval) loading rate (comparable to con-
tinuous load)
2.	Average load discharged per event of overflow
3.	Distribution of load within an event of overflow.
Figure 7 shows the variability of intermittent rainfall events, volume of
precipitation, resulting runoff and loading. Data are usually available on hourly
rainfall or daily totals. Note that several quantities are of importance: the
volume of precipitation, the duration of the event and the interval between
events. The seasonal variation of rainfall should be recognized since the varia-
tion in rainfall intensity may vary by significant amounts throughout the year.
A statistical procedure has been developed (Di Toro, 1978) that allows one
to make an estimate of the mean load and the expected high load events with a
given probability. The procedure requires estimates of the following for each
stream event as shown in Table 2.
	TABLE 2. EVENTS FOR STATISTICAL LOAD ESTIMATION	
Parameter For each storm Mean Coef. of variation^
Intensity	i	I	v
Duration	d	D	v*
Time Between	6	A
Storms	s
Coef. of variation = standard deviation/mean
1-9

-------
These statistics can be computed for a given length of record such as across
all months of the year or within an entire year. Now it can be shown (Di Toro,
1978) that the statistical distribution of the rainfall statistics have a gamma
probability density function. Therefore, one can estimate the high load events
if the coefficient of variation of precipitation is known. Finally, it is assumed
that this coefficient of variation applies also to the runoff resulting from the
events.
3
The simplest estimate of the runoff flow Q [L, /T] is from the so-called
K
Rational formula:
QR= ClA
where I is the rainfall rate (L/Tj, A is the area over which the runoff will occur,
2
[L ], and C is the runoff coefficient. The value of C depends on land uses, popu-
lation density and degree of imperviousness, and ranges from 0.1-0.3 for population
densities of about 1 person/acre Crural) to 0.7-0.9 for heavy industrial and com-
mercial areas with densities greater than 50 persons/acre. Note that if I is in/hr,
A in acres then Q is in acre-in/hr which is equal to about 1 cfs. Therefore Q(cfs)
= CI(in/hr)A(acres)
The mean load per overflow event is given by (Di Toro, 1978):
W_ = c Q
R ^r
where c is the average concentration during the event and is the flow during the
event; assuming that c and Q do not depend on each other.
Table 3 shows the multiples of W that are expected to occur with a given
R
frequency for various values of the coefficient of variation of the rainfall.
	TABLE 3. FREQUENCY OF OCCURRENCE OF LOAD FROM INTERMITTENT SOURCES	
Multiples of W
R
Rainfall Intensity	% of Events with Load > Than Value Shown
Coef. of Variation	50	10	5
0.5	0.9	1.3	1.7
1.0	0.5	2.4	3.2
1.5	0.3	2.5	3.7
3.0	0.1	2.6	5.2
Using Table 3 then, if the coefficient of variation for a given location is
1.5, then 50% of the events would be expected to have a load equal to or less than
1-10

-------
0.3 W , 10% of the events would have loads 2.5 W and 5% of events would yield
R	K
loads of > 3.7 W . In order to convert the % frequency (a relative probability)
K
to number of events, the average number of storms is needed and can be estimated
from
N = T/A
where N = average number of storms and T is the length of period being used.
With N, the % frequency can be converted to number of events. For example, sup-
pose A = 72 hrs (i.e. 3 days between storms), then N = 120 events for T = 1 year.
A 5% frequency then corresponds to about 18 events in a year where the load would
be _> 3.7 times the mean load.
The long term average loading rate can be estimated from
where D is the average duration of storms {Tj and A is the average time between
storms [T]. One should have at least 5 years of rain gage data to estimate these
parameters.
C. Water Quality Variability
A number of water quality standards include the specification of an allow-
able frequency of occurrence and are usually specified under a defined environ-
mental condition, such as the minimum 7 day average flow once in 10 years. The
scientific and engineering basis for these specifications should always be sub-
ject to re-evaluation under given situations of waste load allocations.
Examples of time variable water quality standards include
1)	Fecal coliform bacteria	levels not to exceed a geometric mean of
1000 MPN/100 ml and not	greater than 2000 MPN/100 ml in more than
10% of samples
2)	Dissolved oxygen levels	to be above 5 mg/ "at all times"
3)	Dissolved oxygen levels to be above 5 mg/ for at least 18 hours
of the day
It is important to examine the variation of in-stream water quality vari-
ables to evaluate the expected ranges of that variable under specific environ-
mental conditions. Emphasis will be placed on dissolved oxygen because of the
greater availability of data for that variable.
1 -II

-------
Variability in water quality is of particular importance in the evalua-
tion of the feasibility of criteria and associated standards. The basic math-
ematical modeling frameworks for waste load allocations usually do not include
the many mechanisms that may give rise to water quality fluctuations at a
given location and over a given period of time. In general water quality
variations can be divided into three broad categories:
a)	Variability resulting from direct variability in waste load
input (see preceding discussion)
b)	Variability caused by indirect effects from external inputs.
For DO, as an example, this would include diurnal DO varia-
tions resulting from phytoplankton which in turn may have
been stimulated by nutrient discharges.
c)	"Background" variability representing all other random or
quasi-random influences on water quality
Deterministic time variable models in water quality permit the estima-
tion of at least some aspects of the first two categories and are discussed
in the Water Quality Modeling section of these notes. Background variability
however involves other phenomena and is discussed further here.
1. Background variability
Background variability is the random variation in water quality due to
factors that are not included in a deterministic modeling framework. This
variability is usually associated with random oscillations that are due to
such phenomena as
1)	local velocity and temperature variations
2)	random variations in meteorological variables such as
solar radiation from hour to hour and day to day
3)	random variations in ecosystem behavior such as photo-
synthesis and respiration by aquatic plants
4)	variation due to sampling techniques such as grab sam-
ples composite sampling, sampling of water parcels
Most water quality models do not include these phenomena directly. Time
variable features usually include the more or less regular seasonal varia-
tions in water .temperature and solar radiation and the more or less regular
diurnal variations due to algal photosynthesis. Although it is possible to
construct models that incorporate random variations similar to those des-
i-ia

-------
cribed, operationally such model frameworks are difficult to understand and
implement. As a consequence, the notion of "background" variability is
introduced in an attempt to incorporate some of the above mentioned random
variations. Figures 8 and 9 illustrate these variations for the upper Dela-
ware River (Hydroscience, 1975). The first figure is an interesting example
of two stations having the same monthly mean DO of 7.7 mg/ but with varia-
bility (as measured by the standard deviation) differing by a factor of 2.
The increasing variability for the upstream station at Easton, Pa. to the
downstream station is shown by the frequency histograms. Figure 9 shows a
more detailed analysis of the July 1969 Trenton data and illustrates how one
can interpret and utilize available data on water quality variability. As
shown, when the average daily dissolved oxygen is high the diurnal amplitude
is high, when at the lower end of the daily average distribution, diurnal
amplitude is significantly decreased. This, again, probably reflects the
fact that the daily average decreases as a result of changes in the daily
weather and hydrological patterns, which in turn affects the diurnal ampli-
tude.
In summary, the following estimates for Trenton (the more critical area
for the data shown) were derived from the above analysis:
a)	standard deviation of day-to-day average daily dissolved
oxygen =0.9 mg/1;
b).	average diurnal amplitude during summer months = 1.5 mg/1
c)	diurnal amplitude at 5% frequency level - 0.8 mg/1;
d)-	diurnal amplitude at 5% frequency level = 50% of the mean
amplitude.
The procedure, then, for combining the statistical analysis with a time-
variable water quality model to estimate future water quality conditions
during summer months is:
1.	time-variable model results give mean daily dissolved oxygen
diurnal amplitude under future loading conditions and differ-
ent temperature and flow -conditions;
2.	mean daily dissolved oxygen minus 2(0.9) equals the value of
average daily dissolved oxygen at Trenton which will be ex-
ceeded 95% of the time (.daily dissolved oxygen will be less
5% of the time).
1-13

-------
3.	if 110 change in dissolved oxygen diurnal amplitude is esti-
mated, then the minimum dissolved oxygen value is estimated
to be equal to or less than [[DO - 2(0.9)] - 0.8] mg/1 for
5X of the time,
4.	if a change in the average diurnal amplitude is estimated
(as for example, if the aquatic plants increase in biomass)
then the 5% value of the diurnal amplitude is taken at 50%
of the estimated increased diurnal fluctuation,
For example:
Predicted average daily dissolved oxygen = 8.0 mg/1. Therefore, the
daily average at Trenton is  8-2(0.9) ^ 6.2 mg/1 for 5% of the days
in the month
For no predicted change in diurnal amplitude: The minimum daily value at
Trenton is <_ 6.2 - 0.8 5.4 mg/1 5% of the time.
If the diurnal amplitude is estimated to increase to 3.0 mg/1, the
minimum daily value at Trenton is  6.2 - 0.5C3) 4.7 mg/1, 5% of
the time.
This example illustrates the general procedure for utilizing available
time series data to estimate the percent of time that a particular water
quality variable (e.g. DO) would be expected to be below a certain value.


-------
REFERENCES
Federal Register. 1980. Construction grants program; intent to issue revised
guidance concerning review of advanced treatment project; request for comments.
Vol. 45, No. 121, July 20, pp. 41890-41894.
Hydroscience, Inc. 1975. Time variable water quality analyses and related
studies of the Upper Delaware River - Port Lewis to Trenton. Prepared for
Del. River Basin Comm., West Trenton, N.J., 164 pp. + Append.
Metcalf and Eddy. 1972. Wastewater engineering, collection, treatment, dis-
posal. McGraw-Hill Book Co., N.Y., N.Y. 782 pp.
Mueller, J.A. and A. Anderson. Waste load inputs into marine waters. Draft
prepared for NOAA.
Randtke, S.J. and P.L. McCarty. 1977. Variations in nitrogen and organics in
wastewaters. Jour. Env. Eng. Div. ASCE, EE4:539-550.
Roper, R.E. Jr., R.D. Dickey, S. Marman, S.W, Kim, R.W. Yandt. 1979. Design
effluent quality. Jour. Env. Eng. Div, ASCE, EE2:309-321.
Thomann, R.V. 1980. Principles of waste load allocation. Notes from First
EPA Seminar Series, 1980-81. Manhattan College, Bronx, N.Y., 14 pp.
Thomann, R.V. 1972. Systems analysis and water quality management. McGraw-
Hill Book Co., N.Y., N.Y., 22 pp.
Thomann, R.V. 1970. Variability of waste treatment plant performance. Jour.
San. Engr. Div., ASCE, SA3:819-837.
\-\s

-------
Do
SoJ>
1 Oft. J
I
ul
IVu
(Soa li ^y
H
d*.y

w,

0
1
VaJ,
AH'COlI it h
Load
fc^Bob
<) -y
w
i. j
rroyc
Lv v-
Q v li
m
I I
I '
i
P
v4
r i
i i
! :
I
/
r~'
i
1. $ * p y e S t  Lie >~ ol
prcble *H .
r	1-16
D /j )*< w ce
/da 
-------
FIG. 7. Principal Steps Ch Wcate Load Allocation Process
1-17

-------
1.	Calibration and verification of water
quality model
a. Obtain present estimates of rate
coefficients and sources and sinks
1
2.	Interpret water quality standard
a. Consider "never less than" requirements
1
3.	Choose design population condition, if
allocation is for Publicly Owned Treatment
Works (POTW)
\
4.	Evaluate design river condition
a.	Design flow, e.g. 7-Q 10
b.	Hydraulic geometry at design flow, i.e.
depth, velocity
c.	Reaction rates at design conditions,
e.g. deoxygenation and reaeration coefficients
d.	Sources and sinks at design conditions, e.g.
sediment oxygen demand, photosynthesis,
respiration, sediment toxic release
1
Input secondary treatment load for POTW and
Best Practical Treatment (BPT) load for in-
dustry at design condition
\
Apply water quality model with design con-
dition loads and parameters
\l
7. Is water quality standard achieved?
YES	NO
(cont. steps	(cont. steps
8-11)	12-21)
Figure 3. Steps in WLA Process
l-lf

-------
YES
I
8. "Average" allocation given by applied
loads
9. Relate "average" allocation to maximum
allowable load
I
10. Increment "average" discharge until
standard violated
I
11. Evaluate difference between computed
level and standard as equivalent
reserve capacity
NO
J
12. Increment treatment level at each discharge
13
14
I
Is Water Quality Standard achieved?
Yes i
First estimate of allowable discharge load
given by result
No
1
15. Select reserve factor R
16.
17 ,
1
Allocation = R Load
Reserve capacity = (1-R) Load
I
Is upper bound technological
limit exceeded		Yes.
To step #4
|	18
To step #4
t	19
No
1
Increment design conditions,
e.g. flows, parameters
1
I

Specification
of Permit
Requirements
Evaluate time variable treatment
possibility
1
20. Allocation given by "average" and
for time variable load or upper
bound tech., limit
Reserve factor
<1
Reserve factor
= 1
21
I
Relate allocation to maximum
allowable allocation
Figure 3. (continued) Steps in WLA Process
M<1

-------


JJLLOi
li )i ii iiATVfni II,
\'V^M y " V
c c x < x sc ^ c  /tr -c ^ .x < CS/S^nTa cara;
:aoo i2co tsoo zcoc 2ooooo osoc
T im  OF DAT
Norrr.alilpa Diurrsl Variation in
Concentration of Ammonia in Prmar/
EHIuents
L. AVi.l
;'V\' ,"u' I|VV V' 'I'/': 'V''" v';V,('r j'1
III i1
V  >
TIME SERIES PLOT, PLANT NO. 4, ACTUATED SLUDGE EFFLUENT SEA-
SONAL LOAD VARIATION
FiG. 4- S'-xo.^plpi o"F ie*por*I	<- W<*_jt"e Lo<^(
^	oi cn plow c.ncL fViKG.hy Erf'PliAeht' N Hj
^Prcm	^ M e Cc^c y ^ 71J
c] $ oj weeh!y t fQ.*0heJ Bob Va.nA.t'lcnx	Thc^ank/ ft1o)
i-ao

-------
(O
ro -
&&
Eg If
i i
i >
o* I
^ 10	So
*lc >\ r,~e 
 n fc pl^h"t
b] "XH ust^HCticn of Frequency 1)fitHtn.trion of Viffe^ent
f Effluent CoAcsh'thafc ions
I'll

-------
+J
GL
3
20
Eff las nt zfir.i t hm &t it.Mo. &n
BQD^zforzJ S ~~_^777j /P
derived from secondary 4 AWT plant ddia
	~( Fire hi" Roper: et al }

-------
l*}k
frcu'p.
U*)

Inri.t

l)ui'a.4l#'t - 1 [
iL* rb
iv n
(j>-)
J	l
?
In I
Ev< fcVj
Uto
L o . i
V|kr
(O
A A a A
ujA-w
h
, *\ It+h/t"*** r
Uin
--jjr-fe
UUjlNJ ~
FIG. 7 *) |?rf,^// Im/uK Aj < V .
<) cO L# . d	)k ti" / ^ ft d- /Jc h
n*
1-13

-------

| MEAN = 7.7, STANDARD DEVIATION = 0.8 mg/l
1
Mi77
1
rV/YT1 EASTON, PA.
H !til\ JULY 1969
W /
'hlrk (726 H0URLY VALUES)
NrJ f\
 , , mil ,
mJ/mlTlTrrrTrrTriffl^ i ,
10
11
12
13

MEAN = 7.7, STANDARD DEVIATION = 1.7mg/l
TRENTON,N.J.
JULY 1969
(682 HOURLY VALUES)
rt17 U/IlWWJTTTl^rrni^ 
10
12
DISSOLVED OXYGEN -mg/l
FIGURE 8
HISTOGRAM OF HOURLY DISSOLVED OXYGEN
EASTON, PENNSYLVANIA A, TRENTON, NEW JERSEY

-------
10
AVERAGE-MINIMUM DISSOLVED OXYGEN CONCENTRATION
CONTINUOUS WATER QUALITY MONITOR DATA
TRENTON,N.J.
JULY, 1969
2.4
Avprnyn
Am pi i tude-1.5 rng/1 -
oooo 5
oo o
Dnily AverooR
Mcon = 7.7 (iiy/l
S Id. Dev. = 0.") tng/l
Doily Minimum
Mean Min. = 6.24
St d. Dev.Min =0.76
WaljuQuolity Standard-Never''less than 4 mq/1

0
0 2 O 5 I ?.	5 10 ?0 30 10 f>0 GO 70 60 90 9!> 90 99	99 9 99 9
PERCENT OF TIME LESS THAN OR EQUAL TO
FIGURE S
STATISTICAL DISTRIBUTION OF DISSOLVED OXYGEN CONCENTRATION
AT TRENTON, N.J-JULY,1969
\~1S

-------
MEASURES OF VERIFICATION
Introduction
There are two basic reasons for constructing representa-
tions of natural water systems through mathematical modeling.
First is the need to increase the level of understanding of the
cause-effect relationships operative in water quality and
secondly, to apply that increased understanding to aid the
decision making process. Water quality models are largely
syntheses of a number of phenomena; water transport, complica-
ted reaction kinetics, and externally generated residuals in-
puts. The builder of water quality models acts as one part of
a three part interaction which includes the specialist who
generates process details (e.g., uptake of nutrients by phyto-
plankton) and the manager who is concerned with the problem
specification and ultimately its resolution in some sense.
Figure 1 shows this interaction.
For more than fifty years now, this relationship has con-
tinued in a great variety of increasingly complex water quality
modeling situations. But one of the common threads throughout
this period has been the constantly recurring question of the
validity, credibility, and utility of the water quality models.
Indeed even in the historical roots of water quality modeling,
as embodied in the famous Ohio River dissolved oxygen studies
of the 1920's, this question of model validity was present.
Resurveys of the Ohio River between 1914 and 1930 were con-
sidered critical to a justification of the basic history theory
of deoxygenation and reaeration (Crohurst, ' 1933). Indeed the
works of Streeter and Phelps (1925) addressed the question of
model validity quite directly by numerous qualitative compari-
sons to observed data and through quantitative comparisons by
computing, for example the root mean square error between
*
Robert V. Thomann in: "Workshop on Verification of Water Quality
Models", US EPA ERL Athens, Georgia, EPA-600/9-80-016, April 1980.

-------
dissolved oxygen theoretical calculations and observed values.
One easily gains the impression from a reading of these early
works that analysis of the relationships between observed and
computed values, both qualitatively and statistically was a
normally acceptable and expected procedure
As the issues of water quality become more complex, re-
quiring the interaction of numerous variables in space and time,
the questions of model credibility increase. The responses to
these questions often tend to be somewhat qualitative; e.g.,
"The results appear reasonable" or "The major features of the
observed behavior have been captured" or "The comparison between
observed and computed values is marginal but sufficient for
most purposes." Increasingly, most assessments of model valid-
ity do not seem to directly answer the basic questions of the
manager, the specialist or.the general public. Common questions
are: "How good is the model?", "What is the level of confidence
that we can place on your results?", "How do two models purport-
ing to represent the same water quality phenomena compare to
each other?"
In the light of the questions raised on model credibility,
it is appropriate to address the issue of what measures of
verification, if any, might be useful in today's water quality
modeling setting. However, a brief review of the principal com-
ponents of. a water quality model is necessary to clarify and
propose some language that might be applicable to this issue of
model verification. Within the context of water quality prob-
lems, the basic issues discussed apply also to models of input
generation and water transport.
Figure 2 shows the principal components of a mathematical
modeling framework. The upper two steps enclosed with the
dashed lines, namely "Theoretical Construct" and "Numerical
Specification" constitute what is considered a mathematical
model. This is to distinguish the simple writing of equations
for a model from the equally difficult task of assigning a set
of representative numbers to inputs and parameters. Following
this initial model specification are the steps of a) model
calibration, i.e., the first "tuning" of model output to observ-
ed data and b) the step of model verification i.e., the use of
the calibrated model on a different set of water quality data.
This verification data set should presumably represent a con-
dition under a1sufficiently perturbed condition (i.e., high
flows, decreased temperature, changed waste input) to provide
an.adequate test for the model. Upon the completion of this
verification or auditing step, the model would be considered
verified.
Stages of Model Credibility
The following definitions are therefore offered:
i-n

-------
manager
MODELER
SPECIALIST
FIGURE I. RELATIONSHIP BETWEEN MODELER,
SPECIALIST AND MANAGER IN WATER QUALITY
problem
SPECIFICATION
MODEL
VERIFICATION
NUMERICAL
SPECIFICATION
FIGURE 2. PRINCIPAL COMPONENTS OF
MATHEMATICAL MODELING FRAMEWORK
\-ir

-------
1.	Model: A theoretical construct, together with assignment
of numerical values to model parameters, incorporating
some prior observations drawn from field and laboratory
data, and relating external inputs or forcing functions to
system variable responses.
2.	Model Calibration: The first stage testing or tuning of a
model to a set of field data, preferably a set of field
data not used in the original model construction; such
tuning to include a consistent and rational set of
theoretically defensible parameters and inputs.
3.	Model Verification: Subsequent testing of a calibrated
model to additional field data preferably under different
external conditions to further examine model validity.
The calibrated model, it should be noted, is not simply a
curve-fitting exercise, but should reflect wherever possible
more fundamental theoretical constructs and parameters. Thus,
models that have widely varying coefficients (i.e., deoxygena-
tion coefficients) to merely "fit*' the observed data are not
considered calibrated models.
The verified model is then often used for forecasts of
expected water quality under a variety of potential scenarios.
However, it is apparently rare that following a forecast, and a
subsequent implementation of an environmental control program,
that an analysis is made of the actual ability of the model to
predict water quality responses. This can be termed a "post -
audit" of the model, as shown in Figure 3. Somehow it seems
that once a facility has been constructed, the federal and state
agencies, municipalities, and industries are somewhat reluctant
to return to the scene of a water quality problem to monitor the
response of the water body. A fourth step therefore in deter-
mining model credibility is suggested as follows:
4.	Model Post-Audit: A subsequent examination and verifica-
tion of model predictive performance following implementa-
tion of an environmental control program.
Need for Measures of Verification
Increase in Model Complexity. The most obvious need for
some measures of model verification is the fact that water
quality models have increased greatly in complexity. Figures
4-7 illustrate this progression. From relatively simple two
linear system models of biochemical oxygen demand and dissolved
oxygen for the first forty years of model development to the new
complex non-linear interactive' eutrophication and toxic sub-
stances models, the ability to describe model performance has
become increasingly difficult. The number of state variables in
some models has increased dramatically. It is not unusual today
\-2<\

-------
0
FORECASTED
WATER
QUALITY
PROJECTED
ENVIRONMENTAL
CONTROL
PROGRAM
ACTUAL
ENVIRONMENTAL
CONTROL
PROGRAM
VERIFIED
MODEL
DIFFERENCE
ACTUAL
WATER
QUALITY
MOOEL
ADEQUACY
IN
FORECASTING
J
	^
AUOIT
TO EXAMINE WITH INTENT TO VERIFY

	v
POST- AUDIT
SUBSEQUENT EXAMINATION AND VERIFICATION
J
FIGURE 3. AUDITING AND POST AUDITING OF WATER QUALITY MODELS
8 0

-------
to construct models with up to 20 or more state variables.
Furthermore, as illustrated in Figures 4-7, the physical dimen-
sionality now encompasses the range from the more traditional
one-dimensional streams to fully three-dimensional estuaries,
bays and lakes.
As the number of state variables and physical dimensional-
ity has increased, the overall ability of the analyst to compre-
hend model output has decreased. This is simply due to the
overall size of the model. For example,- if a "compartment" is
considered as a state variable, i = l,...m, positioned at some
spatial location j = l...n, then the total number of compart-
ments to be solved for a fully interactive model is m times n.
Figure 8 shows the growth of the number of model compartments
since the earliest work of the two state variable problems of
BOD and DO. The almost explosive growth in the number of model
compartments, coincidental with passage of major water quality
legislation is evident.
Increase in Complexity of Questions. The second major
reason for some quantitative measures of verification is the
fact that the level of questions in water quality has increased
in complexity. Many of the water quality issues today extend
well beyond the traditional problem of raw or inadequately
treated sewage. In that traditional framework, it generally was
clear that "some treatment of municipal sewage would probably
improve water quality, specifically dissolved oxygen. However,
some of the water quality questions today may involve such
complex interactions that it is not clear that certain environ-
mental controls will in fact produce the classical result. The
Potomac estuary eutrophication problem is a case in point. It
is not clear that nitrogen removal at the Washington, D.C. Blue
Plains plant actually will result in any reduction in the phyto-
plankton population that could not be achieved solely by phos-
phorus control. Similarly, it is not entirely clear that ex-
tensive dredging of PCB deposits in the Upper Hudson will result
in a reduction of the PCB bodyrburden of the striped bass in the
Lower Hudson estuary to levels below the FDA requirement.
The complexity of the problem then leads to the very real
possibility that environmental control measures may be called
for by model predictive analyses when in fact the implementation-
of such controls may produce little or no response in water
quality. The economic, political, and social consequences of
"wrong" answers therefore become more acute in today's problem
setting. Some quantifiable measure of model performance in im-
proving understanding or predictive performance would seem,
therefore, to be of considerable importance.
|-3t

-------
1925-1965
TWO LINEAR SYSTEMS!
WASTE INPUT-
BOD

DO



BENTHAL DEMAND
( PHO TOS YN THESIS A ND RES PI R A T/ON )
ONE-DIMENSIONAL RIVERS AND ESTUARIES!
7/
'* T
_l	i
OCEAN
FIGURE 4. WATER QUALITY MODELS, 1925-1965
1965- 1970
SIX LINEAR SYSTEMS!
800
00
AMMONIA
NITROGEN
NITRATE
NITROGEN
NITRITE
NITROGEN
ORGANIC
NITROGEN
ONE, TWO DIMENSIONAL WATER BODIES!
1	V
k__L
TT
-rr

iOCEAN
FIGURE 5. WATER QUALITY MODELS, 1965-1970
1-3Z

-------
1970  1975
NON-LINEAR INTERACTIVE SYSTEMS
ZOOPLANKTON
CARBON
PHYTOPL ANKTON
CHLOROPHYLL
UNAVAILABLE

available
phosphorus

PHOSPHORUS
l	PHOSPHORUS CYCLE
ORGANIC

AMMONIA

NITRATE
NITROGEN

NITROGEN

NITROGEN
NITROGEN CYCLE
o
z
< .
o
tc
o
PHYTOPLANKTON
SUNLIGHT
NUTRIENT
ui
TEMPERATURE
ONE, TWO-DIMENSIONAL
WATER BODIES
y
i
I OCEAN
FIGURE 6. WATER QUALITY MODELS 1970-1975
1-33

-------
MANY INTERACTIVE SYSTEMS
B/OMASS	TOXICANT
TOP
CARNIVORE

TOXICANT
IN TOP
CARNIVORE

ONE, TWO, THREE-DIMENSIONAL
WATER BODIES
u
7/
ZOOPLANKTON
TOXICANT
IN
ZOOPLANKTON


*OCEAN
PHYTOPLANKTON
SYSTEM
NUTRIENT
SYSTEM
SEDIMENT
NUTRIENT
SYSTEM
WATER
TOXICANT
IN
PHYTOPLANKTON
TOXICANT
DISSOLVED
IN WATER
SEDIMENT
DISSOLVED
TOXICANT
TOXICANT
IN
PARTICLES
PARTICULATED
TOXICANT
FIGURE 7. WATER QUALITY
MODELS
1975 - ?

-------
Some Verification Measures
Qualitative Measures
Probably the most direct and easily understood measure of
model performance is to present qualitative comparisons of ob-
served data and computed values. This is most often done in
the form of overplotting data and theory or tabulating the
comparison between the two and then drawing qualitative judg-
mental conclusions about the adequacy of the model and its
suitability for projection purposes. A plot of data versus
theory can be a most graphical measure of model credibility -
easily understood and clearly visual. But for some problems,
such a simple qualitative measure is not possible or simply not
adequate. This is particularly so for time variable models of
several state variables and multi-dimensional systems. For
models of this type, as well as the simpler model framework,
some statistical comparisons may provide further understanding
of model credibility.
Statistical Comparisons
A variety of simple statistical comparisons may be appro-
priate to quantify model verification status. Such measures
would be intended to supplement the qualitative comparisons.
Examples of'statistical analyses between observed and computed
values are:
1)	Regression analyses
2)	Relative error
3)	Comparison of means
4)	Root mean square error
1) Regression Analyses
A perspective on the adequacy of a model can be obtained
by regressing the calculated values with the observed values.
Therefore, let the testing equation be
x = a + 6c + e	(1)
where a and 8.are the true intercept and slope respectively
between the calculated_values, c, and the observed values, x,
and  is the error of x. _The regression model equation (1)
assumes, of course, that c, the calculated value from the water
quality model, is known with certainty which is not the actual
case. With equation (1), standard linear regression statistics
can be computed, including
a) The square of the correlation coefficient, r2, {the
1 variance accounted for) between calculated and
observed
1-36"

-------
b)	Standard error of estimate, representing the residual
error between model anddata
c)	Slope estimate, b, of 8 and intercept estimate, a, ofa
d)	Test of significance on the slope and intercept. The
null hypothesis on the slope and intercept is given
by 3 = 1 and a = o. Therefore, the test statistics
:- and ot/s
S i		cl
D
are distributed as student's t and n-2 degrees of
freedom. The variance of the slope and intercept,
s, and s are computed according to standard formulae.
A two- tafled "t" test is conducted on b and a,
separately, with a 5% probability in each tail, i.e. a
critical value of tof about 2 provides the rejection
limit of the null hypothesis.
Regressing the calculated and observed values can result in
several situations. Figures 9(b) and (c) shows that very good
correlation may be obtained but a constant fractional bias may
exist (bl); also Figure 9(a) indicates that poor correla-
tion may be obtained with slope = 1 and intercept = 0.
Finally, Figure 9(d) indicates the case of good correlation but
for an a > 0 a constant bias may exist. Evaluation of r , b and
a, together with the residual standard error of estimate, can
provide an additional level of insight into the comparison
between model and data.
2) Relative Error
Another simple statistical comparison is given by the rela-
tive error defined as
e = I* - cl	(2)
x
Various aggregations of this error across regions of the water
body or over time can also be calculated and the cumulative
frequency of error over space or time can be computed. Esti-
mates can then be made of the median relative error as well as
the 10% and 90% exeedance frequency of error. The difficulties
with this statistic are its relatively poor behavior at low
values of x and the fact that it does not recognize the var-
iability in the data. In addition, the statistic is poor when
x > c since under that condition the maximum relative error is
100%. As a result, the distribution of this error statistic is
most poorly behaved at the upper tail. Nevertheless, if the
I-3G

-------
median error is considered, this statistic is a readily under-
stood comparison and provides a gross measure of model adequacy,
It can also be especially useful in comparisons between models.
3) Comparison of Means
A third measure is to conduct a simple test of the differ-
ences between the observed mean and the computed mean. Letting
d = x - c, the test statistic distributed as a student's "t"
probability density function is given by
t =	(3,
Sd
where 6 is the true difference between model and data and s^ is
the standard deviation of the difference given by a pooled
variance of observed and model variability. If these latter
quantities are assumed equal then
= ^25^	(4)
St	X
a
where s- is the standard error of estimate of the observed data
and is $iven by
2
2 Sx	,c.
s5 " S	<5>
4) Root Mean Square Error
Finally, a measure of the error between the model and the
observed data is also given by the root mean square (rras) error
as
As before, the rms error can be computed across a spatial pro-
file or over time at a single location. The rms error is sta-
tistically well-behaved and provides a direct measure of model
error. If expressed as a ratio to mean value (across a profile
or over time), it represents a second type of relative error.
The disadvantage of the rms error is that it does not readily
lend itself to pooling across variables to assess overall model
credibility.
Each of the above measures displays model credibility from
different statistical viewpoints. Some are apparently useful
I-3 *7

-------
700
600
500
400
300
AOVECTION - LINEAR
DISPERSION
200
NON -LINEAR INTERACTION
100
I960
1990
1940
1970
19-30
1950
I960
1920
|l977
AMEND.
1972
ACT
FIRST MAJOR
WATER POLLUTION
FED. ACT
TOXIC
SUBSTANCES
ACT.
FIGURE 8. INCREASE OF NUMBERS
OF MODEL COMPARTMENTS WITH TIME
I -3t

-------
legend:
CALCULATED
 OBSERVED
(a)
/
~ /
/
TIME (days)
/
/
/"T
/
/
I- /
/
1Z	L_
r2 : I
b = i
o=0
0 2 4 6 8 10 12
CALCULATED
TIME (days) y
2 4 6 8 10 12
CALCULATED
10
8
6
4
2
0
0 2 4 6 8 10 12
CALCULATED
10
8
6
4
2
0
0 2 4 6 8 10 12
CALCULATED
TIME (days)
FIGURE 9. POSSIBLE CASES IN REGRESSION
BETWEEN CALCULATED AND OBSERVED VALUES
1-39

-------
for diagnostic purposes while others appear to be directly of
value in succinctly describing model verification status.
Some Examples of Quantitative Verification Analyses
Dissolved Oxygen Models
In order to illustrate the present state of the art of model
calibration/verification, a brief review was made of nineteen
models of dissolved oxygen. This water quality variable was
chosen since DO models have been the most extensively used and
over the longest time period. The engineering reports for the
fifteen water bodies were examined and relative errors, rms
errors, and regression analyses were evaluated. All of the water
bodies were analyzed by Hydroscience, Inc. It was assumed that
the personnel engaged in the modeling analyses carried out the
calibration/verification steps consistent with the definitions
given above and not just to "curve fit" the model to the data.
The models included several small streams in New Jersey
(less than 10 cfs), larger river systems such as the Ohio River
and the Upper Mississippi River, bays and estuaries and a large
model of the entire New York Harbor complex. A listing is shown
in Table 1.
The distribution of the median relative error for these
models is shown in Figure 10. For each water body, the error
represents the median relative error where 50% of the stations
(or times) had errors less than the values shown. Ac.ross all
models, one-half of the models had median relative errors great-
er than 10% and one half of the models had median relative
errors less than 10%.
As a crude measure, therefore, of the present state of the
art of DO models calibration/verification, one might suggest an
overall median relative error of 10%. It should, of course, be
noted that this is not the error of actual prediction but merely
the error representative of a present level of understanding of
observed behavior of dissolved oxygen. The degree to which the
results shown in Figure 10 is representative of all DO models is
not known. More detailed analyses of a larger sample would be
necessary.
Lake Ontario Eutrophication Models
A variety of models have been constructed of the eutro-
phication of Lake Ontario at several time and space scales and
with different levels of kinetic detail (Thomann, et. al., 1979
and Thomann and Segna, 1979). Extensive application of the
above quantitative measures of calibration/verification was made
for a three-dimensional model of the Lake for one year and for a
two segment vertical model over a ten year period.
1-1-0

-------
100
90
80
70
UJ
60
90
40
UJ
FIFTY PERCENT OF MODELS
HAD MEDIAN RELATIVE
ERROR IN D 0 OF C 10%
UJ
30
20
New YO*K
FIGURE 10. SOME RELATIVE ERRORS OF DISSOLVED OXYGEN MODELS
I- + I

-------
TABLE 1
WATER BODIES
EXAMINED FOR DISSOLVED
OXYGEN VERIFICATION STATISTICS
	Location	
1.	New York Harbor
Hudson River
Raritan River
Passaic River
Hackensack River
2.	San Joaquin Delta, Calif.
3.	Wicomico Estuary, Md.
4.	Black River, N.Y.
5.	Jackson R., Va.
6.	Small N.J. Streams
6a. Pennsauken Cr.
6b. Big Timber Cr.
6c. Grt. Egg Harbor R.
7.	Mohawk River, N.Y.
8.	Manhasset Bay, N.Y.
9.	Delaware R. West Br., N.Y.
10.	Savannah Estuary, Ga., S.C.
11.	Wallkill R., N.J.
12.	Hackensack R., N.J.
13.	Ohio R., Ohio
14.	Lake Erie Hypolimnion
15.	Upper Miss. R., Minn.
	Remarks	
425 segment 3 Dimen. model
DO model part of eutrophication
model
A tidal tributary of Ches. Bay
A tributary of Lake Ontario
Tributaries of Delaware River
and Bay
In vicinity of Utica, N.Y.
Bay of Long Island Sound
In vicinity of Cinn., Ohio
DO model part of eutrophication
model - time variable
DO model part of eutrophication
model - time variable
I ~
-------
Figure 11 shows the median relative error across all
variables at three levels of spatial aggregation - 67 segments/
eight regions, and whole lake two layer scale. Five state
variables were included in the pooled error (chlorophyll, total
phosphorus, dissolved orthophosphorus, ammonia, and nitrate).
The median relative error over the year was the highest at the
smaller spatial scale (44%) and lowest at the whole lake scale
(17%). This indicated that the model did not capture more local
spatial phenomena as well as it reproduced overall lake behavior.
Figures 12-14 show the verification statistics from the
analysis of 10 years of data on Lake Ontario using the two layer
model. Two kinetic regimes are shown. Lake 1 kinetics are
fairly standard and Lake 1-A kinetics included a more complex
phytoplankton compartment (diatoms and non-diatoms), silica
limitation and other kinetic changes in nutrient recycle. Figure
12 shows an example of the chlorophyll verification results for
both regression analyses and relative error distribution. The
regression results indicated some improvement in slope with the
increased kinetic complexity but no improvement in the correla-
tion or intercept. The median relative error for chlorophyll
decreased from 42% to 30% with the inclusion of the more complex
kinetics. Figure 13 shows the results of the student's t-test
comparing observed and computed monthly means over the six state
variables. For the indicated standard errors, the Lake 1-A
kinetics gave a verification score of 70%, i.e., 70% of the
variable-months where a comparison could be made showed no
statistically significant difference between observed and com-
puted means. If the standard errors are taken at one-half the
values indicated, the score drops to 40%. Figure 14 shows the
median relative errors for each variable and for all variables.
The latter test indicated an overall relative error for the ten
years of analysis and all variables of 2 2-32%.
A Suggestion
On:the basis of the above concepts and illustrations to-
gether with the apparent growing need to be more definitive in
assessing model credibility, it is suggested that quantitative
measures of calibration and verification of models be an integral
part of modeling whenever possible. This includes a pressing
need to conduct post~auditing studies of model projections and
resulting water quality.
The suggestion for quantitative measures of water quality
model verification is aimed at responding to the many questions
often raised at various stages in the decision making process.
There are, however, advantages and disadvantages to quantitative
measures of model verification. Some of the disadvantages are:
1-43

-------
o
LlJ
z *
Z (jj
UJ (O
i-
~"*	o
cr	uj
O	i-
 <
i V
<	I
_J Q
QJ UJ
tr >
ac
z UJ
<	CO
 OQ
 O
uj _
2 O
O
100
80
60
40
20
0
100
80
60
40
20
0
100
80
60
40
20
0
(a) LAKE 3 SCALE, 67 SEGMENTS
1972 AVERAGE FOR ALL VARIABLES: 44%
1
1

1
M
(b) EIGHT REGIONS SCALE
1972 AVERAGE FOR ALL VARIABLES: 35%

i H
I
I
M

l I

N

N
(c ) TWO L A YER SCAL E
1972 AVERAGE FOR ALL VARIABLES^ 17%
41
23
M
14
N
FIGURE 11. LAKE ONTARIO
MEDIAN RELATIVE ERROR AT THREE SPATIAL SCALES
l-*4

-------
CHLOROPHYLLV IN SEGMENT I AT 0-17 METERS
LAKE IA KINETICS	LAKE I KINETICS
0.47 0.20
2.23
0
b
UJ
2.6
0.279 0

.20 1



&



i
 

* *
J	
e io
CALCULATED CHLOROPHYLL a Mg/I
v>
m
o
v
u
_i
<
0
1
to
m
O

H
<
-I
UJ

-------
Ul
100 -
_ so-
ar
UJ
o
o w
CO I
O o
P2
< I
o LlI
E
oc <
uj q:
> 
u.
o
00
ESTIMATED
STANDARD ERROR
OF MEAN ( jxq/l )
CHLOR.	 0.3
TOTAL f 	 J.O
DISS. 0RTH0. P 2.0
KM, 	 4.0
N0j 	
SILICA
210
50 0
60 -
5 40 
20
VERIFICATION SCORE
ALL VARIABLES! 1967-1976
n
LAKE I
KINf TICS
50
69
AT 1/2 OF
ESTIMATED
STD. ERRORS
AT
ESTIMATED
STD. ERRORS
AT I 1/2 OF
ESTIMATED
STD. ERRORS
FIGURE 13. LAKE ONTARIO
VERIFICATION SCORES, ALL VARIABLES, TEN YEAR ANALYSIS .
THOHANN AND IE*NA IftTtb
i r

-------
LONG TERM ANALYSIS
RELATIVE ERROR! 1967-1976
.229
n
LAKE I
KINETICS
100
80
60
40
20
15
9.5
r>r
CHL-A
TP	D-O-PO4-P	NHj-N N02+N0s-N
VARIABLES
SILICA ALL VARIABLES
FIGURE 14. LAKE ONTARIO
MEDIAN RELATIVE ERROR, TEN YEAR ANALYSIS
\- + 1

-------
1)	An urge would be created to "curve fit" model to data
to improve verification statistics
2)	Not all of the credibility of a model is subsumed in
verification statistics
3)	Good verification statistics do not necessarily imply
the ability to accurately predict future water quality
4)	Single measures of verification may be grasped at too
readily and engineering judgment as a measure of model
credibility may degenerate into "What's your median
relative error?"
The advantages are:
1)	Some measures, albeit imperfect ones, would be avail-
able for decision makers to assess model credibility
and status
2)	A basis would be provided for comparison of models
3)	Some estimate could be made of changes in the state of
the art of model performance
4)	Modelers would be stimulated to question their model
output with quantitative measures
5)	A diagnostic -tool would be available to determine
relative improvement of a given model under more
complex frameworks.
A quantitative measure of model performance,"therefore,
may be a mixed blessing. At the very least, the time appears
appropriate to address the issue of the need and value of such
measures to assess model status. It is through such discussions
that perhaps some consensus can be reached on the advisability
of such measures or on possible alternative means of describing
the validity of water quality models.
Acknowledgments
Part of the work reported on herein was supported by a grant,
from the Environmental Protection Agency, Large Lakes Research
Station, Grosse lie, Michigan to Manhattan College. Additional
support was also received by Kydroscience, Inc. through a con-
sulting agreement. Grateful appreciation is expressed to both
parties for this support. Special thanks are due also to Mary P.
Thomann and Robert J. Thomann for their diligent computations of
the DO error statistics.


-------
REFERENCES
1.	Crohurst, H.R., 1933. A study of the pollution and natural
purification of the Ohio River, IV. A resurvey of the Ohio
River between Cinn., Ohio and Louisville, Ky., including
a discussion of the effects of canalization and changes in
sanitary conditions since 1914-1916. U.S. Pub. Health
Service, Pub. Health Bull. No. 204, 111 pp.
2.	Hydroscience, Inc., 1968. Water quality analysis for the
Markland Pool of the Ohio River., Malcolm Pirnie Engrs.
White Plains, N.Y. 121.pp. and Figs.
3.	Hydroscience, Inc., 1970. Water quality analysis of the
Savannah River Estuary. American Cyanamid Co., Wayne, N.J.,
75 pp. and Table and Figs.
4.	Hydroscience, inc., 1973. Water quality analysis of Man-
hasset Bay. W.F. Cosulich Assoc., Plainview, N.J., 53 pp.
and Figs, and Append.-
5.	Hydroscience, Inc., 1973. Water quality analysis for the
Wallkill River, Sussex County, New Jersey. Sussex Co. Mun.
Utilities Auth., Newton, N.J. 81 pp. and Tables and Figs.
6.	Hydroscience, Inc., 1974. Water quality analysis of the
Hackensack River. Clinton Bogert Assoc., Fort Lee, N.J.,
77 pp. and Figs, and Append.
7.	Hydroscience, Inc., 1974. Water pollution investigations:
Black River of New York. EPA-905/9-74-009 U.S. EPA, Regs.
II and V, N.Y. and Chicago, 95 pp.
8.	Hydroscience, Inc., 1974. Development and application of a
steady^state eutrophication model of the Sacramento - San
Joaquin Delta. Bay Valley Consultants, San Fran., Calif.
228 pp. and Append.
9.	Hydroscience, Inc., 1975. Water quality analysis of the
West Branch of the Delaware River, N.Y., DEC, Albany, N.Y.,
102 pp. and Append.


-------
10.	Hydroscience, Inc., 1975. Water quality analysis of
Pennsauken Creek, Cooper River, Big Timber Creek and Upper
Great Egg Harbor River, N.J. DEP, Trenton, N.J., 163 pp.
and Append.
11.	Hydroscience, Inc., 1976. Water quality analysis of thQ
Jackson River, Vol. I, Westvaco Corp., Covington, Va., 87
pp. and Append.
12.	Hydroscience, Inc., 1978. NYC 208 Task Report, Seasonal
steady-state modeling (PCP Task 314). Hazen and Sawyer
Engrs. N.Y., N.Y., 667 pp.
13.	Hydroscience, Inc., 1978. Upper Mississippi River, 208
Grant, water quality modeling study, preliminary report.
Met. Waste Control Comm., St. Paul, Minn.
14.	Streeter, H.W., and Phelps, E.B., 1925. A study of the
pollution and natural purification of the Ohio River, III.
Factors concerned in the phenomena of oxidation and
reaeration. U.S. Pub. Health Serv., Pub. Health Bull.
No. 146, 75 pp.
15.	Thomann, R.V., R.W. Winfield and J.J. Segna, 1979 a.
Verification analysis of the Ontario and Rochester embay-
ment three dimensional Eutrophication Model. EPA Report
in Final Manuscript.
16.	Thomann, R.V. , and J.J. Segna, 1979 b. Dynamic p^iyto-
plankton-phosphorus model of Lake Ontario. To be presented
at Phosphorus Management Conf., Rochester, N.Y.
I-SO

-------
ONE-DIMENSIONAL TIME VARYING ANALYSIS
OF STREAMS AND RIVERS*
This section presents various time variable mathe-
matical models for describing water quality variations in
streams. -The modeling efforts have progressed to the point
where a sufficient degree of reliability has been obtained
to form the basis for making water quality predictions.
These predictions have been applied almost exclusively to
water quality problems resultihg from the discharge of
wastes from municipal and industrial sources. The classical
mass balance partial differential equations appear to be
reasonably satisfactory for a number of situations. The
time variability of various water quality parameters covers
a relatively wide spectrum, from the hour-to-hour types of
fluctuations resulting from fine microscale phenomena to
the day-to-day and season-to-season types of fluctuations
reflecting broader scale climatological conditions.
Efficient computational schemes are available to des-
cribe the water quality responses in streams due to time
variability of waste loads, water temperatures, and river
flows. A variety of verifications of the stream models has
been accomplished, primarily for-dissolved oxygen. The
dissolved oxygen verifications indicate that the models
generally describe the major features of the time and space
variability in both streams and estuaries.
*
Donald J. OlConnor
o? -/

-------
2.
A general mathematical description of natural systems
of fresh water which exhibit significant variation of water
quality variables in one-dimension are considered below.
The variation is assumed to be along the longitudinal axis
of flow, with uniformity assumed over the width and depth
of channel. Water systems, which may be characterized in
this fashion, include the majority of fresh water streams;
many rivers, both tidal and non-tidal; and some estuaries.
The primary purpose of this section is to develop the equa-
tions which are generally applicable to the analysis of water
_'iality in fresh water streams. In most cases, the stream
ir..w* be defined as a flowing system in which the advective
component of the flux is the significant factor in the mass
transport; hov:ever in some cases the dispersive, component may
be important in time-variable analysis.
BASIC EQUATIONS
The basic equation of an advective system is developed
in -the usual fashion by a mass balance over a differential
volume. Consider a body of fresh water flowing within a
specific, defined boundary. The direction of flow is along
the longitudinal axis (x); th^re are no vertical (y) or
lateral (z) gradients of concentration. Turbulent mixing
is sufficient to produce uniformity of concentration over
the cross-sectional area of flow, but insufficien to cause
a significant spreading or distortion along the flow axis.
A definition sketch is shown below:
5 -=2

-------
A Q
3.
Q 
Direction,x-
axis of flow
x=0
A x 
Element
The origin, x = 0, is usually established at the location of
~-.he discharge of the wastewater to the stream. Uniformity
'_ concentration over the cross-section is usually effected
within a relatively short distance from the outfall. This
condition is brought about by the lateral and vertical mixing
of the stream or by an appropriate diffuser design. In any
case, the assumption of the homogeneity over the cross is re-
alizable from a practical viewpoint.
A mass oalance around the elemental volume (V = A A x)
considers the increase in concentration from c to c + Ac over
the time interval At. At the upstream face the concentration
associated with the flow entering the element is c and at the
downstream face the concentration leaving is c + (3c/3x) Ax.
In addition to the change in concentration, it is also appro-
priate to consider a change in flow AQ over the element Ax.
This condition is characteristic of many natural streams, in
which the increase in flow is due to ground water intrusion
or a decrease due to evaporation. By definition, the transport
into and from the element is negligible. The change in mass
VAc.is the net result of the inflow and sources on the one
hand, and the outflow and sinks on the other. Furthermore,
<3 ~3

-------
4.
allowances for other sources and sinks, including the common
physical chemical biological reactions, are made by incorpo-
rating them in a single term, S:
VAc = Qc At - (Q + AQ) (c + Ax) At  S At	(1)
Expanding, simplifying and dividing by At, there results
v if = - Q |f to - ciQ  sv
Divising through by volum e, V, which equals AAx, and simpli-
fying, equation (1) becomes:
it - - s  (0c) 1 s	)
Equation (2) is the fundamental equation of water quality
models of an advective system, which is appropriate for the
analysis of most natural streams, particularly those which
are either shallow or rapid. The derivative on the right-
hand side of eq. (2) is the rate of change of material with
mass Qc with respect to distance	This derivative can be
expanded as follows:
If the flow rate is constant downstream, the second derivative
is zero, and the coefficient of the concentration derivative
becomes the velocity, U = Q/A. It is sometimes useful to ex-


-------
5.
press the advective flow in terms of the velocity, U, and
the area, A, in place of their product, Q, the rate of flow:
1" 8	x	13	Ct	J.  3U J. cU 3A1	/^K^
" A 17 tQe) = " A 5x (UAo) = " L 57 + c 37 + X 57j (3b)
The expansion indicates the relative influence of the various
parameters and their rates of change with distance and permits
evaluation of the error'introduced by the common assumption
of constancy of the parameters U and A.
INSTANTANEOUS MASS RELEASE
A fundamental experiment which can be carried out in
a natural body of water is an instantaneous release of a
tracer material such as dye. The mass of material, M, is
introduced into the water over a time interval, At, which
is short relative to the time scale of the processes which
govern mass transport in the water body. In the case of a
stream, At should be in the order of minutes. In addition
to being added over a short interval, the mass is usually
distributed over the cross section with area A, of the stream.
Thi6 uniformity over the cross-section is convenient for an
analysis of the results of the experiment in terms of one
spatial dimension, that along the direction of flow.
In the idealization of the mass transport in a stream,
represented by equation (2), the only mass transport mechanism
is the advective flow, Q, in the stream. Thus the mass of
dye introduced at time t = 0 at location x = 0 over the time
interval 0 ^ t ^At will move_down the stream with the water
i -s-

-------
6.
velocity U = Q/A. The basic result of the assumption that
only advection transports mass is that the mass of dye re-
mains in the parcel of water into which it was introduced
and does not spread into any other adjacent parts of the
water. It is further assumed that both the area A and velocity
U are constants. The length of this parcel of water, denoted
by Ax, is Ax = UAt, and the concentration within the parcel is
the mass of dye introduced, M, divided by the volume of water
into which it was introduced, and this volume is given by the
length of the parcel times its cross sectional area A, i.e.
AAx. Therefore the concentration is M/AAx = M/AUAt. The
location of the parcel at any time t is given by the simple
relation that the distance travelled at a velocity U during
a time t is Ut. Having obtained the concentration ofthe dye
in the parcel and its location at any time t, it is now pos-
sible to write an equation for the dye concentration distribu-
tion in space and time resulting from the initial discharge
of mass, M, over 0 -S t $ fit at x = 0. The equation is
c(x,t) =	0t-N
-------
7.
To demonstrate that this behavior is indeed pre-
dicted by eq. (4), let (x) represent the initial concen-
tration distribution in the stream at t = 0 i.e. c(x,0) 
c^ (x). Then by the argument presented above, the concen-
tration at location x at time t should be c^(x) displaced
by the distance travelled during the time from release to
time t, that is, Ut. Hence the solution is:
c(x,t) = ci (x - Ut)	(5)
To see that this solution satisfies the differential equation
? + u - 0	<*>
it is necessary to substitute the solution into this equation
Performing the indicated differentiations:
a	3c. (z) a dc. (z)
 tc.(x - utn ^Is If = -k- <-o>	(7)
a	3c. (z) a dc. (z)
 [C(x- UU1	H If -fe-
where z = x -Ut and the chair rule is used for taking partial
derivatives with respect to x and t. Substituting these
results into eq-. (2) yields
dc.	dc.
" u &r * 0 cnr - 0	(8)
which is an identity for any c^ so that the solution
c(x,t) = c^(x-Ut) does indeed satisfy the conservation of
SL-7

-------
8.
mass equation for a stream. The physical interpretation
of this result is that the only effect of the stream on
the concentration of conservative mass is to transport the
mass downstream without any modification of its shape
whatsoever. This behavior is illustrated in fig. (16).
c^ (x) , due to some irregularity in introducing the dye into
the stream, is also somewhat irregular. This shape is pre-
served exactly as the parcel of water moves downstream; no
modification of its shape occurs. It is this idealization
of the actual behavior of natural streams which is embodied
in equation (6).
The idealization proposed in the previous sections for
the model of-a stream neglected the mechanisms in natural
rivers and streams which cause mixing of adjacent parcels of
water. These mechanisms include turbulent diffusion, vertical
and lateral velocity gradients and the effect of small varia-
tions in the geometry of the river. To account for these
effects an additional mass transport term, the eddy dispersion
term, is included in the conservation of mass equation. The
behavior of this equation is more complex than the purely
advective equation since the eddy dispersion causes adjacent
parcels of water to exchange mass thus producing a smoothing
and spreading of the dye mass as it travels downstream.
It is the purpose of this section to illustrate the
behavior of these solutions and investigate their relationship
tothe solutions of the purely advective model. It is assumed
5-2

-------
9.
that the parameters e, A, and Q are constants in time and
space and that S = 0. It is convenient to investigate the
solution of the river equation to a truly instantaneous dis-
charge of mass, M, at t = 0 and x = 0. In effect, a truly
instantaneous discharge occurs when At, the interval over
which mass is introduced, shrinks to zero. In mathematical
terms, this corresponds to an initial concentration in the
river given by the following limit:
c(x,0> =	o C x * 0 t (9)
= 0	elsewhere
This equation is of course a mathematical idealization since
it requires that an infinite concentration to exist over a
zero length of river. In practice however, all that is re-
quired is that At be small. It should be remarked that the
above equation is not a mathematically legitimate limit. It
is meant to be only indicative of a function which will be
made more precise subsequently, the delta function. In any
case, it represents a very narrow spike of concentration at
x = 0 due to a mass discharge at x = 0. The solution of the
river conservation of mass equation for this initial concen-
tration is:
M	- fx-ut)2/tet	(10)
c(*'t) = 2A.TFt e
The concentration profile which results is illustrated in
Figure (lc). The peak concentration moves with velocity U.
However, in contrast to the stream model solution, the


-------
10.
shape of the concentration profile changes as it progresses
downstream. The peak concentration decreases and the
longitudinal extent of the concentration profile increases
as time elapses. Thus the shape of the concentration pro-
file is modifieu by the eddy dispersion. This occurs because
adjacent parcels of water are mixing both upstream and down-
stream of its original location. In addition, the mass
transport effect cf the velocity ir tc transport the whole
distribution downstream at a velocity U.
To further illustrate this smoothing effect, suppose
the initial concentrntion at x = O and t = 0 is somewhat
irregular as in the stream model example. The resulting
concentration distribution is illustrated in Figure (Id).
The initial irregularity is smoothed out by the action of
dispersion and the concentration profile which results at a
later time is more regular than the original distribution.
It is the importance and degree of this smoothing and spread-
ing	determines which model is used in a particular
pr' :V  .al application".
In addition to the concentration distributions portrayed
at specific times, it is also convenient to examine the dis-
tribution of mass which is observed at specific locations as
time passes as represented by equation (10) . These distribu-
tions are examined in figures (le) and (If). Whereas the mass
distributions are symmetrical with respect to space as shown
2 - / o

-------
11.
in figure (lc), they are markedly skewed along the temporal
axis. This is due to the basic mechanism of dispersion
which produces more spreading as time increases. Thus at
a fixed time the dispersion experienced both upstream and
downstream of the center of the concentration profile is
the same and so the distribution is symmetric in space at
a fixed time. However at a fixed point in space the concen-
tration profile which is observed experiences more dispersion
as time passes so that the initial portion of the profile is
more peaked relative to the later portion observed at a later
t*
-------
12.
c^(x) which describes the concentration distribution at t = 0
for x >, 0 and a boundary condition c^(t) which describes the
concentration at a point x = 0 for t > 0. By combining the
two solutions obtained above, the general solution is:
c (x,t) = ci (x  Ut) x > Ut	(11a)
c(x,t) = cb (t - x/U) x < Ut	(lib)
The solutions for a non-conservative mass discharge
are similar to these equations. The consideration of mass
equation is:
3c	3c
- U ^ - Kc	(12)
and for initial and boundary conditions c^(x) and c^ft), the
solution is:
c (x, t) = cA (x - Ut) e~Kt	X > Ut	(13a)
c (x/1) = cb (t - x/U) e~K x/U x < Ut	(13b)
For example, assuming a variable discharge rate from
a waste treatment plant, which frequently has a typical diurnal
pattern, and assuming a constant fresh water flow and cross-
sectional area of the stream and a simple periodic function
to describe the discharge, the concentration is:
_
, c(x,t) = [lo + a0 sin ^ ~ X//U^ 7tJ e U
Kx
(14)
<2-/2

-------
13.
in which
w
L = K = mean concentration over the period, p, at x=0,
o Q
the location of the waste discharge
aQ = amplitude at x = 0
p = period of the cycle.
The initial variaton, at x = 0, is transferred downstream at
a velocity, U, and is attenuated by the characteristic reaction.
At any location, x, the variation of the concentration lags the
initial by a time interval equal to x/U.
An example of a time-varying waste water discharge, W,
and its effect on the dissolved oxygen concentration in the
Ohio River downstream from the City of Cincinnati is presented
in Figure 2. The four spatial profiles of dissolved oxygen
below the major source of wastewater from the Mill Creek Treat-
ment plant were measured on four successive days following a
weekend, during which period the mass rate of BOD discharge
from the plant is less than the 5-day work week.. The effect
on the dissolved oxygen concentration of the reduced BOD dis-
charge entering over the weekend is clearly evident a.= c-mpired
to that concentration resulting from the weekday discharge.
The peak of the weekend concentration is propagated downstream
at the velocity of stream. This case is discussed more fully
in a subsequent section. The data is presented at this point
to indicate at least qualitatively the nature of the phenomenon
as observed in one river and its counterpart in the equations
above.
A -/3

-------
PHOTOSYNTHESIS AN) THE DIURNAL I-ISSOLVED OXYGEN
VARIATION IN STREAMS *
14.
The concentration of dissolved oxygen is a. significant
factor in the evaluation w-?tr:r pollution and in the manage-
ment of water quality. In rol.uively unpolluted waters the
dissolved oxygen con centration may fluctuate about the satura-
tion va.lue, a stat-:. which results from the dynamic equilibrium
among the biological, chemical and physical components of the
environment. There is a great diversity of species with no one
form predominating, sources and sinks of oxygen are in approxi-
mate balance, and the concentration remains close to saturation/
with some diurnal variation due to the temperature and photo-
synthetic activity of green plants. By contrast, in a stream
receiving untreat'.jJ v;astewaters, the natural balance is upset,
bacteria predominant, and, among many other effects, a marked
depression of the dissolved oxygen results. In many streams,
into which are discharged wastewaters from intermediate or
secondary treatment processes, the dissolved oxygen condition
reflects characteristics of both these extremes and it is quite
common to observe both bncterial and algal effects. The classic
sag in the dissolved eveyyen distribution may be observed, super-
imposed on which is a diurnal fluctuation due to algae growths,
stimulated by the; nutrient:; from the waste source .or from the
end products of earlier reactions. On the one hand, the bacteria
~O'Connor, D.J., Di Toro, D.M., J. ASCE Vol. 96, SA2., April 1970,
A - / V-

-------
15.
produce a typical longitudinal distribution of dissolved
oxygen deficit, the components of which are the carbonaceous
and nitrogenous sources in the wastewater, the latter being
more significant in secondary effluents. On the other, the
algal effects cause a typical diurnal fluctuation, which
generally increases in amplitude downstream from the source,
reaching a peak and subsequently decreasing to levels charac-
teristic of upstream stretches. It is the specific purpose
of this section to present a mathematical formulation of the
effect of these factors on the dissolved oxygen concentration
in rivers, particularly with respect to the photosynthetic
effect.
Theory
The most general form of equation which describes the
longitudinal distribution of dissolved oxygen or any non-
rojervative or conservative substance is developed by a
,.aiance employing the continuity equation. The specific
foi of the equation for a given stream is determined by the
hydrau1^, hydrological and geomorphological characteristics-
of the drainage basin and river channel, on the one hand, and
the various physical, chemical and biological characteristics
of the aquatic environment and wastewater discharges on the
other. For the rivers and conditions considered in this section,
Equation (2) takes on the following form for the concentration
of dissolved oxygen.
it = " i If + Ka tcs ~ c) " KdL(x) - V*(x) +	- R(x)-S(x)
(15)
- / S~

-------
16.
in which
c	= concentration of dissolved oxygen
cg = saturation value of dissolved oxygen
K	= reaeration coefficient
cl
K, = coefficient of carbonaceous oxidation
d	x
~Kr!J
L(x) = LQe = distribution of carbonaceous BOD.U*Q/A
K	= coefficient of nitrogenous oxidation
n	x
~KnU
N(x) = NQe = distribution of nitrogenous BOD. U=Q/A.
P (x,t) = algal photosynthetic oxygen source
R(x) = algal respiration sink
S (x) = benthic bacterial respiration sink.
The common sources of dissolved oxygen are those due
to atmospheric reaeration, the photosynthetic contribution of
the algae and incoming flow, while the sinks are the respira-
tory functions of bacteria and algae in both planktonic and
t*nthic environments. The bacterial respiration is composed
of carbonaceous and nitrogenous components. The bacterial
respiration of benthic oommunity is assigned a9 a separate
sink. The algae in both floating and stationary form are in-
cluded as a single source. For the sake of mathematical
simplicity the spatial distributions of both the photosyn-
thetic source and the respiration sink are assumed to begin
abruptly at x = 0 and remain constant for x > 0. The effect
of any upstream algal activity, i.e. for x < 0, is taken into
account in the boundary condition at x = 0. The temporal form
of the respiration sink is assumed to be a constant R. This
A-(<

-------
17.
is the traditional assumption and it appears to be justifiable
to within the accuracies of the data so far available. The
temporal variation of the photosynthetic oxygen source is a
result of the solar radiation incident on the algae present.
The variation of oxygen production with increasing solar radi-
ation and the attenuation of solar radiation with increasing
*
depth have been investigated. With increasing solar radiation
the rate of oxygen production increases to a saturation value
and then decreases. For a bright day, at the top layer of
water, the oxygen production may be less at midday than during
the morning and afternoon. However, solar radiation decreases
with depth so that in the middle of the euphotic zone the oxygen
may be more or less proportional to the sunlight intensity. If
the average -over depth is taken then the shape of the cross-
sectional average photosynthetic oxygen production rate re-
A *
3-^nbles the shape of the incident solar radiation. For the
c-tke of simplicity the temporal form of the photosynthetic
oxygen source is assumed to be representable by a half-cycle
sine wave. If more complete information is available this as-
sumption can be refined. Let P(t) represent the rate of photo-
synthetic oxygen production as a function of time, thus P(t) is
given by
P(t) =' Pm sin (t-ts)3 ts t ,< ts + p
= 0	ts + P*t^ts + i
* Ryther, John H., "Photosynthesis in the Ocean as a Function
of Light Intensity" Limnology & Oceanography, Vol. 1,1956
,pp. 61-70.
** Westlake, D.J. "A Model for Quantitative Studies of Photo-
synthesis by Higher Plants in Streams" Air and Water
Pollution Journal, Vol. 10, pp. 883-896.
.* -/ 7

-------
18.
where
= the maximum rate of photosynthetic oxygen
production (mg/1 day)
t = the time at which the source begins (days)
s
p = the fraction of the day over which the source
is active (days).
This function is assumed to repeat periodically every day.
Equation (16) specifies P(t) for one day only; its periodic
extension can be expressed as a Fourier series:
P(t) = PM | + "2 bn cos [ 2 IT n (t-ts - p/2)]| (17a)
where
b"= C0S  0^ and an arbitrary
boundary condition Do( t) , Equation frs) has as its solution;
A - / 2

-------
D(x,t) = D0 (t - ) e

Cm
Kd *o
KA - Kd
t'
- Kr " %-&
- e
]
~ [-- *"*_/* *1
% - 1% L	J
+ ii I1-'"***]
- K x
A TT
+ R
[' ]
{
-K X
- pm 1 ^ ^ - e )
^ > i pl	n cos f 2^n(t~t."P/2)_ tftn ( if 11
+ n=l /K^ +(2TTn)	L	8	*KA 'i
-A<
(19a)
(19b)
(19c)
(19d)
(19e)
(19f)
(19g>
-K
:A$ >
- e
2,	n	r	-i/lMj
n-1 /V +(2TTn)2 cos [ 2Tr(t-tB-p/2-x^J5- tan ( KA /]
(19h)
It has been assumed in this solution that the periodic photo-
s} .:thetic source has been active for a long time i.e. a
periodic steady state has been achieved.
2 ?

-------
20.
Equations 19b, 19c and 19d are the well known deficit
solutions due to BOD and benthic sinks of DO. Equation 19a
is the solution for a time-varying initial deficit of DO. The
portion of the dissolved oxygen deficit solution due to the
photosynthetic source and respiration sink is made up of three
parts. The average daily photosynthetic oxygen production
(equation 19f) and the respiration (Equation 19e) portion of
the solution are constant in time and build up to their equili-
brium values of P,,,/K and R/K *-<=ispectively as x/U increases.
SV a	d
The term Equation 19g is independent of position and represents
".he solution after the effect of the initial abrupt beginning
of the photosynthetic source at x = 0 has decayed to zero. The
portion of the solution which is due to the abrupt beginning
(Equation 19h) is multiplied by an exponential which goes to
zero as x/U increases. For large K , as is the case in the
cl
streams to be analyzed herein, the diurnal fluctuation of the
solution due to the photosynthetic source has zero amplitude
at x = 0 and increases to the steady state amplitude given
by Equation 19g.
The following effects have not been included in this
solution: the time variation of the flow, the time variation
of the temperature and wastewater discharges, and the effect
of dispersion. In the streams to which this solution is ap-
plied it is assumed that the primary cause of the diurnal
variation of the dissolved oxygen is the algal oxygen production.

-------
21.
EXAMPLES
Five rivers have been selected for analysis, the Grand River
the Clinton River ^ and the Flint River ^ in Michigan? the
Truckee River ^ in Nevada, and the Ivel River ^ in Great
Britain. The selection is based on the availability of histori-
cal data which is complete enough for the proposed analysis, the
emphasis being on the diurnal behavior of dissolved oxygen and
the effect of the nitrogenous. BOD component. The data available
for analysis was observed during periods when a reasonable ap-
proximation of a steady-state flow and temperature prevailed.
The average cross-sectional area for each river except the
Flint and the Ivel is obtained from the reported time of passage
studies and average river flows. For the Flint River, detailed
cross-sectional information, Figure 9, is available, for the -Ivel
the average depths are reported in all cases except the Grand for
which it has been subsequently obtained and the Ivel for which it
has been back calculated from the reported exchange coefficient.
Using these data, the reaeration coefficient is calculated from
the formula:
Ka " 
-------
22.
known effluent concentrations and flows from treatment plant in
the reaches analyzed are used to establish loads. The carbonace-
ous and nitrogenous reaction coefficients, and Kn, are determined
from a plot of the logarithm of the particular component of the
BOD versus distance from the source. The slope of the line, multi-
plied by the velocity, yields the coefficient. The nitrogenous
and carbonaceous components of the BOD data are obtained in a
variety of ways: nitrification suppression using methylene blue
for the Grand; estimated ultimate first stage BOD, organic nitrogen
and ammonia measurements for the Truckee; 5-day BOD and some am-
monia measurements for the Flint. There is no reported nitrogen
data for the Clinton, and the Ivel is relatively unpolluted, having
no significant concentration of BOD. The concentrations, L and N
o	o
were taken from the direct measurements and checked whenever possible,
by a mass balance upstream and downstream of the waste discharge.
The BOD analysis establishes the sinks of oxygen due to the
carbonaceous and nitrogenous-BOD. There remains the algal source
. nd sink of oxygen. The procedure adopted to obtain Pm and R is
largely one of trial and error based primarily on the magnitude
of the diurnal fluctuation at the various stations downstream and
guided by whatever qualitative information is available about the
algal populations. The two times tfl and p are established using
the time of sunrise and sunset. It has been found that that best
fits are obtained if tg is slightly later than sunrise and if p is
slightly less than the total time between sunrise and sunset.
This is probably due to the fact that the assumed shape of the
photosynthetic oxygen source risas and sets more quickly than
~ ^3. A.

-------
23.
apparently is the case.
The procedure is as follows: the diurnal dissolved oxygen data
at the first station establishes the boundary condition. This
condition, the carbonaceous and nitrogenous BOD sinks, and as-
sumed values of P and R are used for the first uniform segment
m
of river. A uniform segment ends at either a load which alters
the BOD concentrations and possibly the structure of the algal
population, ox^. a discontinuity in area or depth, or a discontinuity
in P and R reflecting a change in algal productivity. At such
m
a point the values of the parameters change and numerical calcu-
lations are initiated again. The boundary condition used is the
diurnal distribution calculated for the end of the previous segment.
In effect, this procedure makes possible the solution of more
general stream configurations which are limited only to piecewise
-instant spatial parameters. Using this technique the values of
~ and R which best fit the data are chosen. The choice of P is
m
g-i ided by the fact that the magnitude of the diurnal fluctuation
at a station is directly proportional to P^ so the change in P^
which is required to fit the data can be calculated after one
trial. The appropriate value of R can be chosen by expressing
the data as deficit of DO and trating the respiration source of
deficit independently of the other sources and sinks. Since the
respiration is assumed to be a constant in time, its effect is only*
to lower the average daily value of the DO. Hence the appropriate
value can be obtained from a spatial plot of the time averaged data.
Using this procedure, then, it is possible to chose P and R more-
m
or less independently since the P^ is chosen using the magnitude
of the diurnal fluctuations as a guide and the R is chosen using
2. - A-3

-------
24.
average values. Therefore under the assumption that respiration
is a constant in time it is possible to separate these two algal
effects. It should be recognized, however, that the respiration
is, in effect, all respdration not accounted for by other sinks of
DO, and to that extent is not necessarily only algal respiration.
For example, it may be benthic respiration which has not taken
explicity into account. On the other hand, the final choice of
R does reflect all that is known about the river oxygen balance,
e.g. benthic respiration can be independently assigned, and, to
that extent, it can be reliably estimated.
Tabulations of hydraulic characteristics, the parameters, and
the boundary conditions employed in this analysis are presented
as follows: Table 1 includes the location of beginning of the
segments, their lengths (X), cross-sectional areas' (A), depths
(H), temperatures (T) and river discharge (Q), reaeration coef-
ficient (K ), and carbonaceous and nitrogenous reaction coefficients
(Kg, K^). The time variable initial conditions of dissolved oxygen
are presented in Table 2. Table 3 lists the parameters defining
the algae effects: the time (t^) at which the photosynthetic
oxygen source begins, the period (p) over which the source is non
zero, the maximum rate (P^) of photosynthetic oxygen production,
the daily average rate of- photosynthetic oxygen production
P^v = 2p	the rate of algal respiration (R) and the ratio


-------
25.
Grand River
The Grand River is located in the southwestern part of
Michigan, flows westerly to Lake Michigan and has a drainage
area of 5,620 square miles. The City of Lansing is located
approximately 150 miles upstream from the mouth of the river.
The analysis of a survey conducted in August 1960 extends from
the discharge of the waste treatment plant to a point about 25
miles downstream. The treatment plant is a biological process
of the activated sludte type. The possibility of nitrification
as an important factor in the oxygen balance was recognized at
the time of the survey and nitrification suppressed BOD's by
methylene blue were also obtained. No benthic respiration is
assumed since the river velocities prior to the survey were large
enough to scour the bottom. Insufficient information is available
upstream of the Lansing waste discharge to include this re'gion in
the analysis. The analysis is begun at the Lansing treatment
plant using river conditions extrapolated from downstream values
as the initial conditions. No diurnal DO fluctuation is assumed
for the boundary condition. The reach up to the Grand Ledge Dam,
Stations 1, 8, 9, 10, is assumed to be spatially uniform. Down-
stream of the dam, Stations 11, 12, 13, 14, profuse attached
aquatic plants ,alter the composition of the algal community and
it becomes much more productive. Accordingly at the dam a new
segment is begun with different Pm and R. A comparison of the
calculated profiles and observed data are shown in Figures 3 and 4 .
In particular it is clear that the nitrogenous BOD is an im-
portant factor in the oxygen balance in streams. For the second
<2. -AS"

-------
26.
segment analyzed two curves are shown corresponding to Pm _ ^
and = 65 mg/l-day. These two curves are intended to describe
the data taken on the two successive days, August 29th and 30th.
The solar radiation data available^, Figure 3, indicates that
the second day was indeed brighter than the first; hence a larger
production of oxygen is expected. This effect is not clearly dis-
cernible in ohe data upstream of the dam. For the first segment
the ratio of average daily photosynthetic production of oxygen to
average daily respiration Pav/R - 0.35, indicating that the
,vsnktonic community is a net liability to the dissolved oxygen
resources of the stream. Downstream from the dam the ratio equals
1.1 and 1.4 respectively which implies the converse. In this
stretch of the stream the algal community includes benthic algae
ana iarger aquatic plants as well as any planktonic algae which
may be present.
Cliv.. on River
The Clinton River, located in the southeast cornner of Michigan
in the Lower Peninsula, discharges into Lake St. Clair. The basin
has a drainage area of approximately 74 0 sq. mi. The reach con-
sidered in this analysis of survey conducted during August 23-25,
1960 starts at mile point 44.87, Station 2, below the Pontiac
Waste Treatment Plant effluent at mile point 46.39 and ends at mile
point 34.98, Station 8. A boundary condition is established at
Station 2 by fitting a two term Fourier series to be observed dis-
solved oxygen data. The reach including Stations 3,' 4, 5 and 6 is
assumed to be spatially uniform. The aquatic vegetation in this


-------
27.
stretch seems to be mainly attached bottom plants. Between
Station 6 and Station 7 the algal population appears to increase
in productivity and the survey report cites "numerous weed beds1'
in this reach. To account for this spatial change a new segment
is established 0.5 miles below Station 6 and includes Stations 7
and 8. In this segment the productivity increases markedly while
the respiration decreases slightly. The ratio of P to R changes
flv
f ' i.". 0.43 to 0.84. This pattern is similar to that encountered
in the analysis of the Grand River. The resulting theoretical
curves are compared to the data in Figure 5.
Truckee River
The Truckee River is located near the western border of
.;vada and. flows in a northeasterly direction from Lake Tahoe
o Pyramide Lake, Nevada, a distance of 106 miles. The reach
considered in this analysis begins at mile point - 2.8 (river
miles below the Reno U.S.G.S. gage) designated as Station 1 and
ends at Station 7, mile point 21.0. The survey was conducted
in the period from July 10 to 25, 1962. within the reach there
are three principle sources of wastewater: the Reno Waste Treat-
ment Plant effluent at mile point 0.7, the effluent from the
Sparks Waste Treatment Plant which enters at mile point 6.0 and
Steamboat Creek entering at mile point 5.7 whose flow is partially
irrigation return waters and agriculture drainage. The latter
two sources will be treated as one combined source at mile point
5.9. For this analysis, therefore, the reach will be divided
into three sections: Station 1 to the Reno.Waste Treatment Plant,
Reno to Sparks - Steamboat Creek, and Sparks - Steamboat Creek to
Station 7.
>2.-3.7

-------
28.
The analysis of the carbonaceous BOD follows that given in the
report of the survey. Five-day BOD's, corrected for the onset of
nitrification, are used to obtain ultimate carbonaceous BOD. The
available nitrogen data comprises measurements of organic nitrogen,
ammonia nitrogen, nitrite nitrogen and nitrate nitrogen. No ap-
preciable ammonia nitrogen is found in section 1. At the beginning
of section 2 the abrupt increase of ammonia nitrogen can be attributed
to the Reno effluent. There follows a substantial decrease of both
ammonia nitrogen and total nitrogen in section 2. For section 3
ammonia is seen to decrease further while total nitrogen is ap-
proximately constant. The nitrate values increase correspondingly.
The ammonia nitrogen values can be converted to their nitrogenous
BOD equivalents using a stochiometric balance (NBOD = 4.6 x NH^-N).
In order to account for the decrease in total nitroger in Section 2
it is hypothesized that the benthic algae in this section are
metabolizing that fraction of the ammonia necessary to account for
th-. decrease in total nitrogen. This is taken in to account by
int.- iducing a benthic sink of NBOD in section 2 only. The remaining
NBOD- is.assumed to oxidize to nitrate following a first order reaction.
The algae population in the three sections are described in the
survey report: Station 2 "...abnormally profuse growth of a filamentous
alga (Cladophora)"; Station 3 "... lack of Cladophora ... in its place
the tolerant blue-green oscillatoria and the green filamentous algae
Stigeoclonium were quite evident"; Stations 5, 6, and 7, "The
tolerant algal forms found at Station 3 were not observed at Stations
5, 6 and 7, however growths of Cladophora were present. Sparce
growths of a rooted aquatic pondweed (Potamoqeton) were present at
a -5 2

-------
29.
Stations 5 and 6, but not at Station 7." Photoplankton samples
at three stations (1A, 3, 5) within the reach were analyzed;
diatoms were, the dominant form and the number per ml. were re-
spectively 1310, 7680 and 6380. Hence the division of the reach
into three sections also coincides with the changes in algal
populations.
An interesting phenonomena is observed to occur between Station
4 upstream of the combined load at mile point 5.9 and Station 5
the next downstream at mile point 8.7. The diurnal fluctuation
DO at Station 4 is 7 mg/1 while at Station 5 it is 2 mg/1.
,71his decrease in diurnal fluctuation cannot be explained as a
result of a decrease in P_ since the effects of the upstream
m
fluctuations at Station 4 would still be quite significant at
Station 5. The decrease in diurnal fluctuation is duG to the
low concentration of DO of the incoming wastewater which not only
lowers the average value of DO but also decreases the amplitude
of the diurnal fluctuation. The value of P in section 3 decreases
m
as can be seen from the distribution of DO at Stations 6 and 7.
The theoretical curves are compared to the data in	Figures 4 and 5.
(8)
In O'Connell's analysis of the reach between Stations 2 and
4, the values of maximum photosynthetic production	(P ) and average
iti
daily respiration (R), as shown in their Figure 5 are Pm = 50 mg/l-day
and R = 17 mg/l-day for Station 2B, which are comparable to the
values arrived at in the above analysis. However as shown in
their Figure 6, they also obtain a spatially varying photosynthetic
production and respiration. Unfortunately detailed dissolved oxygen
data between Stations 2, 3 and 4 is not available in the survey
reports so that further analysis is not possible. There are good
A-2 7

-------
30.
physical reasons to suppose that che algal photosynthetic source
and sink do not change abruptly as has been assumed herein,
however for the data currently available, this simplification is
warranted.
Ivel River
The Ivel River, located in Great Britain, is a shallow chalk
stream. Diurnal dissolved oxygen data is available at two sta-
tions; each station was sampled every 15 minutes for 24 hours
during May 1959. Following the same procedure as previously
outlined, the upstream station diurnal dissolved oxygen data is
pproximated using a two-term Fourier series and the data at the
downstream station is compared to the theoretical prediction.
The result is shown in Figure 8; the parameters are listed in
Tables 1 to 3. In order to fit the afternoon data, the period
of sunlight is extended one hour more than is justifiable from
the solar radiation data. Since the solar radiation measurements
were taken 16 miles from the river site there is a possibility
that this data is not representative. A comparison can be at-
tempted between the photosynthetic production and respiration rates
(5)
estimated by Edwards and Owens and those indicated in Table 3.
Unfortunately the average depth of the Ivel is only an estimate
based on the reported exchange coefficient and formula for the
reaeration coefficient.	However using this value of
H = 0.45 m, Edwards' and Owens' estimates in concentration units
are:-Pm = 58 mg/l-day and R = 17 mg/l-day which are comparable to
the estimates arrived at by this analysis.
<2. -? o

-------
31.
Flint River
The Flint River, located in the eastern-central portion of
Michigan, has a drainage area of 1,350 sq.mi. The reach analyzed
in this paper extends from Station 6, Stevenson St., Flint, to
Station 15, Dodge Rd., of the July 28-29, 1959 Survey of the
Michigan Water Resources Commission. River cross-sectionings at
500 ft. intervals are available and the cross-sectional area and
depth are presented in Figure 9. The variation of the cross-
sectional area and depth as a function of distance downstream
necessitates the division of the reach under analysis into five
uniform segments which approximately account for the observed
variations. The two major point sources of BOD and DO deficit
are the Flint and the Flushing Sewage Treatment Plants, both of
which are trickling filters. The carbonaceous and nitrogenous
BOD concentration of the effluent of the Flint STP is reported?
the corresponding information for the Flushing STP is estimated
from the availably river BOD and nitrogen data. The existence
of a benthal deposit is reported below the r"lint STP and its ef-
fect on the oxygen balance is estimated from the river DO data.
Although the carbonaceous BOD information is adequately representa-
tive, the nitrogenous BOD information is somewhat limited, compris-
ing four ammonia concentrations taken a week before the actual
survey.
At the beginning of section 1, the initial conditions are es-
tablished from the repotted river data (Table 2). A relatively
high rate of nitrogenous BOD oxidation in this section is confirmed
<2 -3 (

-------
32.
by the available river ammonia data. The Flint load marks the
beginning of section 2. As usual materials balance between the
reported loads of CBOD, NBOD, and an assumed dissolved oxygen
concentration of zero in the effluent with calculated distribu-
tions establishes the initial conditions. In this short segment,
a beni-mc respiration load due to a reported sludge deposit is
included. Since no independent measurement of the oxygen uptake
rate of the sludge deposit is available it is difficult to dis-
tir.au.Ish its effect on the river dissolved oxygen from the algal
respiration. Hence the assumed benthic and algal respirations
are arbitrarily assigned although the magnitude of their sum is
that required by the observed oxygen data. The diurnal distribu-
tion of dissolved oxygen at Station 10 is a result of both a
decrease of algal productivity due to water quality conditions
which sure not conducive to algal growths and the deficit contribu-
ted by the Flint Treatment Plant. This phenomenon has also been
observed in the Truckee.
The dissolved oxygen data in section 3 reflects the increased
photosynthetic production of oxygen. The authors report that
this section of the river is "nearly choked with submerged grass-
like aquatic vegetation probably Vallisneria or Sagittaria". As
a consequence the afternoon dissolved oxygen distribution reaches
nearly a saturated level at the end of the section. However the
morning distribution shows almost zero DO throughout the stretch.
With these low DO concentrations prevailing during part of the day
it is reasonable to assume that no appreciable nitrification is
a -3a

-------
33.
occurring in this section. Although not explicitly confirmed by
the river ammonia data, this assumption seems justifiable in
light of the concentrations of both ammonia and dissolved oxygen
in the section.
It is interesting to note that there are significant departures
from the theoretical diurnal dissolved oxygen distribution and the
observed distribution at Station 12 (see Figure 10). Here the DO
is substantially zero during the late evening and early mornina
hours. This low dissolved oxygen appears to be affecting the
bacterial and/or algal activity, as indicated by the shape of
the diurnal dissolved oxygen curve.
The dissolved oxygen data at Stations 13 and 14 in section 4
after the Flushing STP show a recovery and also indicate that a
phytoplankton activity is significant. The amount of rooted
aquatic vegetation is reported as sparce; yet the diurnal dis-
solved oxygen data indicate that the average photosynthetic
oxygen production is P_ =19. In section 5, the average daily
av
oxygen photosynthetic production increases to P = 22, in ac-
dv
cordance with the observed increase in the amount of grass-like
aquatic plants from spapce to moderate.
The spatial distribution of dissolved oxygen at the two times
reflecting the extreme conditions are presented in Figure 9.
The theoretical diurnal curves are compared to the data in Figure 10.
A -3 3

-------
34.
CONCLUSION
The computations based on the proposed formulation agree
reasonably well with observations in various fresh water streams.
Both carbonaceous and nitrogenous components of bacterial activity,
atmospheric reaeration, benthal deposits and the photosynthetic
and respiratory contribution of the algae and other aquatic
plants have been considered. Although primarily directed to an
analysis of the dissolved oxygen condition, the analysis may be
urrid for productivity and respiration studies of aquatic communities.
Tl * photosynthetic effect can be the dominant factor in the diurnal
variation of dissolved oxygen as shown by the rivers investigated
in this paper. These effects are primarily due to algae, al-
though larger rooted plants may be important in some cases. The
growth of the"aquatic vegetation is stimulated by nutrients dis-
charged to the streams from the various sources within the drainage
basin, particularly the effluent waters from treatment plants.
Correlations of computed profiles and observed data in both
the spatial and temporal domains are favorable. Therefore,
more confidence can be placed in the ability to predict the ef-
fects of wastewater discharges on receiving waters. Particularly
important is the effect of the demand of the nitrogenous component
on the oxygen resources. It is significant to date that all of
the streams analyzed in this paper receive effluents from biologi-
cal treatment plants. The importance of nitrification has been
demonstrated indicating the need to take this factor into account
with respect to secondary treatment. It can be generally expected
that this pattern of increased algal activity and nitrification
-R, -3 V-

-------
35.
will occur when secondary treatment facilities are installed.
The method of analysis presented provides a further technique
for water pollution analysis and should be useful in compre-
hensive planning of water pollution control facilities.
Further work should be directed to analysis of stream con-
ditions before and after treatment facilities ire constructed
'ad of time variable phenomena such as rresh water flow,
temperature and wastewater discharge.
Acknowledgment
This work was supported by a research grant from the Federal
Water Pollution Control Administration - WP-01468.
A -3 5~

-------
36.
APPENDIX IV.NOTATION
The following symbols are used in this paper:
A
=
cross-sectional area;
bn
=
nth Fourier coefficient of photosynthetic oxygen source;
cS
=
saturation value of dissolved oxygen;
c{x,t)
=
concentration of dissolved oxygen;
D(x,t)
=
dissolved oxygen deficit concentration;
D0(t)
=
boundary condition of dissolved oxygen deficit;
dl
=
dlffusivity of dissolved oxygen;
H
=
river depth;
Ka
=
reaeration coefficient;
Kd
=
deoxygenation coefficient of carbonaceous BOD;
K*k
L{x)
=
deoxygenation coefficient of nitrogenous BOD;
=
carbonaceous BOD concentration;
L0
=
L(o);
Mx)
=
nitrogenous BOD concentration;
N0
=
Mo);
Pit)
=
photosynthetic oxygen source;
Pm

maximum rate of photosynthetic oxygen production;
P
-------
37.
References
1.	Courchaine, Robert J., State of Michigan Iteport on Oxygen
Relationships of Grand River, Lansing to Grand Ledge, 1960
Survey, Water Resources Commission, Mich., May 196z.
2.	Gannon, John J., River BOD Abnormalities, Dept. of Environ-
mental Health, School of Public Health, Univ. of Mich.,
Nov. 1963.
3.	Courchaine, Robert J., State of Michigan Report on Oxygei.
Relationships of Flint River, Flint to Montrose, 1959 Survey,
Water Resources Commission, April 1960.
4.	O'Connell, R.L. et al. Report of Survey of the Truckee
River, Field Operations Section, Technical Services Branch,
Div. of Water Supply & Pollution Control, PHS, July 1962.
5.	Edwards, R.W., and Owens, M., "The Effects of Plants on River
Conditions IV. The Oxygen Balance of a Chalk Stream*, J.Ecol.
50, pp 207-220, Feb. 1962.
6.	Churchill, M.A., Elmore, H.L., Buckingham, R.A., Prediction
of Stream Reaeration Rates, Proc. ASCE J. San.Engr.Div.,
SA 4 p. 1, July 1962.
7.	Strommen, N.D., Personal Communication, Weather Bureau,
East Lansing, Mich.
8.	O'Connell, R.L., and Thomas, N.A. , "Effects of Benthic Algae
on Stream Dissolved Oxygen", J. San. Eng. Div., ASCE, Vol. 91,
No. SA3, June 1965, Proc. paper #345.
i-37

-------
A-1
APPENDIX
NUMERICAL CALCULATION METHODS*
For cornclex natural systems it is often necessary to
solve the conservation of mass equations numerically.
Consider the following qeneral ecruation:
|| + U(x,t) | = S (c,x,t)	(1)
in which t = time; x = distance downstream; c(x,t) = concen-
tra; ion of the substance being considered; U(x,t) = velocity
of Lhe stream; and S(c,x,t) = distributed sources and sinks
of the substance being considered.
For a boundary condition at x = 0
c (0, t) = cb (t) t > 0	(2a)
and an initial condition at t = 0
c (x,0) = ci(x) x i 0	(2b)
the solution of Eq. 1 specifies the concentration over the
reqion x > 0, t > 0.
Two analytical techniques have been emoloyed to obtain
solutions for this equation: the method of characteristics
(9,10), and the LaPlace transform (5,12).
The method of characteristics which was develooed by
J.'Massau in graphical form, has been successfully aDDlied to
*Di Toro, D.M., J. ASCE, Vol. 95, SA4, Auq. 1969
3.-3 2

-------
A-2
propagation problems (1) and particularly to problems of
open channel flow (4). The LaPlace transform is a Dowerful
technique for obtaining solutions to the preceding equations
in certain simplified situations, i.e., when the eauation i9
linear, and the parameters are functions of time only. How-
ever, for the general equation with the velocity as a function
of both space and time and for the source term involving pos-
sibly a nonlinear expression in concentration (e.q. a second
order reaction tern) no known general solution for arbitrary
initial and boundary conditions is available. It is of interest,
'^refore, to inquire into numerical techniques that are ap-
'cable to these more complex problems in stream analysis.
The basic technique for obtaining numerical procedures
for the solution of differential equations involves the replace-
ment of the derivatives in the equation with finite difference
a}. i.-:oximations. A summary has been given (2,3) of techniques
applicable to Eq. 1 for which the x,t plane is divided into
a rectangular grid and the derivatives with respect to x and
t are expressed as differences. Both explicit and implicit
techniques have been investigated. Implicit techniques become
unwieldy when Eq. 1 is nonlinear since the resulting simultaneous
equations which must be solved at each time increment are also
nonlinear. Explicit techniques tend to become inaccurate for
initial conditions and parameters which are not smooth. The
resulting increase in computing time and computer memory necessary
3. ' 3 ?

-------
A-3
to preserve accuracy can be significant since the sDacmq of
the spatial grid, Ax, and the temporal grid, At, must satisfy
a stability criterion: UAt/Ax < 1. Also, there is no method
available to estimate the resulting error for a specific choice
of Ax and At so that the accuracy of the resulting calculations
is in doubt.
A second class of numerical techniaues which are appli-
cable to the solution of Eq. 1 are based directly on the
original idea of Massau, i.e., the equation is integrated alonq
its characteristics. The analytical basis of the proposed
numerical method is the observation that Eq. 1 can be reduced
to a coupled pair of ordinary differential equations using the
method of characteristics. These equations can then be integrated
using standard numerical techniques for a set of ordinary dif-
ferential equations. A direct application (8) of the method
of characteristics to Eq. 1 transforms this eouation into two
ordinary differential equations.
? [x(t),t]	(3a)
dc[xU) ,t] = s {c [x (t) , t] , x(t),t)
(3b)
The curves x(t) obtained from the solution of Ea. 3a are
called the characteristics of Eq. 1 and this family of curves
specifies the direction along which the solution propagates.
*2 -

-------
A-4
The method is based on the well known idea of integrating
quasi-linear partial differential equations along the
characteristics of the Eq. 6. However for the case of Eq. 1
the important difference which makes this method superior to
the methods based on a rectangular grid is that, in contrast
to other equations, Eq. 1 has only qne family of characteris-
tics, all of which allow propagation only in the downstream
direction. Hence the solution along each characteristic can
be obtained independently of the solution along neighborinc
characteristics.
A physical argument can be given which expresses the
content of the method of characteristics. The consequence
of having assumed that dispersion is not of significance is
that cross-sectional segments of water of differential thick-
ness in the x direction retain their identity as they flow
downstream. If the velocity is known then it is possible to
calculate the position of any segment of water and to follow
it downstream. It is as if a segment of water is tagged with
dye, so that its position can be determined as a function or
time (11). What occurs inside this segment of water is des-
cribed by an ordinary differential equation in tine Eq. 3b.
The coefficients of this equation which are functions of time
can be evaluated directly since time can be determined, e.g.
by a clock; the coefficients which are functions of position
or position and time can also be evaluated since the position
of the segment of water being considered is known from the
A - v- /

-------
A-5
solution of Eq. 3a. Hence, the behavior of each differential
segment of water can be calculated once its initial concentra-
tion is established at some initial point in soace and time.
This initial point corresDonds to the point at which an
initial or boundary condition is established.
The initial conditions for Eqs. 3a and 3b are determined
from the initial and boundary conditions of a. 1. Consider
the segment of water which passes x = 0 at t = t for some
t > 0. The initial conditions that apoly to Eqs. 3 are es-
tablished as the segment Dasses into the region under considera-
tion. Hence the initial conditions are given by the boundary
condition (Eq. 2a) of Eq. 1, i.e. for t = t ,
o
x(to) = 0	(4a)
c(0,to) = cb (tQ)	(4b)
For these initial conditions, each solution of the pair of
differential equations, Eq. 3, specifies the behavior of c(x,t)
wi-thin the segment of water that passes x = O at t = tQ.
For those segments that are already in the region of
interest, x > 0, at t = 0, the initial conditions for	pair
of Eqs. 3 are specified by the initial condition, Eq. 2b, of
Eq. 1. That is for the point x = xo, xq > 0 at t = 0, the
initial conditions for Eq. 3 are
x(0) = xq	(5a)
c (xo'0) = ci (xq)	(5b)
<2 -V-J.

-------
A-6
For these initial conditions, each solution of the pair of
differential equations (Eq. 3) specifies the behavior of
c(x,t) within the segment of water that is at x at t = 0.
By choosing initial positions, xq, along t = 0 and
using Eqs. 5 as initial conditions, and choosing initial times
t along x = 0 and using Eqs. 4 as initial conditions, it is
possible to obtain c (x,t) over the region x > 0, t > 0.
Hence the complete solution is calculated by repeatedly solving
Eqs. 3 for the various initial conditions.
The accuracy of the resulting solution can be estimated
in the following way. Since the transformation from the partial
differential equation, Eq. 1, to the pair of ordinary differ-
ential equations, Eas. 3a, b, is exact, no error has been
introduced. The accuracy of the numerical solution of the
ordinary differential equations can be controlled using the
predictor-corrector methods (7) for the numerical solution of the
ordinary differential equations. These techniques are quite
efficient and can be programmed to adjust.the time increment
At to maintain a specified level of error. The exror in the
calculations is independent of the choice of the spacing of the
initial points xq and t along the boundaries. Hence a coarse
grid can be specified for the calculation with a resulting sav-
ing in computation time without regard to a stability criterion.
3. - +3

-------
A-7
APPENDIX - REFERENCES
1. Abbott, Michael B., Introduction to the Method of Character-
istics, American Elsevier, New York, 1966.
2.	Birkhoff, Garrett, Partial Difference Methods in Proc., IBM
Scientific Computing Symposium Large-Scale Problems in Physics,
IBM Corp., 1965, pp 20-21.
3.	Birkhoff, G. and Kimes, T. F., "CHIC Programs for Thermal
Transients," Report WAPD-TM 24 5, Bettis Atomic Poser Laboratory,
Pittsburgh, Pa., 1962, Appendix B, po. 12-16.
4.	Chow, Ven Te, Open-Channel Hydraulics, McGraw Hill Book Co.,
1959, Chapt. 20.
5.	Di Toro, D.M. and O'Connor, D.J. "The Distribution of Dissolved
Oxygen in a Stream with Time Varying Velocity," Water Resources
Res. 4(3), June 1968, pp. 639-646.
6.	Forsythe, G.E. and Wasow, N.R., Finite Difference Methods for
Partial Differential Equations, John Wiley and Sons, N.Y. 1960,
p. 64.
7.	Hamming, R.W., Numerical Methods for Scientists and Engineers,
McGraw Hill Book Co., New York, 1962, Chapt. 15.
8.	Hildebrand, F.B., Advanced Calculus for Applications, Prentice-;
Hall Publishing Co., 1963, pD. 379-382.
9.	Ippen, Arthur T. and Harleman, Donald R. F.,"One Dimensional
Analysis of Salinity Intrusion in Estuaries," Tech. Bull. No.5
Committee on Tidal Hydraulics, Corps of Engineers, U.S. Army,
Vicksburg, Miss., June 1961.
10.	Li, Wen-Hsiung, "Unsteady Dissolved Oxygen Sag in a Stream,"
Journal of the Sanitary Engineering Division, ASCE, Vol. 88,
SA 3, Proc. PaDer 3129, May 1962, Dp. 75-85.
11.	O'Connell, R.L. , et a-2rr Report of Survey of the Truckee River,
July 1962, Robert A. Taft Sanitary Engineering Center, PHS.,
Cincinnati, Ohio, 1962, pp. 32-33.
12. O'Connor, D.J. and Di Toro, D.M., "An Analysis of Dissolved
Oxygen Varition in a Flowing Stream," Advances in Water Quality
Improvement, E. F. Gloyna and W.W. Eckenfelder Jr., Eds.,
University of Texas Press, 1968, pp. 96-102.


-------
Ctx.tl
la.
c.(x)
t
c(x.t)	cCx.t)
IC.
cC*.tl
c(x.t)
le.
c (x.t)
t
FIGURE 1
IMPULSE RESPONSE FOR STREAM
2. - V-i"

-------
ao-
2 o-o.
t *
 >-o>
L0>
t.o-
.'0-
-
a #.e-
f 4.0 
2 8.0 -
K.0-
1.0 
SUft'j" SAt~j
MONOAY, OCT, 2S, 196}
* "
2 0.0
I
8 
*jO
14
4
7,0
j 6j0
j' M-
1 **>
g M
*4-

TUESDAY, OCT. 29,1959
I	1	*1
< SUN. | SAT. (
WEDNESDAY, OCT. 90, IMS
	"I	1
SUN. | SAT. |
THURSDAY,OCT, SI, 19*9
l KILL a
-aowurr itdut wmkb
>miu. am www vera
4^S
'Husor cwtK
4604SS
MI14S BELOW PITTSBURGH
490
Fig. 2. Effect of weekday and weekend waste discharges on
Ohio River dissolved oxygen.


-------
GRAND f*VER
taw
n.rao
  (y>'.<3> .  5
awe wvct
4 8 II B 20 
MLES Fpnn I A>Nr. 8TP	
^80
Isl
s|S*
ibl20
twe 0m.' 'oooo' 1600 ' soo"oaoo iSr 5co
AUQ 2*1960
Mjg30,l960
Fig. 3
CUNTON RIVER
1 6
I 10
noi a
n; u
mnt	# ,
nv it
		r
TME Ofrx 0600 1200 (0QO
10
flT10N i IfflCND  HA n, to
Hf 13	 MA 14, to
rmoN 
JTITXH I
24
-------
_ 0
TWIQge RMP
a
UMJtM a

0 0800 I2 IBOO
mc ( mrs)
c8
u	I	I	I1 I I
ntm 1200 1800 2100
T1IC ( HPS)
Pig. 7
600
400
fUNT fHVER

 

 *
" * *
r'
 e
-V. , s
*  y' /

 s

vnor I ' ' Ai
^ V S
	anNS T*M*fT I
^(pcp (f	cp
< rmi
4	B	II
m "I FTOM STATION 6
IVEL RIVER
(4
12
10
e
e
4
- 2
F o
. rnre 
uf oo
	
oeoo izoo leoo
twe (ws)
2400
_L_
I I i	LL
0600	IZOO IBOO
TIME (WW
2400
Fig. 8
FLWT BVER
0
e
v
I 4
* 1 1 '
srv1
?w m  om  .
' 1 '
ETA1
rmn ii
time om OEOO 1200 IBOO MOO 0 CBOD 1200 IBOO &je~\
Fig. 9
Fig. 10
A - H-Z

-------
Fig. 12 Spatial and temporal variation of diaaolvad otiysen
deficit (millljrarai per lltar) for eoMtant treatment.
*ig . 11 Condition* for tin* wUbl* treatment eohei

1.1
Fig. 13 Spatial and temporal varlatloo of diaaolved myya
deficit (milligram* per lUer) for aeaaooal txaatmect.
a.-+.9

-------
4.0
NHL CREEK LOAD IMG
OCT. 28 TO NOV. 2. 1967
OBSERVED
SUNDAY
MONDAY
TUESDAY	WEDNESDAY
THURSDAY
DEFICIT AT MILE 490
FROM MILL CREEK CBOD
5.0-
4.0-
a
SB
O
o
UJ
o
e
MONO AT
TUESDAY
Figure 14
EFFECT OF DISP&HSION ON DISSOLVED OXYGEN DEFICIT
H -s~o

-------
I
tIt tJI
f
h
I' llf H
r
u
i!
5 5 5
CINCINNATI-
5 !
!V If
^MIAMI FORT -1-
i IJ
I
\
J	L
J	lilt
i
i
12
16
20
24
26
TOTAL OEFICIT
BACKGROUND BOO
AND OEFICIT
DEFICIT FROM HILL CREEK LOADINGS
J	1	1	1	I	I	I I 1 
8	12	16	20	24
SEPTEMBER 1967
. Figure 15
CALCULATED AN D OBSERVED TIME VARIABLE DEFICIT
26
a. -s~/

-------
TABLE 1.HYDRAULIC AND PHYSICAL CHARACTERISES
U*m
a
BafXDtti
Bum bar
>
lo-
Ceo. la
jnllfi
(3)
SofTBWt
Ueftb. U
mlloa
W
Croaa-
M0tkMJ
uaa, ^
to aqu*ra
(Mt
(8>
Dapth.
H. l&
taat
(6)
Taapcr-
tear*. T,
to dt*
PMI
a)
Dli*
efaarfft.
O.lB
ouhlo
fa* pr
nnud
(6)
Ami*
Uqd  K%,
par day
(
CBOD
KBOO
I>MK7Y*aA0an
*T
m
Xfl. par
toy
au
Onad
!
9.0
12.0
320.0
l.M
36.0
298.0
M>
0J0
1.90

1
13.0
U.I
220.0
1.90
26.0
tM.O
6.6
0.90
1.90
CUstfla
1
0.0
5.8
44.6
1J6
11.0
*3.0
6.0
3*6
-

1
6.3
14
44.6
IM
11.0
31.0
e.o
3.8
-
Ttook**

M
3.A
140.0
1.67
Ifi
1*0.0
6.6
0.49
2.4


0.T
1.2
160.0
i.er
VT.6
196.0
6.1
0.49
2.4

3bl
5.9
16.1
160.0
1.67
tli
1TI.0
6.0
1J
2.4
fral
1
0.0
0.33
76.0
1.1
16^
11.2
2.4
-
-
TIM
I**
0.0
4.1
110.0
1.1
26.0
1)4.0
4.2
0.7B
2.0

|b4
4.9
1.8
310.0
2.6
19.0
174.0
3.6
0.95
0.1

a*
4.7
4.5
400.0
1.8
26.0
174.0
2.1
0.96
0.1

*4
11J
1.0
360.0
1.1
26.0
204.0
6.1
0.96
2.60

5

1.9
400.0
l.t
26.0
304.0
2.7
0.96
2.60
CBOD rOmted tram mar date.	dlnltul HBOD otlauUtad uatag P/Q
brutal CBOD eilffuliled ustof */
Pf |/
mtlUfframa
par lllar-day
(4)
A
mllllgrama
par lltar-4ay
13)
(6)
'*
Sunrfaa
(?)
p, la
parlod-hour
16}
Grand
1
22.0
T.6
22 0
0.33
0700
13

2
SO 0
17.3
16.0
1.1




65.0
22.5

1.4


Clintoa

27 0
8.6
20.0
0.43
0600
12

2
47.0
16.0
18 0
0.64


TnekM
1
30 0
11.2
7 0
1.6
0600
14

2
50.0
18.6
8.5
2.0



9
2S.0
9.3
12.0
0.76


Jvel

33.0
18.7
10.0
2.0
0700
14
Flint
1
38.0
11.1
18.0
0 74
0600
12
2
5.0
1.6
3.0
0.32



2
45.0
14.3
13.0
0.96



4
90.0
18.1
17 0
1.1



S
TO.O
22.3
20.0'
1.1


* 8o Tabta 1 for bytinjalia aad pfeyaleal data of agmenu.
?. *" 5" 3.

-------
TIME VARIABLE WATER QUALITY MODELS ^
ESTUARIES, HARBORS, AND OFF-SHORE WATERS
I. INTRODUCTION
For certain problem contexts, a need exists for
describing the dynamic variation of water quality in brack-
ish and marine waters This is especially true for problems
concerned with localized effects in the immediate vicinity
of waste discharges or for problems concerned with the sea-
sonal variation of water quality. A spectrum of time scales
exists, the range of which extends from modeling hOur-to-hour
fluctuations in salinity or temperature to seasonal or year-
to-year fluctuations in phytoplankton populations.
A major task in dynamic, time variable Wdter qual-
ity modeling in the marine area is therefore a proper choice
of its dominant time and space sca-le. Figure 1 shows two
examples of different scales of phenomena. Such a choice
requires a careful examination and articulation of the ques-
tion posed in each specific problem context. A model that
represents short term fluctuations may not be appropriate from
*
Robert V. Thomann
<3. -ST3

-------
a computational viewpoint for analyzing seasonal effects.
Conversely, if the problem context demands information on
the short term (hour-to-hour or day-to-day) oscillations,
then the water quality model must incorporate the hydrody-
namic and reaction kinetics on that tim6 scale.
Several problem contexts that require time variable
models are discussed below and range over the time spectrum
mentioned previously. These problem contexts are:
a)	In Boston Harbor, the movement of
digested sewage solids throughout a
tidal cycle when the solids are dis-
charged only during the first three
hours of ebb tide;
b)	In off-shore areas, the settling
and dispersion of waste material
{over several hours) discharge after
from a moving barge;
c)	Seasonal variations in water cruality.
for the Delaware and Potomac estuaries.
In each of these problem contexts-, the underlying
hydrodynamic regime is assumed to be-known. If the circula-
tion and/or transport patterns are not known, a separate
hydrodynamic model must be employed.
? - S~y.

-------
II THEORY
a) Basic Equations
In all cases, the appropriate starting point is
a mass balance of the water quality variable, s^, around an
infinitely small fluid volume. The appropriate equation in
three dimensions is given by:
3 s	d s  k 3s*	J* 3s,
Tt = 7s	+ ?y{Ey"5y) + T5(EzTz)
7x (Uxsl} ~ 7(UySl) " ?(Uzsl) " K11(x,y,z,t,s1)s1
(1)
+ W(x,y,z,t)  (x,y,z,t)
where E _ are the dispersion coefficients in each respec-
x,y,z
tive spatial direction, U	is the velocity in each di-
x 9 y, z
rection,	is the decay coefficient, W(x,y,zrt) represents
the waste input of variable, s^, and (x,y,z,t) represents
all other sources and sinks of s^. Note that the decay coef-
ficient is written in a general form as a function of the
variable, s^ For first order decay, of course, the reaction
coefficient is independent of s^. In vector form, Equation
(1) is:
3s.
y- = (V  [E] (VSl) - V  Us1) -	+ W  I	(2)
- A-5-

-------
where [E] is a diagonal matrix of dispersion coefficients,
(Vs^) is a column vector, U is the velocity vector and:
n - 3 + , 3 *f , 3 ?
V="5i';L + -5y:,+yik
The first two terms in Equation (2) represent the dispersive
and advective field given by the hydrodynamic circulation
and degree of turbulence. As indicated above, the field of
motion is assumed to be given. In time variable models, this
field of motion may be quite important, as for example, in
irjtra-tidal models for estuaries where the x-component of the
U vector dominates.
If the variable, s^, interacts with a second vari-
able, call it s2, then one can write the equation for the
second variable as:
3s-	^
= (7  [E] (7s2) - 7  Us2) - K22s2 + K12s1 + W2  Z2
where K^2 is the feed forward coupling of variable s^ to vari-
able s2 In the most general case, one can examine the inter-
action between n variables, s^f s2**sn where feedback as well
as feedforward loops occur. Therefore, a complete set of
equations is given by;
3 - ST 
-------
CIS
I = (7-IE] (7Sl) - 'US1) - KnSl + K21S2 + ...Knlsn + Wx  ^
~Tt
^ = (7*tE] i the reactions are feedforward reactions, for j < i,
the reactions are feedback reactions, and for j = i,	is
the total reaction for variable s^ where, in general,
Kii > l*ij^ 4 i) In state vector form, Equation (4) can
be written as:
24!^- = (V  F) + [K]T(s) + (W)(D
dt	;	;	+
hydrodynamic reaction source and
field	kinetics sink field
(5)
where (V*F) is an n x 1 vector representing the effect of the
" T
hydrodynamic field on water quality (F = [E]Vs - Us);[K] is
the transpose of the reaction kinetic matrix ( n x n) given by;
IK] =
-Kll
K12
K13
  
Kln
K21
~K22
K23
  *
K2n
K31
K3 2
-K33
K34 **
3n

Knl
Kn2
Kn3
  *
0
Knn
oi -5"7

-------
(s) is an n x 1 state vector of water quality and (W) and ()
are n x 1 vectors of input sources and sinks. The major com-
ponents of the general water quality problem are therefore
made clear by Equation (5) The first term on the righthand
side represents the dispersion and advection of the water
quality state variable, the second term represents the kine-
tic interaction between each of the water quality variables,
and the final term represents the discharge or input of a
waste material and incorporates any other sources or sinks.
As indicated in the Introduction,- the essence of time vari-
able modeling (indeed all water quality modeling) is the pro-
per assessment of the role of each of these factors and with-
in that determination, a proper assessment of the need for
complete time and space detail. Once the determination of
the relative importance of the flow field, reaction kinetics
and input field has been made, two steps follow: (a) a rep-
resentation fo the spatial derivatives in Equation (4) by
finite difference approximation and (b) an exact specifica-
tion of the reaction kinetics.
	Spatial Approximation
In approximating the spatial derivatives of Equation
(4), the region of interest is segmented into n finite volume
* - S"S

-------
segments. Dispersion and advection phenomena now must incor-:
porate the actual cross sectional area of the water body in
the direction of the fluid flow. Consider first the finite
difference approximation in the x-direction. Figure 2 shows
the notation where V is the volume of the segment and Ax-is
the length of the segment. For simplicity, each segment is
considered equal in length, although in general this need not
where the subscript k on the derivative indicates an evaluation
of the derivative in the center of segment k, s^ is the
concentration at the boundary between segment k and k+1 and
s)c_1 k is the concentration at the boundary between k-1 and k.
In Equation (6) let the boundary concentrations be linearly
related to the concentrations in the center of each adjoining
segment, Sj^ and sk+1. Thus, let:
be soc
A finite difference approximation to the first der-
ivative of s is given by ^ :
sk,k+l ~ "sk-l,k
Ax
(6)
sk,k+l = ak,k+;sk + Bk,k+lsk+l
(7)
and:
^ -5-7

-------
sk-l,k " k-l,ksk-l + 6k-l,ksk
where a is a weighting fraction (to be specified later) and
S = l-Oo With Equation (7), Equation (6) can then be written
as;
,ds, _ Bk,k+lsk+l + (ak,k+l " 6k-l,k)sk ~ ak-l,ksk-l
l3xJk	Sx	1 '
Two cases are of interest. For all a = ^ = B, one obtains:
/dsx _ sk+l " sk-l
fe'k	2EE		(9)
which is a central difference approximation to the derivative.
For all a = 1 (6=0), one obtains:
/ds \ _ sk " sk-l
(a^}k	Sx		(10)
which is a backward difference approximation to the derivative.
For arbitrary a, the approximation Equation (8) weights either
upstream or downstream concentrations more heavily. A stabil-
ity criterion for choosing the weights (or equivalently, speci-
fying the segment size) is given below.
Several points should be noted. For the backward
difference scheme, Equation (10), a Taylor series expansion
f 21
for	about s^ can be shown to give1 :
- 
-------
In one dimension then, the solution of the difference equation
where higher order errors have been neglected. It can be seen
in Equation (11) that an additional amount of psuedo or "numer-
ical5' dispersion has been introduced into the equation. Only
for Axlul << E does the difference approximation approach the
original differential equation. For larger Ax|u|/2, special
care must be taken in interpreting the results of the calculation.
[2]
is equivalent to solution of the equation given by :
(11)
Returning to Equation (6), the second derivative ap-
proximation is given by the derivative of (6) evaluated at
x = K or:
/d s. 2 li ,ds.	_ /dsx	
k ~ 2x(l3x'k,k+l 3x k-l,kj
sk~ k-i' '">
The advective terms in Equation (1), i.e., terms
g
of the form -j^(Us) can therefore be written [using Equation
(8)] ass
(13)
3. - 4 /

-------
where Q is the mass flow rate, A is the cross sectional area,
and U = Q/A
The dispersive terms in Equation (1), i.e., terms
3 3s
of the form -j-E-j- can be written (using Equation (12)) as:
s TxTr [Ek,k+l(sk+l ~ sk} + Ek-l,k(sk-l " sk)] (14)
In one dimension, therefore, and for a single vari-
able;	the differential equation can be written as:
Vk~3F^ = lQk-l,k(ak-l,ksl,k-l + 6k-l,ksl,k)]	(1)
" tQk,k+l(akfk+lsl,k + Bk,k+lsl,k+in	(2)
+ Ek-l,k 
-------
Equation (15) can therefore be arrived at by consid-
ering a mass balance equation around a finite reach of the
estuary. Complete details are given in (3,4).
For multi-dimensional systems, the mass transport
and dispersion terms interact with additional segments so
that the differential equation for a single variable, s^, is:
Vk dt'k = E(~Qkj (akjsl,k + ekjsl,k)} + Ekj (sij " sik}
(16)
" Kll,k(sl,t) Bl,kVk + Wk * ^k
where the summation extends over all j segments bordering on
k.
Note that for both the one dimensional and multi-
dimensional system, the advective and dispersive fields are
assiu;..2d known.
C. - Numerical Dispersion Positivity and Stability
Since the Equations (15) and (16) represent spatial
approximations to derivatives, some errors are introduced into
the analysis. Primary among these is the numerical dispersion,
which appears in certain forms of the differential equations
due to the assumption of a completely mixed finite volume.


-------
Equation (11) shows the nature of this dispersion. Other as-
pects of the differencing scheme must also be considered.
All solutions to any water quality model should be everywhere
positive in order to reflect the physical nature of the prob-
lemc Also.- solutions to the finite difference forms of the
mass balance equations should differ from analytical solutions
tc the assigned equations by a fixed, hopefully small, error,
which remains bounded throughout the simulation. Stability
of tne solution is therefore mandatory.
Unfortunately, there are no set procedures that one
can follow to optimally choose a spatial grid size and/or time
step for numerical integration. The size of available compu-
tational facilities and the nature of the problem (i.e., the
effects of numerical dispersion) are important considerations.
However, certain guidelines can be given.
First, consider the requirement of positivity, i.e.,
iihat all solutions be positive and examine Equation (16).
These equations can be written in matrix form as^ where the
subscript designating the variable has been dropped, therefore,
s^f s2oSn rePresents distribution of a single variable
in the n finite segments of the water body.


-------
all(at)sl + a12s2	+ a13s3 +  + alnsn W1 * ^1
a21sl	+ a22(3t)s2 + a23s3 +  a2nsn	= W2 * ^2
(17)
anlsl	+ an2s2	+	+ann(3I)sn " Wn * ^n
Equation (17) become tridiagonal in form for one-dimensional
estuaries. It can be shown that for a positive solution, the
terms off the main diagonal must be negative. The terms below
the diagonal are always negative. Those above the diagonal
are of the form:
Bijij = Eij
Thus, for these terms to be negative:
aij > 1 Elj/'Qij
or:
aij > 1 " EVU	<18>
Two courses of action are now possible: a grid size (^x) can
be chosen a priori depending on the size of the computational
facilities available. If Equation (18) is satisfied by in-
ternal. computation of a, then positivity will be guaranteed,
and the spatial condition for stability will be satisfied.
<2 -4

-------
On the other hand, one can solve Equation (18) for Ax as:
Ax < E/U(1 - a)	(19)
so that if central differences are used (a = ^) :
Ax < 2E/U	(20)
Note that if a = 1, (a backward difference),
Ax < 
implying that positivity (and spatial stability) are always
guaranteed regardless of mesh size for backward differences,
and note also that if E - 0,
Ax < 0
implying that it is not possible to find a finite difference
scheme whicn will have zero dispersion and will always generate
positive solutions. As soon as a difference scheme is chosen,
one must be willing to accept a certain level of numerical
dispersion.
It can also be shown that in order to maintain sta-
bility for an explicit time differencing, the main diagonal
term must be all positive. This leads to the following gen-
eral stability criterion (for constant coefficients)s
S - c. 6

-------
1 + (B - a) -	- KAt > 0	(21)
Ax	Ax2
For central differences, (a = B = y), this criterion becomes:
2E + KAt < 1	(22)
Ax2
and for K s 0, a conservative substance,
 * TZ	(23)
Ax2 ^
This is the usual expression given for stability. Note
however, that the criterion given by Equation (23) assumes
central differences and conservative substances. For a fixed
spatial grid, the effect of introducing first order decay is
to require a reduction in the time step necessary for stability.
Returning to Equation (21), for a completely advec-
tive system and backward difference (o = 1), the criterion
simply becomes:
1 " Usl ~ KAt > 0	(24)
and for K = 0,
UAt < Ax	(25)
As indicated previously, (Equation (11)), the numerical dis-
persion introduced by a backward difference is UAx/2.
=1-4 7

-------
In addition, numerical dispersion is also introduced
(7)
by the explicit time differencing. Therefore, for a variable
spatial differencing scheme and forward explicit time differ-
encing, the dispersion introduced is given by
Enum "	[<" " !/2' " 2ll]	(26)
Now the issue is clear Cat least for explicit schemes).
If central spatial differences are used (a = 1/2) , the numeri-
cal dispersion due to spatial truncation is eliminated and if
enough additional dispersion is added to the original equation
(i.e. equal to u2At/2Ax) then the solution will not have any
jnerical dispersion. However, the space and time constraints
of Equations (20) and (22) must still be met. This nav re-
sult in small spatial grids and small time steps. In any
event, each situation must be considered separately.
Choosinq proper spatial and time grids for approxi-
mations to the partial differential eouations is still very
much an art. Considerations of comDuter size, nature of
problems and degree of accuracy, and simplicity of the re-
sulting finite difference eauations, all influence the choice.
a -6, 2

-------
REFERENCES
Shaw, F.S., Relaxation Methods, An Introduction to
Approximational Methods for Differential Equations.
Dover Pub., Inc., 1953, Mew York.
^ ^ Torrance, K.E., Comparison of Finite-Difference Com-
putations of Natural Convection, Jour, of Res., Nat.
Bur. of StcTs., Vol.72B, No.4, October-December, 1968
pp.281-301
^ Thomann, R.B., Systems Analysis and Water Quality
Management, in press, to appear 1971, Env. Sex. Serv.,
Prit. Co.,.Wilton, Connecticut.
f4]
1 J Thomann, R.V., Mathematical Model for Dissolved Oxygen.
ASCE, Jour. San. Engr. Div., Vol. 89, No. SA5, October
1963
^ Kent, R., Diffusion in a Sectionally Homogeneous Estuary
ASCE, Jour. San. Engr. Div., Vol. 86f No. SA2, March
1960, pp. 15-47
Leendertse, J.J., Digital Techniques; Finite Differences
Chapt. VI, Solution Techniques in Estuarine Modeling:
An Assessment, Prep, for Nat. Coastal Res. Prog., WQO,
EPA by Tracor, Inc., Austin, Texas, 1971, pp.277-302.
Bella, D.A., ftrennev, W.J. Finite  Difference Convection
Errors. Jour. San. Enqr. Div., Vol. 96, No. SA6, Dec. 197 0
dp. 1361-1375.
3 -6 ?

-------
III. APPLICATIONS OF,TIME VARIABLE WATER QUALITY MODELS
A. Inter-Tidal Seasonal Models
Time variable water quality models have been used to
determine the effect of waste load removal programs on the low
frequency variations of water quality, especially seasonal oscil-
lations. Specific applications have been made to the Delaware
and Potomac estuaries, among others. The time scale of interest
is therefore considered to incorporate one year with the smallest
time inverval as a tidal cycle or daily average. The independent
variable in Eq. (5) is therefore interpreted in this manner.
Seasonal variations are particularly important in large
estuaries and bays since these bodies of water tend to "dampen"
any input fluctuations of short term (hourly) frequency. Further-
more, large1scale waste treatment programs will generally affect
day to day variations in water quality. Local spatial and short
term fluctuations are gradually controlled by other influences
such as specific manner of disposal (see Boston Harbor application
below) or details of the geomorphological structure.
An inter-tidal time variable model has been constructed
for water quality (especially dissolved oxygen) for the Delaware
Estuary. First order kinetics were used throughout and two basic
partial differential equations were utilized. Thus.Eq. (5) becomes
:a || ) - K; !L+ W(x,t)
(27)
:A If ) + K,2L+ k22 (cs-c)  2c
9L
1
auL
1
'd
3t
A
ox
A
oX
3c
1
3uc ,
1
J_
at
A
~ +
A
9x
oJ-7o

-------
where L  oxygen demanding material (cai iionaceous and
nitrogenous)
c = dissolved oxygen
K2i  reaeration rate
c = saturation value of dissolved oxygen
s
The reaction coefficient matrix is therefore a simple
interactive first order system given by
IK]
- K, K.J
0 - K22^
For the Delaware estuary, the reach from Trenton, N.J.
to the entrance to Delaware Bay, a distance of about 86 miles,
was divided into 30 sections as shown in Figure (3). Two
spatial grid sizes were used;- Ax was chosen as 10,000 feet
in the area of greatest spatial gradients and 20,000 feet
otherwise. A variable weight differencing scheme was used
in the time variable simulations with L and  (Eq. 15) computed
at each step in the program. This insured stability and posi-
tivity. The amount of numerical dispersion introduced by this
scheme for the Delaware ranged from a high of about 1-5 m^2/^ay
during transient high runoff conditions, to a minimum of about
0-0,5 mi2/day during most of the low flow months of the year,
the critical times. It should be noted that the velocity in the
above model is the net tidal velocity, usually a low number dur-
ing critical months of the year. The numerical dispersion is
therefore usually not critical in inter-tidal average models such
as the Delaware. The previous values of the numerical dispersion
2-1

-------
can be compared to actual values of dispersion used in the
model of 4-7 mi2/day.
In the Delaware computer program, a set of initial values
is chosen and numerical integration is used to compute the solu-
tion at the next time step. After each step is completed, the
new values of the dependent variables are downgraded to become
the initial values for the next time step. Jeglic (7) controls
truncation errors by a halving and doubling procedure which/
while sacrificing some computational time does not require the
user to specify an integration interval.
The computer runB that have been made indicate integration
intervals of four to fifteen steps per prototype day. The
average problem for the Delaware required about four IBM-7094
minutes per simulated month.
Verification analyses have been minimized at length by
(8)	(3)
MacEwen& Tortoriello and Thomann . These analyses have
indicated relatively good agreement between the model and the
prototype observations. However, transient fluctuations (order
of several days period) were not duplicated by the model implying
the presence of other, probably higher order effects on water
quality which are not incorporated in the model.
After verification, the model has been used for a variety
of simulations. Pig. (4) shows a typical temporal distribution
of dissolved oxygen in section 13. The "normal loads" plot is
for 1964 base line conditions. The 95% removal plot considers
2-7^

-------
carbonaceous waste removal only. The time variable effects of
variable waste discharge can therefore be assessed. Note the
major effect of waste removal during summer months due to in-
creased reaction rates.
Fig* 5 shows the complete time-space surface generated by
the DO model for the Delaware. The regions of low DO appear as
depressions and the objective of a water quality management pro-
gram is to improve both the time and space variations of DO to
a "desirable" level. Spatial profiles at specific times of the
year and temporal variations at specific locations are obtained
directly from the contour plot.
For the Potomac estuary, the river was divided into 28
sections with a Ax ranging from 13 to 8.6 miles. Details of
(9)
the model and applications are given in Hetling and Jaworski
(10,11). Equations similar to (27) were finite differenced with
a variable differencing scheme on the advective term. This is
similar to the Delaware estuary applications. Fig. 6 shows a
comparison between observed DO values and those computed by the
time variable model. Recently, Jaworski'^' has reported on the
use of an intra-tidal model that is run out to a dynamic steady-
state for several water quality variables. Fig. 7 shows the
results of this use of intra-tidal model that is run out to a
dynamic steady-state for several water quality variables. Fig. 7
shows the results of this use of an intra-tidal time variable
model. Fig. 8 shows a comparison between the chloride concentra-
tions at Possum Point and a seasonal inter-tidal conservative
a.-7 3

-------
variable models For this case, Eq. (5) becomes simply:
If - -XTl + 5 3 IEH' +w(x't) (2B>
where c is now chloride concentrations and W{x,t) is simply
the source of salt at the mouth of the estuary. The reaction
matrix [K] is zero everywhere. Fig. 8 thus illustrates the
application of a seasonal type time variable model to another
water quality variable, the amount of sea salts that enter an
estuary. This becomes particularly important during times of
drought when the presence of salts may interfere with the use
of the estuary for municipal water supply.
B. Intra Tidal Models
Several mtra-tidal {hour to hour) models have been
constructed primarily of conservative substances such as salt
or simple first-order kinetic systems such as coliform bacteria.
(12)
Leenderste	for example has constructed a detailed hydro-
dynamic and water quality model for Jamaica Bay. For that work,
a grid size of 500 feet was used which resulted in 4,758 grid
made points equivalent to about 2,000 segments. Relatively
elaborate input and output hardware and software was used to
prepare the problem for computation and to display results in
a readily obtainable form. Graphic computer input and output
devices greatly facilitated the representation of data. Details
are found in (12) .
Another example of the application of intra-tidal modeling
is given by Boston Harbor where two problem contexts were examined


-------
a)	preliminary evaluation of time and space distribution
of coliform bacteria due to transient storm water over-
flows .
b)	preliminary evaluation of the fate of digested sludge
solids discharged only in certain stages of the tidal cycle.
For the second application, conservation of mass equations
were employed as before except that the segments are oriented
both along the axis of flow in Boston Harbor (the x-direction)
and vertically across the depth of the harbor (the z-direction).
Bottom segments were added to act as repositories for the sludge
solids that reached the bottom. The equations for the segments
in the column into which the sludge solids are discharged are
formed as follows for the top segment, call it k:
dcv-	_
Vk dt~ = E'k,ki-1 ^k+r'V " ^kfk+lS " ^ Qkj (t)cj (29)
where u is the settling velocity of.the sludge. The terms on the
righthand side of this equation represent, respectively, the
vertical turbulence, the settling velocity mass transport, and
the tidal flow.
For the middle segment, k+1, the conservation of mass
equation is:
dck+1
Vk+1 ~dt = E'k,k+1 (ck"ck+l) + E'k+1,k+2(ck+2~ck+l)
(30)
+ uAk,k+lck " uAk+l,k+2ck+l " | Qkj(t)Cj+W(
<2-7 5"

-------
where W(t) is the source of solids due to the sludge discharge.
The third segment equation is similar to the equation for seg-
ment k. The bottom segment equation is:
^Ck+3
k+J = uA. ,  i., iC, , ~	(31)
k+3 dt	k+2,k+3 k+2
Thus, this equation accumulates the settling solids in each
column, and the rate at which the solids build up is the deposi-
tion rate.
These equations are used for all columns in the model with
fie exception of the first column at the head of the Inner Harbor
a.-l the last column at the ocean boundary where no transfer is
sy-cified across the edges of the boundary. Thus, the only sink
of 3ludge solids is deposition on the bottom.
The ax for this model varies from about 0.2 mile in the
immediate vicinity of the major discharge to about .1.5 miles at
distances removed from the input. The Az (vertical grid size)
varied depending on the depth of water but generally averaged
about 15 feet in each of three vertical segments. An additional
bottom segment of arbitrary Az = 1 foot was included as noted above.
A variable time step was used with smaller steps- being employed
during load discharge, At therefore varied from .01 hours to J)5
hours. With this model, the behavior of the sludge as discharged
at specific intervals could be tracked. The most important effect
however was the build-up of sludge solids on the bottom. Fig. 9
shows the end result of the application of this model and does in-
dicate that sludge solids may be deposited in the Inner Harbor area
(mile 0.0 to mile 7.0).
a-i (c

-------
Additional References
7.	Jeglic, J.M. DECS III, Mathematical Simulation of the
Estuarine Behavior. Prepared for FWPCA by General Electric
Re-Entry Systems Dept,, Philadelphia, Pa. Dec. 1966.
8.	MacEwen, PK. and Tortorieilo, R.C. Forecasting of Water
Quality Data in the Delaware River Estuary Proc. Nat. Symp.
on Data & Instrumentation tor Water Quality Management, J.E.
Kerrigan Ed., Univ. of Wise., Madison, Wise. 1970 pp 99-123.
9.	Hetling, L., A Mathematical Model for the Potomac River -
What it Has Done and What it Can Do. Presented at 1966
Fall Meeting of Interstate Comm. on Potomac River Basin.
10.	Jaworski, N.A. et al Nutrient Management in the Potomac
Estuary. Tech. Rpt. 45, Ches. Tech.Supp. Lab,, WQO, EPA,
Annapolis, Md. Jan 1971, 61 pp.
11.	Jaworski, N.A. et al A Technical Assessment of Current Water
Quality Conditions and Factors Affecting Water Quality in
the Upper Potomac Estuary. Tech. Rpt. No. 5, Ches.Tech.Sup.
Lab. Mid-Atl, Reg., FWPCA, March 1969, V Chapt.
12.	LeendersteJ.J. A Water Quality Simulation Model for Well-
Mixed Estuaries and Coastal Seas. Vol. I, Principles of
Computation. Memo. RM-6230-RC, The Rand Corp., Santa Monica,
Calif.
13.	Development of Water Quality Model of Boston Harbor Prep, by
Hydroscience, Inc., Westwood, N.J. for Commonwealth of Mass.,
Water Res. Comm., Boston, Mass., March 1971.
3.-11

-------
J5ea$onal
100 miles
Tidal
Daily
10 miles
1 mile
Iday I2hrs. Ihr.
Iday
lhr.
lyr.
lOyrs.
A	B
FIGURE 1
Two Examples of Significant Time and Space Variations in Water Quality
(A) Dissolved Oxygen in Delaware Estuary
(B) Iron in Off-shore Water After Discharge from Moving Waste Barge
Spatial scale represents horizontal distances.

-------
Water
Quality
Variable,
Fig. 2 Approximation in x-direction

-------
s
' v
DELAWARE
ESTUARY
SECTIONS
Figure 3
95% Of MAJOR EFFLUENT 10AOS REMOVED
normal loads
HCUNU
Figure 4 Temporal Distribution of Dissolved Oxygen
2- to

-------
to
iO
-0
O
' ,TTTTTT5

-------
I	B
14
13
It
II
10


 
 





LEGEND.
CALCULATED BY THE MOOEL

. .T\
-v.- .

L* ~






FROM DC.
DEPT. OF
SAN. ENQR.
 /
 /
s* /
Vv
V /
  * 
V- *









V/ M

V* /



 








v 




V-
\ 








1


\
\  *
v *  
v
1























1
1
V 







 ^




V
* 





 

 *
* * /










 
  
/ v




\
 \




  
 i

'  .





 
K*
 *

%

1 <


' 

-  7
 1 /
 /'
 








 
 
 \
/.A "
 
/*

y i |






 

*  \
 

 
. -
   J
   
 
a



1













O
fi.
JAN.
FEB.
MAR.
APR.
MAT
JUN.
M 0
JUL.
NTH
auo.
StPT
OCT.
NOV.
OEC.
POTOMAC ESTUARY
DISSOLVED OXYGEN CONCENTRATION AT
WOODROW WILSON 8RIDGE
Figure 6

-------
DO CONCENTRATIONS
rr-OMAC ESTUARY
SEPT. 22. 1968
li-
re-
9-
e-
7-
PREOICTED
6-
O
a
Flow = I.4O0 eft
TEMP. = 26.0* C
5-
4-
3-
2-
45
35
5
IS
30
40
0
20
25
10
MILES BELOW CHAIN BRIDGE
Figure 7

-------
LEGEND:
2 800
DAILY VALUES MEASURED BY VEPCO
AT POWER PLANT
2600
VALUES MEASURED BY D.C. OEPT.
OF SAN. ENGR.
2400
RANGE OF VALUES PREDICTED
BY THE MODEL
2200
2000
I 800
I 600
Ui
1400 a
1200
000 
800
600
400
200
JUNE
JULY
AUG.
APR.
MAY
SEPT.
OCT.
NOV.
DEC.
MONTH
POTOMAC ESTUARY
1963 CHLORIOES AT
POSSUM POINT

-------
1.10
DEER ISLAND
A SETTLING VELOCITY = 12/HR.
O SETTLING VELOCITY  6*/MR.
a SETTLING VELOCITY * 3*/[
-------
Relationship Between Waste Load Variability and
Water Quality Response^
Theoretical Background
In a one-dimensional stream or estuary with a wasteload discharged at x = 0,
the time rate of change of dissolved oxygen (DO) as a result of the discharge
of waste material expressed as biochemical oxygen demand (BOD) is given by the
following pair of partial differential equations:
Various authors have utilized this pair of equations under a variety
of assumptions and obtained either analyticalsolutions or solutions to
difference forms of equations.
The equations as they stand are linear, and as such the principle of
super position applies. From the point of view of systems analysis, the
notion of a frequency transfer function is particularly relevant to des-
cribing the relationship between waste load variability and water quality
response. This notion can be developed and derived by assuming a harmonic
variation in the waste load, W and developing the periodic output response.
The ratio of the harmonic input to the harmonic output is formally termed
the "frequency transfer function." For the case of streams where E approaches
zero and the stream parameters are constant, one can examine the response of
the system by assuming the input to be varying with a specific frequency and
^Robert V. Thomann
(1)
(2)
where
L	= carbonaceous BOD and/or nitrogeneous BOD
c	= dissolved oxygen
Q	= net river flow
A	= cross-section area
E	= dispersion coefficient
I	= sources and sinks of DO and BOD, respectively
L, C
  2

-------
zero lag. Thus,
L (t) = L + L .sintot	(3)
o	o oA
where L (t) is the time variable initial stream BOD due to a waste load of
o _
W lbs/day, L is the mean BOD, L . is the amplitude, and u) is the input
O	OA
frequency equal to 2tt/T where T is the period. If equation 3 is used as
an input forcing function for the constant parameter stream case of
equation 1 given by:
= -  |k . K L	CM
dt A dx r
where is the removal of BOD from the stream, the solution is given
by:
_	 -K x/u
L = [ L + L .sin(tot - )]e r	(5)
o oA	u
where u = stream velocity. Equation 5 can be written as:
_ -K x/u
L = LQe r + ALLQAsin(wt - 0^	(6)
where
-K x/u
AL = e r	(6a)
0L = f	(6b)
A and 0 are known as the amplitude characteristic and phase characteristic
of the system. In general, these quantities are both functions of to; although
as can be seen here, the amplitude characteristic for constant parameter stream
case is independent of input frequency. In complex notation:
4>(ico) = ACio)ei0Cw)
where <{>(ito) is the frequency transfer function and i = ./ -1.
For the case of dissolved oxygen deficit, D = c - c, the constant parameter
s
3. - 27

-------
stream model for zero initial conditions is
 = -u | - KaD + KdL(t)	(7)
where K is the atmospheric reaeration rate and L(t) is given by equation 6.
Under these conditions,the amplitude and phase characteristics can be shown
to be
K -K x/u -K x/u
S-iTTT-'* r 3 >	(8a>
a r
en = 	(8b)
D u
and
D(x) + ApLo^sin(wt - (nx/u)	(9)
where D(x) is the classical DO deficit profile given by
K,L K x/u -K x/u
	d o , r	a v
D - K-rr'6	- e	>
a r
It is seen, then, that once the frequency transfer function in terms of
its amplitude characteristic and phase characteristic is known, the harmonic
response due to an input of varying frequency can be determined via equation
6. The frequency transfer function forms a very useful descriptor of how
the system will behave to a wide variety of time variable waste load inputs.
For example, the formal Fourier transform of the frequency transfer function
yields the so-called "impulsive response" function. This impulsive response
function represents the time-variable response due to a delta function input
of waste load. A convolution operation can thus be carried out with the im-
pulsive response function to yield the time variable response in BOD or dis-
solved oxygen due to any arbitrary waste load input (Thomann, 1972). Thus,
knowledge of the frequency transfer function or the impulsive response func-
tion provides one with the ability to describe analytically the time variable
response in dissolved oxygen due to a harmonically varying input, a delta
function type input, or an arbitrary functional form.
2. - 28

-------
An additional important class of waste load inputs is the stochastic case,
i.e. the case where the input is randomly varying with a known variance. It is
assumed therefore that the variance of the waste load input is known. If a
linear system such as given by the dissolved oxygen equation for a stream is
considered (equation 7) and the transfer function is known, it is appropriate
to begin the analysis of the output response by inputting the variance of the
input waste load to the system.
For the case of streams the amplitude characteristics are given by
equations 6a and 8a, respectively. The BOD output variance as a function
of x is given by
2 / x *2 2
 L " A L LO
or
2	-2K x/u 2
c/L(x) = (e r }a\o	(10)
The DO deficit variance as a function of x is given by the following expres-
sion :
2D<*>  aVl	(11)
or
2	*D V/u 2 2
0 DW = [T"^F(e	)] 0 Lo
a r
It should be recalled that equations 10 and 11 are for constant stream
parameters and no upstream BOD or deficit. If the upstream conditions include
BOD or deficit, this can be taken into account usually under an independence
assumption. Dispersion is also not included.
For the BOD equation 10 shows that the variance decays with distance at
twice the rate that the mean decays. The variance in the DO generally has the
same shape as the mean, with a maximum variance at the point of maximum deficit.
When dispersion is included, the amplitude characteristic is frequency dependent
due to the inclusion of the tidal dispersion term in equations 1 and 2 (Thomann,
1972).
a - 2
-------
Effect of Dispersion on Stream Water Quality Response
Thomann (1973) has derived some general rules for the effect of dispersion
on the amplitude characteristic and hence on the degree to which waste load
variability is transmitted downstream (see also Di Toro, 1969 and Li, 1972).
In that work, the effect of dispersion was related to the following dimension-
less quantities
P = KE/u2
*
to = co/K
* ,
x = Kx/u
As a general guide [Hydroscience, Inc., 1971], P = <0.01 for upstream
feeder streams, 0.01-0.5 for main drainage rivers, 0.5-1.0 for large rivers,
1.0-10.0 for tidal rivers, and >10 for estuaries. Primary interest therefore
centers about the range of P from 0.01 to 1.0. That is, What is the effect
of dispersion equivalent to these levels on the dynamic response of water
quality? Since frequency and distance are given in dimensionless terms that
depend on K and u, Table 1 provides the conversions necessary to interpret
readily the range of these numbers.
As is shown in Table 1, for waste load inputs varying with a period of
*
7 days, w ranges from 9.0 to 0.9; the higher value is. associated with slowly
reactive substances (K = 0.1/day) such as BOD.
Figure 1 shows the amplitude attenuation as computed from Eq. (1) compared
with the zero dispersion case Eq. (.5). This figure therefore represents the in-
stream amplitude concentration change expected from a unit 'input amplitude
*
varying with a period corresponding to w . The substantial difference between
*
the zero dispersion case and the case for P > 0 can be seen at increasing oj .
Figure 2 is a plot of the amplitude characteristic over a wide range of P and
*
for fixed w .
A
TABLE 1. Period Equivalent to Dimensionless Frequency u)

Period of Input, days
K - 0.1/day
K - 0.5/day K =
1.0/day
360
0.17
0.03
0.02
30
2.1
0.42
0.21
7
9.0
1.80
0.90
1
62.8
12.6
6.28
Z ~ ?o

-------
The use and interpretation of Figures 1-2 can best be seen by means of two exam-
ples.
Example 1, Biochemical oxygen demand. Assume that a waste discharge input
is varying with a period of 7 days and discharging biochemical oxygen demand
into a river where the organic matter decays at a first-order rate of 0.1/day.
The river velocity is 0.2 ft/sec (.3.2 mi/day). Dye dispersion studies in the
2
river have indicated a longitudinal dispersion coefficient of about 1 mi /day.
Then P = KE/u2 = 0.01, u>* = 2tt/TK = 9.0 (.Table 1), and K/u = 0.031/mile. Table
2, constructed from Figure 1(a) and the preceding information, shows the effect
of longitudinal dispersion on the response of biochemical oxygen demand. Thus
at 10 miles downstream the difference between responses is already 24%, and at
TABLE 2. Amplitude Characteristic for Example 1, Biochemical Oxygen Demand
mg/1 Water Quality
Amplitude per mg/1 Waste
^	Input Amplitude	
x, miles x P = 0	P = 0.01. Difference, mg/1 Difference, %
0	0	1.0	0.98	0.02	2
10	0.3	0.74	0.56	0.18	24
30	0.9	0.41	0.20	0.21	51
60	1.8	0.16	0.05	0.11	69
*
= 9.0, P = 0.01, K/u = 0.031/mile.
30 miles downstream the difference is 51%. Figure 3 shows this effect. If the
system is highly reactive, the situation is different. The effect can be shown
by reexamining example 1 for an order of magnitude increase in decay rate.
Example 2, coliform bacteria. In this example K = 1.0/day, T - 7 days,
u = 0.2 ft/sec, E = 1 mi2/day, P = KE/u^ = 0.1, oj = 0.9, and K/u = 0.3/mile.
Table 3, using Figure 4, shows the comparison. As is shown in this table, be-
cause of the high reaction rate the process is almost entirely complete when
TABLE 3. Amplitude Characteristic for Example 2 - Reactive Variable, K = 1/day
mg/1 Water Quality
Amplitude per mg/1 Waste
^ 	Input Amplitude	
x, miles x P = 0	P = 0.01 Difference, mg/1 Difference, %
0	0	1.0	0.84	0.16	16
2	0.6	0.55	0..43	0.12	22
5	1.5	0.22	0.17	0.05	23
10	3.0	0.05	0.035"	0.015	30
a - 
-------
x = 3.0, at which point maximum differences are about 30% but are at very low
concentrations. Intermediate differences are about 20%. For the same river
situation therefore the effect of longitudinal dispersion is less pronounced
for highly reactive substances than for more slowly reactive substances for
input periodic fluctuations to about 30 days. For shorter-term input fluctua-
tions (e.g. 7 days or less) the effect becomes progressively more important.
For variables such as dissolved oxygen, the amplitude attenuation is
evaluated from Eq. (7). Figure 4 shows the amplitude attenuation of the maxi-
mum dissolved oxygen deficit relative to the waste load input amplitude ex-
pressed in mg/ at the outfall, i.e. W/Q where Q is the total river flow noted.
The effect of dispersion on a time variable waste input is generally less for
upland rivers than for larger rivers, as is shown in Figure 4. In Figure 4a,
with a reaeration ratio (K /K, =5), if the input is varying with a period of
& a
7 days or less, the effect of assuming zero dispersion may become important.
For P = 0.1 and a = 0.5, characterizing some main drainage rivers, the effect
of dispersion is most pronounced as shown in Figure 4b. The magnitude drops
significantly where for an input of 7 days, the response for P = 0.1 is about
30% of the response for P = 0.
The effect of dispersion in the large rivers, which are generally more
sluggish and have a lower reaeration, is even more pronounced, as is shown in
Figure 4c. Indeed, input fluctuations varying with periods of about 7 days
or less are completely attenuated under a condition of P = 0.5.
These results indicate in general that estimates of the time variable
effect of waste discharges should recognize the potential importance of stream
dispersion in attenuating effluent variability. This especially true for
larger main stream rivers. However, for most small stream situations where
K /K is large, and velocities greater than about 0.5 ft/sec, the effect of
3 Q
dispersion on the water quality response due to a time variable effluent is
small and can generally be neglected.
4-

-------
REFERENCES
Thomann, R.V. 1972. Systems analysis and water quality management. McGraw-
Hill Book Co., N.Y., 287 pp.
Thomann, R.V. 1973. Effect of longitudinal dispersion on dynamic water qual-
ity response of streams and rivers. Water Res. Res. 9(2):355-366.
Di Toro, D.M. 1969. Stream equations and methods of characteristics. J. Sanit.
Eng. Div. Amer. Soc. Civil Eng., 95(SA4), 699-703.
Hydroscience, Inc. 1971. Simplified mathematical modeling of water quality.
Westwood, N.J., pp. 36-46.
Li, W. 1972. Effects of dispersion on.DO-sag in uniform flow. J. Sanit. Eng.
Div. Amer. Soc. Civil Eng., 98(SA1), 169-182.
* - ? 3

-------
\ > 11 11> i i 	(I) m  ni/Ji -	V / ' In / if" I' ij	/j.
''	(b)	/,,l)
Figure 1. Amplitude characteristic of a single nonconsecutive variable, w* = 0-10; (a) P = 0.01 and
(b) P = 0.1; P = KE/u2

-------
p  l/J1
Figure 2. Amplitude characteristic for nonconservative variable
for variable P = KE/u2 and for to* = K/w = 10
I

I
:iP2 D'S-5iON


S --CfiC D'SPCS-ON


' \ ^P00. /

^ \ /
> \ /
\ /" *" /
\/ N/

/ x
-'A / X
"" ^ s \ / ^
V
,, X
.	/
It)
figure 3. Water quality response for example of biochemical oxygen demand:
j	a) waste load input; and BOD response at b) 10 miles and c) 30 mi.
A-?-r

-------
Figure 4. Amplitude characteristic for maximum DO deficit for three river
systems: a) K /K. =5; b) K /K, = 0.5; c) K /K = 0.2.
3 d	3 Q	3 Q


-------
Example of Time Variable D.O. Modeling
Upper Delaware River^
The purpose of this modeling analysis (Hydroscience, 1975) was to
evaluate the effect of increased BOD loading on DO and the impact of a
projected regional STP load for the Upper Delaware River (Figures 1 and
2). Flows in the Delaware average about 12000 cfs at Trenton and low flows
of about 2500 cfs. Depths vary from 2-10 feet. The analysis was compli-
cated by the presence of significant rooted aquatic macrophyte beds in
the lower reaches of the study area (Figure 3). The impact of the weed
bed on BOD was interesting and is shown in Figure 4. The upper panel in-
dicates the particulate BOD upstream of the weed bed while Figure 4(b) shows
the particulate BOD above and below the weed bed and indicates that about
30% of the particulate BOD is removed from the overlying water column as it
passes through the weed bed. The flow during this period was about 4380
cfs, a rather high summer flow.
The model consisted of two reaches of 141 finite difference segments
for Mile 218 to Mile 175 and 136 segments for Mile 175 to Mile 134. This
is a total of 277 segments of about 0.3 miles in length. Figure 5 shows
the depth distribution over the study reaches. The model was run in a
backward difference mode so that the numerical dispersion introduced was:
E - UAx
num 2
for Ax as the segment length. For a velocity of about 0.5-1 ft/sec. (8-16
mi/day) for Reach 2 and Ax = 0.3 miles, this results in numerical dispersion
2
of about 1.2-2.4 mi /day.
A dye study conducted on the upper Delaware permitted an estimate of
river dispersion. Typical results are shown in Figure 6 where the total
2	2
dispersion ranged from 1.6 mi /day at Frenchtown to 4 mi /day at Trenton.
Examples of the time variable calibration to the DO data at Trenton
are shown in Figures 7 and 8. The variations in waste treatment plant
effluents were dampened rapidly in the calculation due to the river dis-
persion. Phytoplankton and weed mass DO production did however contribute
markedly to variations in DO. Figure 7 shows the progressive increase in
diurnal variation of DO as calibrated by the model and the accompanying
^Robert V. Thomann
*-?7

-------
observed DO. The model did not completely calculate the diurnal range
however especially in terms of calculating the minimum values. Figure 8(a)
indicates that the model approximately duplicated the observed daily ranges
but did not properly respond to a day to day transient weather effect of
cloudy days from July 18-23. The rapid drop of daily mean values of almost
3 mg/ was generally not captured by the model (DW is a weed respiration
rate). Figure 8(b) shows that the diurnal amplitude was modeled correctly
but the mean value did not respond as rapidly as the observed data. These
results illustrate the random day to day fluctuations in DO which are diffi-
cult to model because of uncertainties in photosynthesis and respiration
effects.
Based on the modeling analysis, Figure 9 shows the estimated number of
days/month that the instantaneous daily DO will be less than a given level
under different loading conditions. For example, the projections indicate
under condition (B) that about 7 days per month would have minimum DO levels
less than 5 mg/ for the region below Eastern. Table 1 shows the number
of days/month that the minimum DO will be less than 4, 5 and 6 mg/ for
different river discharges.
Table 1
No. of days <
River Discharge

-------
NEW _YORK
Pennsylvania
LEHIGH RIVER
E ASTON
MUSCONETCONG
RIVE R
-STUDY AREA
DELAWARE
LEHIGH
,RIVER
PENNSYLVANIA
MARYLANO
DELAWARE
. BAY
ATLANTIC
o u
Z|C
OCEAN
'<

-------
I) PORT JERVIS.N.Y.
DINGMANS /C\
FERRY W
P.A.
SHAWNEE STP-
PACKAGING CORP-
OF AMERICA

DELAWARE WATER GAP
o
SAMPLING STATIONS
(?) BELVIDERE, N.J.
-J.T.8AKER CO.
LEHIGH
RIVER
EASTON STP
(l)
(5) PHILLIPSBURG, N.J.
WHJPPANY PAPER CO.-
-PHILLIPS8URG STP
-RIEGEL PAPER CO. (RIEGELSVILLE)
-RIEGEL PAPER CO.(MiLFORO)
(S) FRNCHTOWN ,N.J.
	FRENCHTOWN STP
(7) LAMBERTVILLE, N.J.
	LAMBERTVILLE STP
COLO SPRINGS CO-
8) TRENTON, N.J.
FIGURE .. 1
SCHEMATIC OF THE DELAWARE RJVER
4-/00

-------
DRBC RIVER MILE 166.2

A
N
i
PENNSYLVANIA
32
AQUATIC MACROPHYTE
DENSITY(KG WET WT./M2)
DENSE -3.14
& V; - MODERATE-0.43
- LIGHT -013
FRENCHTOWN
NEW JERSEY
12
frenC'htown
S.T.J?
LOCATION OF WEED DENSITY SAMPLING
AUGUST 23,1973
SCALE  MILES
DRBC RIVER MILE 167.9
AFTER:MAZA ANO CRAIGHEAD, 1968
FIGURE 3
DISTRIBUTION OF AQUATIC MACROPHYTES
VICINITY OF FRENCHTOWN, NEW JERSEY
- (a i

-------
2 5.
20.
Q
o 10.
5
SAMPLE COLLECTED AUGUST 18,1972
samples collected above weed bed
TSENTON,NEW JERSEY
o- UNFILTERED
a-FILTERED
0 ...0. .: y.-.
ooo
O %. V,	.*c;-
*Sy > 
^
>tr.
0	 '
 - -&vr-::

A A
0-,
 A A
0 <
* z
A 4
PARTICULATE BOD
(A)
0 Lsjiiu
i i j
J_
10
15
		 i  i i .
20
25
30
25.
20.
f 15.
a
o
m 10.
5.
'0
SAMPLES COLLECTED BELOW WEED BED
TRENTON,NEW JERSEY
O-UNFILTERED
A -FILTERED
A	a a
o o
2 a a
'
o o o	:"*
o .e-wrr:r:vv^vfe'::^
1 * 4 A - "* *
PARTICULATE BOO
10
15
20
25
30
15.
10.
o*60D UNFILTERED - BOD FILTERED
(ABOVE WEEDS)
As BOD UNFILTERED - SOD FILTERED
'BELOW WEEDS)
o
c
9a, * A
o O
A A
JO
15
TIME ID AYS}
20
(C)
25
30
FIGURE . H-
EFFECT OF WEED ON LONG TERM BOD
Ji ~ So ^

-------
CORPS OF ENGINEERS DATA
196 4-1365
rLOW AT TRENTOH-ISOOCfS TO 2SOOGFS
FIVE STATION MOVING AVERAGES
CHANNEL DEPTH w
@ @     @@ @
  <2> 
CD  
MODEL:REACH
MOOtL:REACH t
II tie 312 204 204 300 l 1*2 It* 1*4 1(0 IT* IT2 l* IC4 ItO IS* Itl 144 144 140 |M tit
0. R.8.C. RIVER MILES
FIGURE 5"
RIVER CHANNEL CHARACTERISTICS- DEPTH

-------
DATA FROM U.S. ARMY
CORPS OF ENGINEERS
DYE RELEASE-JUNE 1,1970 (EASTON PA.)
TRENTON FLOW - 6500CFS
	CALCULATED (NORMALIZED)
	 OBSERVED
FRENCHTOWN
LAMBERTVILLE
.TRENTON
0.5
2.0
2.5
TIME OF TRAVEL FROM RIEGELSVILLE - DAYS
FIGURE 
OBSERVED AND COMPUTED DYE CONCENTRATIONS

-------

o>
Z
Ul
e>
>-
x
o
Q
CJ
>
_l
o
to
CA>
O
TRENTON
FRENCHTOWN
BELVIOERE
DELAWARE WATER GAP
DELAWARE RIVER MODEL
AUGUST, 1973 VERIFICATION
TRENTON FLOW= 5812 C.F. S.
	COMPUTED
 MEASURED
12 18 24 6
18 24 6
6

12
18 24 6
12 18 24 6
6
(2
6
TIME (HOURS)
FIGURE. 7
DISSOLVED OXYGEN VERIFICATION -AUGUST, 1973

-------
14.0
TRENTON, N.J.
13.0
12.0
11.0
10.0
9.0
8.0
7.0
6.0
5.0
4.0
3.0
2.0
1.0
MODEL - Dw = ,0015/DAY

I '
n
OBSERVED:
DAILY MAXIMUM
DAILY MEAN
DAILY MINIMUM
MODEL-Ow=
0.006/DAY
MODELED
DIURNAL AMPLITUDE
OBSERVED
DIURNAL AMPLITUDE
14
15.
16
17
18
19 20 21 22 23 24
JULY- 1969
FIGURE
COMPARISON OF COMPUTED AND OBSERVED
DIURNAL DISSOLVED OXYGEN
A- tote

-------
- 4mg/l
-	5mg/l
-	4mg/l
30
25
NUMBER
OF DAYS 20
PER MONTH
0.0. <
Q - 6mg/l 13
^ " 3mg/l
10
QTRENTON 5
4700 cfs
30
25
NUMBER
OF DAYS
PER MONTH
0.0. < 20
Q - 6mg/l
IS
10
QTRENTON
2700 eft 5
0
3 4 9 ft 7 8
ft
STATION
REGION

~~~~~a
STATION
REGION
STATION
E
1 Us
1
STATION
REGION
STATION
REGION
STATION
/
/
/
/
/
/
/
/
H
REGION
ro C
i=i
REGION
30
25
NUMBER
OF DAYS
PER MONTH 20
WHEN D.O. <
<4mg/l IN
STUDY AREA 13
10
ESTIMATED
RECURRANCE 5
INTERVAL ON
THE BASIS OF .
FLOW ONLY
MINIMUM NUMBER OF DAYS THAT
0.0. STANDARD IS VIOLATED
UNDER PROJECTION CONDITIONS
r_f
YEARS
KEY:
STATIONS:
3	DELAWARE WATER AF
4	BEIVIOIRE
3 EASTON
 FRENCHTOWN
7 LAMBERTVILLE
 TRENTON
REGIONS:
U ABOVE EASTON
L BELOW EASTON
CONDITIONS:
(A)	PRESENT
(B)	FUTURE-INCREASED LOAM
AND BIOMASS .
(C)	FUTURE-INCLUDING A
LARGE REGIONAL
S.T.R LOAD
FIGURE 7-
SUMMARY OF MODEL PROJECTIONS
R - /o 7

-------
The Eutrophication Problem ^
Introdubtion
Even the most casual observer of water quality has
probably had the dubious opportunity of walking along the
shores of a lake that has turned into a sickly, greew"pea soup."
Or perhaps, one has walked the shores of a slow moving estuary
or bay and had to step gingerly to avoid rows of rotting,matting,
stringy aquatic plants. These problem areas have been grouped
under a general term called eutrophication. The unraveling of
the causes of eutrophication, the analyses of the impact of
man's activities on the problem and the potential engineering
controls that can be exercised to alleviate the condition
have been a matter of interest for only the past several decades.
Eutrophication is the excessive growth of aquatic plants,
both rooted and planktonic to levels that are considered to be.
in interference with desirable water uses. The growth of
aquatic plants results from many causes which will be explored
in this chapter. One of the principal stimulants,however, is
the level of nutrients such as nitrogen and phosphorus. In
recent years, this problem has been increasingly acute due to
the discharge of such nutrients by municipal and industrial sources,
as well as agricultural and urban runoff. Figure 8-1 shows the
general problem framework. It has often been observed that
there was an increasing tendency for some bodies of waters (e.g.
lakes, reservoirs, estuaries) to exhibit great increases in the
severity and frequency of phytoplankton blooms.
This increased phytoplankton production results in several
consequences:
a)	Aesthetic and recreational interferences - algal mats,,
decaying algal clumps, odors
b)	Large diurnal variations in dissolyed oxygen (DO) can
result in zero DO at night; which,in turn, can result in death
of fish
c) Phytoplankton biomass settles to bottom - creates benthal
oxygen demand, which, in turn, results in low values of DO in
hypolimnion of lakes and reservoirs.
d)	Large diatoms and filamentous algae can clog water treat-
ment plant filters and result in reduced time between backwashing.
e)	Extensive growth of rooted aquatic macrophytes interfere
with navigation, aeration and channel carrying capacity.
f)	Toxic algae have sometimes been associated with eutrophica-
tion in coastal regions and have been implicated in the occurrence
of "red tide," which may result in paralytic shellfish poisoning.
The eutrophication problem can then be defined as:
The input of organic and inorganic nutrients into a body
of water which stimulates the growth of phytoplankton or
rooted aquatic plants resulting in the interference with
Robert V Thomas

-------
Oi. fe Alitor
/ &-) Si Iritvlkiir* yfr'flSkl
>  ,j?P
r s fjTr&i
* . . CtaL *
A/ * r
Urtit &'$ J
<& 7 -
Ut.fi -y  r' ,/ .if ^
-/ / / / Mwmp*l
^y' 7^ r~ *j\ p
/iv^t J'* t
F/^uy^c $-j S o f r t < i y U "f v/t *1 A.1 j>i  u iro p jui (_ a //j'n
p >-0 lo/ w ,
140 
120-
100-
BO-
Western
60  Lake 
Erie
San
 Joaquin 
Delta, Calif.
"Excellent"
Appro x.
"Obiective"
Potomac
Estuary
40 _ Eutrophic
Appro x
ObTective"
Lake
Superior
"Excellent"
!*-. ?s
"Objective
Approx.	
'Objective"
Phytoplankton Chlorophyll "a"
(Micrograms per liter)
S - 2., Pd-nje ej, C. h itvapkyf) "ts"
C ni f V* f/I	J " t t H VSi ''

-------
desirable water uses of aesthetics, recreation, fish
maintenance and water supply.
The condition of a water body is then described in terms
of its trophic state, i.e. its degree of eutrophication or
lack thereof. For lakes, three designations have been used:
1)	Oligotrophia - clear, low productivity lakes
2)	Mesotrophic - intermediate productivity lakes
3)	Eutrophic - high productivity lakes relative to a
basic natural level.
The level of eutrophication due to excessive amounts of
phytoplankton can be measured using several criteria:
a)	Counts (Number/ml) of specific phytoplankton species,
e.g. Asterionella formosa. This is the most direct count of
species trends but requires a considerable effort by trained
specialists in phytoplankton identification. Also, conversion
to biomass measures is difficult because of variations in cell
sizes for given species.
3
b)	Cell volume (ym /y.) of species. An excellent measure
permitting ready conversions to biomass as dry weight or carbon
and grouping of data into different categories (e.g. "diatoms"
and "others"). However, this measure requires an extensive
analytical and data reduction effort.
c)	Chlorophyll a concentrations (yg/). A measure of the
gross level of phytoplankton, easily obtained without extensive
effort in laboratory. However, chlorophyll does not provide
information on species levels nor does it permit grouping
into classes of phytoplankton. Chlorophyll a is the most common
measure used in eutrophication studies.
"Undesirable" levels of phytopiankton vary considerably de-
pending on water body. For example, the following levels repre-
sent present levels which,in some way, are considered undesir-
able :
Open Lake Michigan - 2-5 yg chlorophyll/i
Open Lake Ontario - 5-10 yg chlorophyll/i.
West-ern Lake Erie - 30 yg chlorophyll/i,
Sacramento, San Joaquin Delta - 50-100 yg chlorophyll/5.
Potomac Estuary - >100 yg chlorophy1l/
Objectives for "Desirable" levels of chlorophyll vary widely
depending on the type of problem and the nature of the water
body. Figure 8-2 illustrates the range in present observed
chlorophyll concentrations and that level considered desirable
in some sense. In general, lakes and reservoirs tend to have
lower desirable levels of phytoplankton. Chapra and Tarapchak
(1976) have summarized several objectives for North Temperate
lakes as follows :
Z-j0

-------
Eutrophic - i 6 to 10 yg chlor a/I
Mesotrophic - 1 to 10 yg chlor a/l
Oligotrophic- < 1 to 5 yg chlor a/i
Some other levels that have been cited include the Potomac
estuary at 25 yg chlor a/i and the Sacramento-San Joaquin Delta
at 25-50 yg/i.
Basic Aspects of Eutrophication
Principal Mechanisms
The essence of the photosynthetic process centers about the
chlorophyll-containing plants which can utilize radiant energy
from the sun, convert water and carbon dioxide into glucose,
and release oxygen as a by-product. The photosynthesis reaction
can be written as
Photosynthe sis
6 C2 + 6 H20 	^ C6H126 + 6 2
The production of oxygen is accomplished by the removal of
hydrogen atoms from the water, forming a peroxide which is
broken down to water and oxygen. The water body is now sub-
jected to an "atmosphere" of pure oxygen as compared to the
water surface where reaeration comes from an atmosphere con-
taining only about 20% oxygen. Since all saturation values of
DO are referred to the standard atmosphere, photosynthesis can
result in supersaturated oxygen values. Values as high as
150-200% of the air saturation levels are not uncommon. Because
the photosynthetic process is dependent on solar radiant energy,
the production of oxygen proceeds only during daylight hours.
Concurrently with this production, however, the algae require
oxygen for respiration which proceeds continuously. A number
of trace elements are required and are usually available in
most natural systems. As indicated above, nutrients such as
nitrogen and phosphorus are also necessary for phytoplankton
growth.
The basic phenomena underlying the process of phytoplankton
growth in the North Temperate regions are summarized in Figure
83. Increasing solar radiation provides the energy source for
the photosynthesis reaction. Phytoplankton biomass then begins
to increase as water temperature increases and as a result,
nutrients in dissolved form are utilized by the plankton. This
mechanism continues until nutrients reach levels that will no
longer support growth at which the increase in phytoplankton
biomass ceases. A decline is then observed, due often to zoo-
plankton predation and often a late summer-early fall bloom may
,be observed again due to nutrient recycling. Biomass then de-
clines as solar radiation and temperature decrease to the lower
levels of late fall and early winter.
The principal variables of importance then in the analysis
of eutrophication are:
*-//

-------
r
Sojuv
3^^
7< rnjp<>^4/r"C
'i
Oh,	)j4	i*V
T/ne y  ~
A/p
ah * cUr.
tJ j i yi t * ^
, UK.	Whi	4{T*,
7") ~* < < ^ f v
toui *H*i"H
(
8 ~3 &AJH ^yoCtJi	k^4-&p/  k l-JH- HjIyiih-I
ivi-k/^ cf /d *.
.^
Dissolved Reactive (Available for
Phosphorus	phytoplankton
(orthophosphorus) growth)
Total Dissolved
s"	^Complex Dissolved
Total Phosphorus/	Organic Phosphorus

^Inorganic
Total Particulate
Detritus
V	yf'
^Organic^
^ Phytoplankton
8-4 (a)
^^Detritus
Particulate
>rganic Nit.'*	^Phytoplankton
^Dissolved	f
f Available for
rotal.Nitrogen^	Ammfinia Nit.^-Inorganic Nit. < phy toplankton
/ growth
kN0 & NO Nit.
2	3
8-4 (b)
figure 8-4 Principle components of nutrients: (a) Phosphorus
(b) Nitrogen
- //oi

-------
a)	Solar radiation at the surface and with depth
b)	Geometry of water body; surface area, bottom area, depth,
volume
c)	Flow, velocity, dispersion
d)	Water temperature
e)	Nutrients
i) Phosphorus
ii) Nitrogen
iii) Silica
f)	Phytopiankton - Chlorophyll "a"/%
g)	Zooplankton - mg carbon/i
It should be recognized that the nutrients above are present
in several forms in a body of water, and not all forms are readily
available for uptake by the phytoplankton. The more important
categories are shown in Figure 8-4 (a) and 8-4 (b). Total phos-
phorus is composed of two principle components: the total dis-
solved form and the total particulate form. The dissolved form,
in turn, is composed of several forms, one of which is the dis-
solved reactive phosphorus. This form of phosphorus is available
for phytoplankton growth. The particulate phosphorus forms include
inorganic soil runoff phosphorus particulates and the organic
particulate phosphorus which include detritus and the phytoplank-
ton phosphorus.
Total nitrogen is composed of four major components, the
organic", ammonia and nitrite plus nitrate forms. The latter three
forms make up the total inorganic nitrogen and is the form utilized
by the phytoplankton for growth. The organic form of nitrogen
represents both a dissolved and particulate component. The particu-
late form, in turn, is composed of organic detritus particles and
the phytoplankton.
Figure 8-4 A shows the phytoplankton dynamic behavior for
the epilimnion of Lake Ontario. The schematic of the lake shown
in Figure 8-4A(a)shows the principal inputs and physical mechanisms
that influence the phytoplankton growth. As shown in Figure 8-4A(b),
the chlorophyll a level for the upper layer of.'Lake- Ontario is low
until the spring when solar "radiation and water temperature increases.
A peak value of about 5-10 yg chlor. a/. is reached in the May-June
period. Concurrently, available phosphorus levels (Fig. 8-4A(d))
were reduced to levels that caused a cessation of phytoplankton
growth. Fig. 8-4A(c) shows the growth of zooplankton in the summer
through predation of the phytoplankton. This interaction of the
zooplankton on phytoplankton growth is discussed in more detail
later.
Figure 8-4 B shows similar dynamic interactions between
chlorophyll and phosphorus for Saginaw Bay and southern Lake
Huron. The concentrations of chlorophyll in Saginaw Bay of
between 20-40 yg chlor.a/fc are indicative of the eutrophic status
of that .body of water.
- / / 3

-------
NUTKlgNT INPUTS
MAGARA RiVtR
TRIBUTARIES
MUNICIPAL
INDUSTRIAL WASTES
vertical
Exchange
ENVIRONMENTAL INPUTS
sola* AAOiaTiOn
WATER TEMPERATURE
light extinction
system parameters
EPILIMNION
TRANSPORT	17U
i 1 1 U-| -l-M
MYPQUMNlON
0	-
H
1	O
o|
I Q_
> o
X cc
a. o
!_!_]_ L_L_L
BENTHOS
I IIMTlU I "HIJII Mil I'M'JII H III! IIW Mill nil l|| II
(00
 1970	RANGE OF MEAN 1 STANDARD DEVIATION U.)
 1969	\ ////,,. LAKE-WIDE MEAN. 
 E 0.08
5
O-
o
o
M
NOTE: ZOOPLANKTON CARBON
IS FOR 0-50 METER HAUL
0.04
0
 l	l	i	i	

l\j*rw\IO I* 1^.	Sckf <1^-
b) fhyh . th lo v A.,	O iet p, CuvijH,	/. nliij
(, (H JfcV TV I ia *i n
J?- //y^

-------
TOP LAYER
0-15 mcttrs (main latt)
a-bottom (Saginaw Bay)
PHYTOPLANKTON
CHLOROPHYLL a, jig/I
fou&trH	J/*Wi
40.0
8.0
~ CCIW
O CLRO
4.0
0.0
0.0
SOLUBLE REACTIVE
PHOSPHORUS, mg/l
0.004
0.032
O CCIW
O CLRO
0.002
0.000
0.000
J 1 F 1M' A
O' N1 O
f-^6 Vky h pi	8*y,	SovH^rn )*Ai 14*
ft/ To** 4*4	lli*)
=? - //3

-------
External Sources of Nutrients
As shown in Figure 8-1, the principal external sources of
nutrient inputs are:
a)	Municipal wastes
b)	Industrial wastes
c)	Agricultural runoff
d)	Forest (commercial) runoff
e)	Urban and suburban runoff
f)'	Atmospheric fallout
Table 8-1 to 8-3 and Figure 8-5 summarize some of the data on
these inputs from several sources (Eisenreich et al., 1977;
Gakstatter et al., 1978; Hydroscience, 1977a, 1977b; Rast and
Lee, 1978; Thomann, 1972; IJC, 1978).
TABLE 8-1
Mean Nutrient
Inputs from Municipal
Was tewaters
Phosphorus (as P)
Total P-W/detergent
W/0 detergent
Ortho P-W/detergent
W/0 detergent
N i trogen (as N)
Total N
Inorganic N
Influent
(mq/1)
5-10
2-5
2-5
50
30
Conventional Secondary After Phosphorus
Treatment Effluent Removal Processes
	(mg/l )	 	(mg/1)	
7.0
4
5
3
18
8
1-3
1-2
14
7
-3 / /

-------
NUMMft
Of SUSS
5) FOREST
no mostly forest
52	MIXED
II	MOSTLY URBAN
	MOSTLY AGRIC.
91	AGRICULTURE
MEAN TOTAL PHOSPHORUS CONCENTRATIONS
vs
LAND USE
DATA OH n tV/nOnJklHAGI Ant * s In
mstchn uNirro wrst
] 0.014
j 0.01S
| 0.0 40
] 0.066
~l 0.044
0.11]
'
MILLIGRAMS PER liter
0.10
FOREST
MOSTLY FOREST
MIXED
MOSTLY URBAN
MOSTLY AGRIC.
AGRICULTURE
MEAN TOTAL NITROGEN CONCENTRATIONS
vs
LAND USE
o*r* oh *n ftu&DAAiMAGC amai m
(AS'IRH UNHID STAICi
3 0.J0
I 0.15
_J 1.3B6
3
MIILlGRAMS PfR LtTCR
gure 7. Mean total phosphorus and total nitrogen concentrations in streams draining different lnnd
use categories. (From Bartsch and Gakstatter, 1978).

-------
TABLE 8-2
Great Lakes Basin - Rural Land
Phosphorus Loads Developed by
International Joint Commission
Land Use
Sand
kg Total p/ha-yr
Type of Soil
Coarse	Pine
Loam	Loam
Clay
Row Cropping
(> 50% row crops)
Mixed Farming
(25-50% row crops)
Forage
(< 25% row crops)
Grassland
0.25
0.10
0.05
0.05
0.65
0.20
0.05
0.05
1 . 05
0.55
0 .40
0.05
1 .25
0 . 85
0.60
0 .25
Type
TABLE 8-3
Other Non-Point Source
Loadings
kg/ha-yr
Total Phosphorus
Mean	Range
Total Nitrogen
Mean	Range
Forest-Natural
Atmospheric
Urban
Agricultural-
General
0.4
0.2
2.5
0.5
( .01-.9)
( . 08-1.0)
( .1-10)
(0.1-5)
2.9
5.0
5.0
(1.3-10.2)
(1-20)
( .5-50)


-------
Table 8-1 and Figure 8-5 show typical concentration values
for nitrogen and phosphorus; the former from municipal point sources
and the latter from non-point sources in the eastern United States.
Tables 8-2 and 8-3 provide estimates of loading of phosphorus and
nitrogen. The Great Lakes Basin loads shown in Table 8-2 represent
the results of a wide spread sampling program of phosphorus loading
from differing agricultural practices and Boil types. As shown in
Table 8-3, the range of loading from all non-point sources is
rather wide and reflects various ranges in the flow or precipita-
tion rates. The values given in Table 8-3, however, are useful as
general guidelines.
Omernik (1977) has summarized nutrient data from non-point
sources from a nationwide network of 928 watersheds under the
National Eutrophication Study of 1972-1974. A simple regression
model was used to relate runoff concentrations to the percent of
land in agricultural use and the percent of land in urban use.
Tables 8-4 and 8-5 show these results for total phosphorus and
nitrogen concentrations for different regions and land use dis-
tribution.
Sediment Release Rates of Nutrients
In addition to the external sources of nutrients, the release
of nutrients from the sediments may also be important. Of course,
it should be recognized that the presence of excessive levels of
nutrients in the sediments of water bodies is due to the external
sources. However, for some situations, the problem can be separated
and the effect of nutrient release on phytoplankton dealt with as
a continuous source. The impact of sediment nutrient release can
be significant and result in continuing eutrophication problems
even after point sources have	substantially reduced. Table
6-5 a shows some reported -nutrient fluxes from the sediments under
both aerobic and anaerobic conditions. The latter situation greatly
increases the flux of nutrients.
Simplified Lake Phytoplank~ton Models
A considerable effort has been expended in the past 10 years
to develop empirical and theoretical analyses of eutrophication
that could be easily applied. All of the efforts to date have
focused on lakes and incorporate several key assumptions in the
analysis. The simplified phytoplankton models have proven to be
of significant value in first estimates of the probable effects
of reduction of nutrient inputs. Some of the key references are
listed at the end of this section.
The basic approach underlying several of the models is the
mass balance of the assumed limiting nutrient-phosphorbs. Total
phosphorus is used as the indicator variable of trophic status.
Vollenweider (1968) in his first paper, of a largely empirical
.j~?

-------
TABLE 8-1+ESTIMATED MEAN TOTAL PHOSPHORUS CONCENTRATIONS (mg/1)
.FOR NATIONWIDE AND REGIONAL MODELS *
Nationwide			Regional Models 		
Model	East	_Central	 	West	
X Ag +	67%	67%	67f~	67%
XUrb Ave P Cone Limits	Ave P Cone Limits Ave P Cone Limits Ave P Cone Limits
0	0.020	(.010-.042)	0.015	(.008-.026)	0.018	(.008-.037)	0.028	(.013-.060)
25	0.033	(.016-.067)	0.026	(.014-.048)	0.032	(.015-.066)	0.048	(.022-.103)
50	0.052	(.025-.106)	0.045	(.024-.083)	0.058	(.028-.120)	0.083	(.038-.178)
75	0.083	(.041-.170)	0.078	(.042-.144)	0.103	(.049-.213)	0.141	(.065-.303)
100	0 133	(.065-.272) 0.136	(.073-.251)	0.185	(.089-.382)	0.240	(.111-.516)
FROM OMERNIK (1977)
TABLE, 8'S" ESTIMATED MEAN TOTAL NITROGEN CONCENTRATIONS (mg/1)
FOR NATIONWIDE AND REGIONAL MODELS *
Nationwide _	Regional Models	
Model	East	 	Central		West
tfii
i%il>i
67%	67%	67? 	67%
Ave N Cone Limits Ave N Cone Limits Ave N Cone Limits Ave N Cone Limits
o	0.57	(0.35-0.92)	0.51	(0.33-0.77)	0.57	(0.37-0.88)	0.63	(0.34-1.16.)
xf	0.90	(0.56-1.46)	0.87	(0.57-1.32)	0.83	(0.54-1.28)	0.95	(0.52-1.75)
fo	1.45	(0.89-2.34)	1.49	(0.98-2.26)	1.22.	(0.79-1.88)	1.42	(0.77-2.61)
	2.31	(1.43-3.74)	2.55	(1.68-3.88)	1.78'	(1.15-2.74)	2.13	(1.16-3.92)
ioo	3.69	(2.28-5.97)	4.37	(2.87-6.64)	2.61	(1.69-4.02)	3.19	(1.73-5.87)
FROM OMERNIK (1977)
S. - / 3. O

-------
Flux - Aerobic Conditions
Location
Tot.Diss P
mg/m -day
nh3-n
Si-Silicon
Muddy R., Boston
MA
Lake Warner,
Amherst, MA
3.2
0.4
Lake Ontario
0.2
Lake Erie-
Western Basin	6.0
Central Basin	3.0
Eastern Basin	.2.0
44
30
22
White Lake,
Muskegon Co.,
Michigan
Cape Lookout
Bight,No.Car.
LaJolla Bight
40 (winter)
325 (sumn er)
2.4 (-13
to 16)
Potomac Estuary
1-10
Flux - Anaerobic Conditions
mg/m2-day
Tot.Diss P NH3~N Si-Silicon Reference
16(32 Max)	Fillos & Swanson
(1975)
13(8 Max)
Bannerman,etal.(1975
DiToro  Connolly
(1980)
34	44	297	Freedman fi Canale
(23)	(1977)
Martens et al-. (1980)
Hartwig (1975)
USGS Data

-------
2
nature, related external nutrient loading in g/m of lake surface
area per year to depth and noticed that the population of lakes
divided into two broad areas related to the state of eutrophication
From that work, other investigators have continued to incorporate
a more basic theoretical structure and have necessarily relaxed
some of the earlier levels of judgement that were required in the
analysis. These latter efforts have also attempted in semi-empirical
ways to estimate not just the phosphorus level but the more rele-
vant variable of phytoplankton chlorophyll. Chapra and Tarapchak
(1976) have summarized the simplified scheme as the following
series of steps:
a)	Estimate loading of total phosphorus to the lake
b)	Determine mean annual concentration of total phosphorus
in the lake
c)	Estimate the spring concentration of total phosphorus in
the lake from mean annual concentration
d)	Compute mean summer concentrations of chlorophyll a from
spring concentrations of total phosphorus.
Basic Mass Balance - Nutrients
The assumptions used in the simple analysis are:
a)	Completely mixed lake
b)	Steady State
c)	Single Nutrient Phosphorus limited - Max level of phos-
phorus specified
d)	Total phosphorus used as measure of trophic status
The third assumption indicates that only one nutrient need
be considered, i.e. that all other nutritional requirements for
phytoplankton are met. For lakes, phosphorus is often but not always
nutrient that limits growth and, therefore, is	often the
cause of increased phytoplankton resulting from phosphorus dis-
charge s.
The last assumption is particularly interesting. Instead
of attempting to describe all of the complex interactions indicated
previously (solar radiation, temperature, nutrient and phytoplank-
ton), a surrogate variable is chosen to represent the state of
the lake. The measure of trophic status,therefore, in the simple
mass balance lake models is the total phosphorus. Empirical re-
lationships are then used to relate the total phosphorus concen-
tration to phytoplankton chlorophyll levels.
The basic, mass balance equation is given by following the
principles of Chapter 5 for a completely mixed lake. Figure 8-6
shows the schematic of the system. The equation is:
Vd
= Q. P - K pV - Op
dt in o s
(8-1)
3 - / SI 2.

-------


7rt i >r* i
it 4 t >m < H *1
Q*f>
Loiw Yi./4ri I *1**^ /a lit
' t     ' ' 	' ' t I . . . , I	!	J	I	T . T '  f
rtniivoj phaifh aft J
Kf'oi
EUTROPHIC
M-
0.1-
excessive
loading
acceptable
loading
OLIGOTROPHIC
iii i i i n|	ri> i I'm	1ii i i 11.
"to in /yr
Nutrient loading/lake trophic condition after Yollenweider {1975}
^ -/A 3

-------
or V^ = w _ K pv - Qp	(8-1?
d t	s
where:
V = volume of lake [L^]
p = phosphorus (total) in lake, [M/L3]; e.g. yg/2.
Q = outflow ^	3
Q = inflow [L /T]; e.g. m /S
in
p = influent phosphorus concentration, [M/L ]; e.g. Vg/&
o
W = external sources of phosphorus, [m/t]; e.g. g/s
K = overall loss rate of total phosphorus due to settling
3 of particulate forms, [l/T]; e.g. (1/day)
At steady state, Eq. (8-1) is given by
p(Q + K V) = Q. p
s	mo
or
Q. Pn Q.	1
p s i n = AiP (	) p
Q+KsV V +Ks 
and if it is assumed that Q. = Q, then
in
P ^p + K )p0 for p = = I where t, = detention time ,0
s	v t.	a	j- , ,
d	of lake
A second form at steady state is given from Eq. (8-la):
. 1
P = V p + K
s
W	1	21
= 	 (~) for A = lake surface area [L J; and then
- p+ k	s
A z	s
s
 W '
P = ;'P " '.)	(8"31
Z	S
where W' = areal phosphorus loading rate = - [^] ; e.g. g/m2-yr.
A _ _ 4
T-L
and z = average depth of the lake [l]; e.g. meters.
The difficulty of using Eqs. (8-2) or (8-3) is that K , the
net loss rate, is not readily known nor can it be measuredsin a
direct experimental way. However, if information is available
on the input and output from the lake, an estimate can be made
of K . Suppose,therefore, that a number of lakes are examined
where p, W', z and p can be estimated,-then Eq. (8-3) permits
estimation of K . Vollenweider (1975) deduced that
2. - / 2

-------
K  12.	(8-4)
s
z
-1
for z in meters and K in yrs
s
V
Since K =  where v is the settling rate [L/T], then for v =
s	-	s	s
z
10 m/yr., Eq. (8-4) is equivalent to a net settling	rate of
.0274 m/day. Other estimates of 16 m/yr. and 12.4 m/yr are dis-
cussed by Chapra and Tarapchak (1976). Given the empirical rela-
tionship of Eq. (8-4), Eq. (8-3) can be written as
W'
P = 			(8-5)
10 + zp
Note that zp = 7- *  = = qe The quantity Q/A is the areal
A	V	A	S	S	3	2
water loading orS "over f lo rate", and is designated as 
-------
p _	W '	
z (p + /p)
w1
P = 				(8-8)
zp(l + /1/p)
Attempts have also been made to extend the above analyses
to include other measures of the state of eutrophication. Rast
and Lee (1978) give the following expressions for North American
lakes:
Chlorophyll "a": log [ch]	= 0.76 log [p] - .259 (8-9)
for chlorophyll in U9/& and phosphorus in
mg/m^.
Secchi depth: log (zj = - .359 [p] + .925	(8-10)
for secchi depth in meters
Eq. 8-10 relates the total phosphorus to the secchi depth
as a measure of clarity. Other relationships of total phosphorus
to the dissolved oxygen problem are explored later.
Figure 8-8 shows the relationships between median total phos-
phorus and mean chlorophyll a concentration for a number of lakes
and reservoirs in the northeastern U.S. (Gakateller, 1978). The -
empirical relationship shown in the figure compares reasonably well
with Eq. 8-9 of Rast and Lee (1978) . The notation of trophic
status provides an approximate division between the three states of
oligotrophy, mesotrophy and eutrophy.
These empirical relationships permit estimation of chlorophyll
a, secchi depth	if the
total phosphorus in the lake can be estimated from data or from
equations such as Eq. (8-3) or (8-8) .
The approach of Chapra and Tarapchak (1976) follows the steps
outlined in the introduction above and begins with Eq. (8-3)
which relates external loading to total annual phosphorus in the
lake. The spring concentration of total phosphorus is given em-
pirically by~
p = 0.9ps	(8-.'
2-/34

-------
1000
L69l0  0.007 LOjpTP - 0.194
po
100
ED
O  OliQOtrophic
A  Mesotrophic
~ * Eutrophic
1.0
1.0
100
1000
10000
MtDIAN TOTAL PHOSPHORUS CONCENTRATION (pg/|)
Figure ?.-V The relationship between chlorophyll A and total phosphorus concentrations in northeastern
U.S. lakes and reservoirs included in the 6urvey. (From Bartsch and Gakstatter, 1978).

-------
21 .
where p is the spring total phosphorus. The final step of comput-
ing mean summer chlorophyll is given by Dillon and Rigler (1974) as
1 4 4 9
Chi a = .731 (p )	(8-12)
s
Eq. (8-12) , and (8-13) were then combined to give
1	4 4 9
Chi a = 1866 [W'/(q + 12.4)] "	(8-13)
s
2
where Chi. a is in g/ , W' is in g/m -yr and q is in m/yr and a net
sedimentation rate of 12.4 m/yr was used. This equation permits
estimation of the mean summer chlorophyll directly from the external
loading, a very desirable trait.
Eq. (8-14) can also be rearranged to evaluate the loading re-
quired for a given chlorophyll level. Thus,
0 6 9
W' = .0055 (Chi. a)	(q + 12.4)	(8-14)
s
Ch.apra and Tarapchak (1976) chose the following mean summer
chlorophyll levels as objectives:
Acceptable: Chi- a = 2.7 Ug/i	(8-15)
Excessive: Chi a = 9.0 Ug/i	(8-16)
These levels are equivalent to total annual phosphorus levels
of 13.4 and 30.7 ygP/i for the acceptable and excessive levels
respectively. With the objectives of expressions (8-15) and (8-16),
W	0.011 (q + 12.4)	(8-17)
acceptable	s
W	. = 0.025 (q + 12.4)	(8-18)
excessive	s
These expressions are essentially identical to Eqs. (8-6) and (8-7)
lending support to the credibility of each. As. such, the loading
rates of Figure 8-7 separate a trophic status of lakes from about
3 yg chlor/i at the acceptable level to about 9 Ug chlor/i at the
excessive level. It should be stressed again that all these re-
sults apply as a general criterion for lakes only and as a rule,
only for lakes in the North Temperate regions of the world.
Variability of Net Effective Settling Velocity
The completely mixed nutrient mass balance equation which
forms the basis for the simplified Vollenweider analysis rests
heavily on the assumption that the net effective settling velocity
is 10 m/yr. When only external loads are considered, this para-
meter in the mass balance incorporates phenomena such as
1)	fraction of incoming phosphorus in particulate form
2)	concentration of suspended solids in the lake
3)	resuspension of particulate phosphorus from bottom
sediments
4) diffusive flux of dissolved phosphorus from the sediments.
S. - t 3l 2

-------
21 -A
The net effective settling velocity may, therefore, be
expected to vary as a function of these mechanisms. There is no
simple direct way to represent all these phenomena in a single
parameter reflective of all lake and impoundment situations.
The range in v is large as shown in Figure 8-8A. The data for
this Figure art from U.S. lakes and impoundments and were compiled
from Rast and Lee (1978), Bachmann and Canfield (1979), Schreiber
and Rausch (1979), and Higgins and Kim (1981). Only positive
values for v are plotted; for some reservoirs (e.g. see Higgins
and Kim, 198?) the computed net settling velocity is negative
which indicates that the mass output of the impoundment exceeds
the input mass. This could result from net positive resuspension
in the reservoir.
It is clear from Fig. 8-8A that the variability in v is
great. The U.S. lakes, as distinct from impoundments, vary within
about one order of magnitude (approximately 3-30 m/yr.). This is
a sufficiently large range and could markedly influence the cal-
culation of the allowable phosphorus load.
Impoundments,in general, vary about three orders of magnitude
with no clear correlation to the hydraulic loading rate. The net
settling rate for impoundments is, however, generally greater
than that for lakes by a substantial amount. This probably re-
flects an increase in particulate phosphorus fractions and associated
settling velocity.
Figure 8-8A shows the importance of not relying too heavily
on the simplified Vollenweider plot of Figure 8-7. Each individual
lake and impoundment will have an associated v that should be
evaluated on a rite specific basis.	s
However, from the point,of view of engineering control, the
simple nutrient mass balance equation coupled with the empirical
expressions indicated above provide an excellent starting point
for assessing the efficacy of proposed nutrient reduction programs.
For other situations where a) the assumptions used for the simple
analyses are no longer sufficient, b) water bodies such as estuaries
and bays must be analyzed, and c) additional quantitative under-
standing of the processes of eutrophication is desired, it is
important to explore phytoplankton relationships with a simple
dynamic modeling framework.
PHYTOPLANKTON GROWTH AND DEATH
A simple mass balance equation for the phytoplankton can
be obtained by following the basic principles outlined previously,
i.e. summing all sources and sinks of phytoplankton. Therefore,
considering a completely mixed lake, the equation is:
dp
V jf = V(G - D ) P - A v P+Q. P. -QP	(8-19)
dt	p p	s	in in
where P = phytoplankton chlorophyll [M/L^]; e.g. yg/
a. - / z j

-------
12 -00 J
IfifiOr
\ V0LCE"Mty7&e/^~Tr~z*r^~*7ySeT'
3 J 5 6 7 S 9 10
2*	30 to 5fi 6 X> 9P 9o:00
^H/aao
00	30O 4CO 500 Sov	-OCO
HV&RAuuic.	Ot(m= bzf>r hi /j-. -r/rr.'
8-3/J	Se.H/)'"<* v-e/oc/^wj <* i a
hy j> u /o
-------
22 .
P. = phytoplankton chlorophyll [M/L3] Ln incoming
in flow CM/L3)
G = growth rate of phytoplankton [T ^],e.g. (1/day)
p	-1
D	= death rate of phytoplankton [T ]
P
v	v	= settling rate of phytoplankton [M/T]/ e.g. (m/day)
"s	2
A = area through which settling is occurring [L ]
The first term on the right hand side of Eq. 8-19 represents
the net growth rate of the phytoplankton, i.e. growth minus death.
This term is a new term in the mass balance equations for completely
mixed systems considered thus far. The second term, is the mass of
phytoplankton lost to the sediment from settling. Note that:
Vv

s H	"p
-1
A v = ^ = VK
where H is the mean depth [L] and K [T ] is the net loss rate =
v /H.	P
s
Estimates of v range from about 0.1-0.3 m/day and represent
the net loss of phytoplankton through the bottom interface of the
water body. This net settling depends on phytoplankton species,
time of day and nutritional status of the plankton. In general,
living phytoplankton have settling velocities that are consider-
ably less than non-living particulate matter. Burns and Rosa
(1980) carried out a series of experiments using special in situ
settling experiments. Table 8-5B summarizes some of theirre-
sults.
TABLE 8-5B
Some Results of In Situ Settling
Experiments in Lake George
(From Burns and Rosa, 1980)
Settling velocity
Particle Type	m/day	
Particulate	Organic Carbon
1-10 m	0.2
10-64 m	1.5
>64 m	2.3
Phytoplankton
sconedesmus	acutiforms	0.10
selenastrum	minutum	0.15
cryptomonas	crosa	0.30
The third term is the mass of phytoplankton chlorophyll
entering the lake with the inflow. The last term is the usual
mass transport of phytoplankton out of the system due to lake
outflow.
3.- /3 (

-------
2 2 -A
The growth and death of the phytoplankton -represents an
important term and will be explored more fully. Consider then
the kinetic expression:
dP
 = CG - D )P	(8-20)
dt	p	p
as representative of phytopiankton behavior in a batch type vessel.
The solution to this equation for initial condition PQ is:
P = P exp (G - D ) t	(8-21)
o	P P
Several conditions are now possible, i.e.
Gp >	(Net production of phytoplankton)
G = D (Stationary growth)
p	p
G < D (Net decline in phytoplankton)
P P


-------
Figure 8-9 shows the time behavior.of these three conditions.
The principal dynamics of phytoplankton growth are therefore,
contained in behavior of the growth and death of the phytoplank-
ton over the seasons of the year. A more detailed evaluation of
the behavior of these kinetic terms is of some importance in
understanding the interaction of nutrients and phytoplankton
chlorophyll.
Phytoplankton Growth - G
The growth rate of the phytoplankton, as noted earlier,
depends on three principal components:
i) Temperature
ii) Light
iii) Nutrient
The classical approach is to assume that these effects are
multiplicative, although there is no a priori rationale for
this assumption. The use of a multiplicative effect of each
of these components is, however, somewhat justified from data
collected from laboratory experiments (DiToro, et al., 1975).
The growth rate can then be written as:
G = [Temp Effect]  [Light Effect]  [Nutrient Effect]
P
= G (T)  G (I)  G (N)	(8-22)
Temperature Effect
Now consider a situation where the available light for
growth is at an optimum level and nutrients are plentiful.
Then the growth of the phytoplankton will be dependent only
on the temperature effect. This relationship of temperature
and growth rate can be determined from work by Eppley (1972),
among others and is approximated by
T-20
G(T) = G	(1 .066)	(8-23)
max
where G = 1.8/day (approximately)
ma X
This relationship between the growth rate and., temperature
is shown in Figure 8-10. Note that the relationship expresses
the maximum growth rate as a function of water temperature
assuming that no other effect (e.g. light or nutrients) is
limiting growth.
The value suggested for G	of 1.8/day is
condition for a mixed phytoplankton population.
of phytoplankton, however, have - different growth
general, the range of G is about 1.5-2.5/day.
-	max
Light Effect
If now the temperature is held constant and the available
an average
Various species
rates, and, in
Z-/33

-------
* ?
Ifc

t t m I
P = Pa ef (tf- t)^ )t
(> r > D,
SL
x
a
"a.
>
/
Ptait
a) &P * dp
i
a.
r
OttNi i-
>
(tl C-p c DP
T *'<. - DyJ
t-*! Tt > ^ V>  ( A
c\* j i ^ /k* /vv v	^ V 4 W Hs.
l.o
G(t)
CM
/.O
 (r)o.j(Au)
T-IO
/0
If
*'t *
l o
.r
VVn^ F/Hf^ ' c.
Pi-/:?*

-------
light is allowed to vary, it is observed that as the radiation
increases, photosynthesis increases up to a maximum level.
Further increases in light levels tend to result in photoinhibition
and a subsequent decrease in photosynthesis. Figure 8-11 (from
DiToro et al., 1971) shows this effect and also indicates_that
the optimum light intensity varies for the different phytoplankton
groups.
An equation that represents Fig. 8-11 (a) is given by
F (I)
exp [-1/1 + 1]
(8-24)
where I  saturating light intensity (gm-cal/cm ), i.e. the
light intensity at which the relative photosynthesis is a maximum.
Values of I for mixed populations of phytoplankton are approxi-
mately 100-toO ly/day with 300 ly/day as an approximate average.
Note that when I  Ig, F(I) = l. Eq. (8-24) represents the
relative photosynthesis as a function of light intensity at any
given point in space and time. Often, however, the modeling
analysis is more tractable by calculating average conditions
over a given depth of water and over a fixed interval of time
(usually one day). Following DiToro et al. (1971), and referring
to Chapter 2, Eq. 2-4, it is known that
I(Z)
I exp (-K z)
o	e
Substituting this equation into Eq. 8-24 gives F(I(Z)).
But, the incoming solar radiation, I , is of course a function
of the time of day as shown in Fig. 8-12. If the simplifying
assumption is made that
0
-------
1.0
(a) P*, oj
M
91
u
r
K
f

?
i.e.

OUlamt
1.0
LIGHT INTENSITY (FOOT CANDLES 110s)
Ato"*+Jik\ I rul* *	vt. MiVurf
?*')?> D,Ta" +**i IW uu*9 d*4*
1*4 H*4rthi~t tvJ"* S+4*Jt ('***); '"'"V **),<)
+*.4 {4), 4	fly
Io(0
Tl nie - i
\ $~fSi (*) # c * v *
1(0
	<)*y (I)	f. rw ^ * 1,4 "*3'"a ,
Tim' - D*>yj
iT^v i <^y t-v
<2 - /i>6

-------
the phytoplankton levels. Eqs. 2-7 and 2-8 indicate these
relationships.
G(I), the light effect as given by Eq. 8-26 is dimensionless
and is used as a multiplier in Eq. 8-22. The behavior of G(I )
is'shown in Fig. 8-13(a). For a typical range of I of 250-500
ly/day, the value of G(I ) ranges from 0.10 to 0.50, i.e. the
overall effect of non-optional light. conditions due to light
extinction with depth is to reduce the growth rate by about
50-90%.
Nutrient Effect
The final effect on the growth that must be evaluated is
the effect of varying nutrient levels on the growth rate of the
phytoplankton. Therefore, consider again all conditions on tempera-
ture and light to be constant and at optimum levels and consider
the nutrient concentrations to be varying. The result of this
effect is quite significant and is shown in Figure 8-13 (b). At a
nutrient level of zero, there is, of course, no growth since, as
noted previously, the phytoplankton requires at least some critical
nutrients to begin or stimulate the growth of the population. As
the nutrient level is increased, growth commences, i.e. G(N)>0.
However, as nutrient levels continue to increase, the effect on the
growth rate of the phytoplankton is reduced and asymptotically
approaches unity. An expression for this effect on the growth of
the phytoplankton is
G(N) " K +N	8-27
mN
where N is the concentration [M/L3] of the nutrient needed for
phytoplankton growth (e.g. phosphorus ^r nitrogen) and K is
the concentration of the nutrient [M/L ] at which the nutrient
effect, G(N), 1/2. K is called the "Hichaelis" constant after
the work of Michaelis-MeSton on uptake kinetics of organisms on
substrates. The implications of this effect are' quite profound.
Suppose a present nutrient input is such as to result in a concen-
tration of the nutrient that is substantially greater than K ,
ifflN
 e 
N >>K
b mN
where is the nutrient concentration before any nutrient re-
duction. If a nutrient control program is initiated, but the
reduction in input load only reduces the nutrient concentration
to a level of about two-three times the Michaelis constant,
then there will be no effect on the phytoplankton growth. The
treatment program may then be ineffective. The nutrient effect
on phytoplankton, therefore, is a marked contrast to other types
of water quality problems where reductions in input load (as in
BOD reduction) can generally be considered as being advantageous.
Table 8-6 shows some typical values for the values of K
for different nutrients.	mN
3 - f 3 ~7

-------
?0 o
(t)

13 *)	A hilt eUet-t f,,
a V yC
&*>J Attrtf ji jTk4 J	- Jo# A/^y, $? * J*<
kj tft Jkfri'A
.2 - / J 


-------
Table 8-6
Typical Values for K 
mN
Half Saturation Constants for Phytoplankton Growth
Nutrient	K
mN
Nitrogen	10-20 yg N/
Phosphorus	1 - 5 Jig P/.
Silica(for	20-80 yg Si/l
diatoms only)
When more than one nutrient may be important in the problem
context, then the nutrient effect is given by
N1	N2
G (N) - Min {-		 ; 		. ..}	(8-28)
mN. + N1	mN, + N
1	2 2
where the minimum of the expression in brackets is to be taken
as the nutrient effect. That is, the individual nutrient limita-
tion expressions are computed and the minimum value is chosen
for G(N).
The full expression for the phytoplankton growth rate is
therefore given from Eqs. (8-23),(8-26) and (8-28) as
G - G (1.066)T~20 [2-]18f (exp(-a.) - exp (-a)]
p max	K z	1	0
6
N1	N2
[Min (		 ; 		; ...]	(8-29)
m^ + Nx	mN2 + N2
Phytoplankton Death - Dp
The second component of phytoplankton kinetics is the over-
all death or mortality rate of the plankton. The basic components
of D_ are:
P
i) Endogeneous respiration rate at which phytoplankton
oxidize their organic carbon to CO^ per unit weight of phyto-
organic carbon, and
ii) zooplankton predation or grazing of the phytoplankton.
The death rate can, therefore, be written as the sum of
these two components, i.e.
DP " P1 (T) + Dz	(8-30)
where D ,(T) is the endogenous respiration rate as a function of
temperature, T and D is the death rate due to zooplank.ton grazing.
A-/3J

-------
The endogenous respiration rate is given by:
D - 0.1(1.08)T"2	(8-31)
for D_. in day ^ and T in C/ Fig. 8-14 shows this relationship.
J
The loss of phytoplankton due to grazing by herbivorous
zooplankton is, proportional to the number or concentration of
zooplankton that is present. The death rate due to grazing,
D_ can, therefore, be written as
z
= C z
c
(8-32)
where C is the grazing (filtering) rate of zooplankton (liter/
day-mg/3oopl. Carbon) and z is zooplankton concentration in
equivalent carbon units (mg C/l). Much work has been done on
measurements of the zooplankton grazing rate and Table 8-7
summarizes some of the data (DiToro, et al., 1971, Thomann, et
al. , 1975). The filtering rate of the zooplankton is, of course,
a complicated function of the age, size, temperature and species.
Table 8-7
Range of Zooplankton Grazing Rates
Grazing Rate
Organism or Location	liter/day-mg Zoop. Carb
Rotifer (0.1 yg)	1.5-4
Copepod and
2-5
Cladoceran (1-10 yg)
Georges Bank	2-3
Lake Ontario	1.5-3
Eq. 8-32 introduces the zooplankton as a new variable.
The concentration of the zooplankton may be known or can be
estimated. If so, the known concentration can be used in the
equation either as an average value during grazing periods or
as a time variable value. It is preferable to attempt to cal-
culate the concentration and then compare such a calculated
concentration to the observed zooplankton levels. One can,
therefore, write an equation for the growth and death of the
zooplankton in a manner similar to the phytoplankton (Eq. '8-20).
Thus,
a. - / y-o

-------
^ 1?""/*/	Pllj	Lv J jp | vu >>w V*A A i 0i
HJcill ^ /" 't

f/J K
3 - / V- /

-------
If - tGz - V 2	(8":
where G and D are the growth and death rates respectively of
the zoo$lankto&. The growth rate of the zooplankton depends on
the rate at which the zooplankton feed on the phytoplankton
(the grazing rate/ C ), the amount of phytoplankton available
(the chlorophyll levll, P) and the efficiency of assimilation
or conversion of phytoplankton biomass to zooplankton biomass.
The growth rate can then be written as
G = a'C (a P)	(8-34)
Z 1 g Zp
where a' is the efficiency of assimilation (mg Zoopl. Carb./
my Phyto. Chlor.) . A balance of the units is:
mg Z(cbn) 		 mg Z(cbn) mg P (chl)
y = mg P(Chl) * day-mg Z(cbn) mg P(chl) I
It is also known, however, that the efficiency of assimila-
tion, a is not a constant and depends on the phytoplankton con-
centration, i.e. at high dense concentration? of phytoplankton,
the zooplankton simply cannot assimilate the phytoplankton.
Therefore, let
a; = a,
K
_2_
or
1 1 K + P
g
where K is the phytoplankton chlorophyll concentration at
which z8oplankton efficiency is limited by a factor of one-half.
Substitution into the growth rate, Eq. (8-34) gives
K
G  a a 	2_ q p
Z p 1 Kg + P g
G = a a K C (-	-?)	(8-35)
z	p 1 g g K + P
g
This latter expression indicates that	the growth rate of the
zooplankton reaches a saturation level at values of P>>K . Typical
values for the coefficients are: a =50-100 and a^=0.6. ^Thomann,
et al. (1975) used K =10 pg chlor/J^for Lake Ontario and DiToro
et al . (1977) used 6 yg chlor/& for the Sacramento-San Joaquin
Delta'.

The death rate for the zooplankton biomass is simply the
sum of the respiration, individual death rate and predation by
the next level in the food chain. Thus,
D K (T) * Di	(8-36)'
z z	z


-------
where K (T) is the respiration of the zooplankton and is about
.02/dayZat 20C and D1 represents the other losses of zooplankton
due to death and highlr order predation. This latter coefficient
is usually an empirical parameter to be adjusted unless high
order forms are also modeled.
The growth and death of phytoplankton is, therefore, a
function of several environmental variables: water temperature,
sunlight, turbidity and zooplankton. From a water quality engin-
eering viewpoint, the time and space dependence of phytoplankton
also depends most significantly on the nutrients available for
growth. Such dependence is quite non-linear as shown in Fig.
8-13 (b) and, as a result, reductions in ambient nutrient con-
- >ntrations may not always result in reductions in phytoplankton
omass. It is important then to examine the relationship be-
tween phytoplankton and nutrients in some additional detail.
Nutrlent-Phytoplankton Interactions
With the basic principles of phytoplankton growth and
death in hand, the interactions of the nutrient and phytoplank-
ton systems can be evaluated by first considering the nutrient
mass balance equations with the direct and explicit inclusion
of the phytoplankton. It is instructive to begin with a single
nutrient that is limiting, say phosphorus and all other nutrients
are in 'excess supply. For phosphorus then, assume that dissolved
reactive phosphorus (see Fig. 8-4) is available for uptake by
the phytoplankton as shown in Fig. 8-15. The phosphorus thus
absorbed is incorporated into the phytoplankton cellular material.
Upon respiration and cell lysis (cell disintegration), the cellu-
lar phosphorus of the phytoplankton is released in two principal
forms: as particulate organic (detrital) phosphorus and as com-
plexed dissolved organic phosphorus. Both of these forms are
grouped under a general heading of "less available" phosphorus.
Bacterial degradation and hydrolysis reactions then convert
these less available organic forms to the inorganic phosphorus
from which is again available for phyto.plankton uptake, thus
completing the cycle.
This simplified phosphorus-phytoplankton cycle can now be
used to illustrate several important points. Consider this
cycle to be operative in a completely mixed system such as shown
in Fig. 8-6. The mass balance equation "for each form is then
given by the following equations:
dpl
V	dt~ " W1 " Qpi  K22VP1 + W	<8"37>
dP2
V	Ht~  w2 " CP2 " K12Vpi " Gpapp	(8-38)
V	St " W3 " QP " Vs3AP + 
-------
In the equations, and are the unavailable and available
phosphorus |orms respectively and P is the photoplankton chlorophy
all in [M/L ].	and are the inputs [M/T] of less available
and available phosphorus respectively; W is the input of phyto-
plankton chlorophyll; K is the rate [1/T] of conversion of
unavailable to available phosphorus; and	t*ie ^oss rate of
p due to conversion to available phosphorus as well as any
settling of particulate forms, i.e.
Vsl
K = K +	(8-40)
22 12 Z
for v as the effective settling rate [L/T] of particulate forms
of lets available phosphorus. Similarly, in Eq. (8-39), v is
the settling rate [L/T] of the phytoplanJcton and finally,
a is the phosphorus to chlorophyll ratio of the phytoplankton
[S-P/M-Chl], The first two of these equations require some
additional discussion. The third equation has already been
reviewed (see Eq. 8-19).
Eq. (8-37), the mass balance equation for the less avail-
able phosphorus form includes a source term, D Va p. This
term represents the production of less available phosphorus forms
due to the death rate of the phytoplankton, D .
P
Typical units are:
D	V	a	P
P	P
r	l_i ro i fyg Phos. . ,yg chl. yg Phos
1 day 11 'yg Chl. J 1 I J day
The second equation (8-38) includes the generation of available
phosphorus due to degradation of less available forms in the
term K V p . In addition, the uptake of available phosphorus
is given by G a P. The rate of growth of the phytoplankton
and conversioK Sf the inorganic phosphorus to the phytoplankton
biomass is accounted for stoichiometrically in the nutrient
equation by this term. The production of phytoplankton
chlorophyll is, therefore, accompanied by a reduction in the
available phosphorus. For each yg/i. of chlorophyll produced,
the available phosphorus is reduced stoichiometrically by a ,
the phosphorus to chlorophyll ratio. This can readily be sSen
by assuming for Eqs. (8-37) to (8-39) a batch reactor vessel
that has no external inputs, no flow through the vessel, is
kept stirred so the settling velocity is zero and the rate of
conversion of less available to available phosphorus forms is
fast. Only two variables then need be considered; the avail-
able phosphorus and the phytoplankton. Therefore,
dp2
-- = -G aP + DaP=> - (G -D )a P	(8-41>
dt	pp	pp	PPP
4 - /<* V-

-------
and
(8-42)
Now a P represents the available phosphorus equivalent
of the phytoplankton, thus
 a P
P
and Eq. (8-41) becomes
asr " -(W p2
(8-43)
During the active growth phase of the phytoplankton then,
where G>D , (see previous discussion on Eq. (8-21)), an
equivalint^uptake of phosphorus occurs. At the end of the
growth phase of the phytoplankton, where, for example, 100 UgChl/l
were produced, then the product of a and the 100 ygChl/ is
the amount of available phosphorus tSat had to be supplied.
Phytoplankton - DO Relationships
Introduction
The relationship between the growth and death of phytoplankton
and the dissolved oxygen is a particularly important one. From the
DO balance point of view, photosynthesis can result in significant
variations in oxygen in a water body (See Chapter 6). Also,
the production of phytoplankton biomass due to the discharge
of nutrients can result in the deposition of phytoplankton cells
to the sediment. The oxidation of this organic material then
becomes part of the sediment oxygen demand and can significantly
influence the DO. An example is shown in Figure 8-16 where the
DO for the central basin of Lake Erie is shown. The rapid
decline of the DO in the hypolimnion in the summer is clearly
indicated and is due,in large measure, to the phytoplankton
production in the epilimnion. The DO balance equation includes
the effect of photosynthesis and respiration by aquatic plants.
These terms are given as
+ p (mg 0,/-day) -Photosynthesis
A V	2
- R' (mg 02/-day) - respiration
and represent the direct input or utilization of oxygen through
the phytoplankton dynamic of growth and death discussed above.
The mass balance equation for dissolved oxygen discussed in
Chapter 6 includes these effects as source and sink terms, i.e.
av
A -I i

-------
^ Yl	J-
Can adii.


) 3
Eijt
0-17 MSTEftS
C IK+VU I
O-BOTTOM
12.00

J 1F ^ M1 A1M1 J 1 J 1A1S'O'NlD
U)
- 17 METERS-BOTTOM
' .--17-22 METERS
CENTRAL BASIN HYPOUMNIQN
tc/J
^.S-	fe< E'vie a) Loccnh** *j e.f!i*u/t.
yejimi ,   (r	e pi Ji ***-* d < i> t * f '**> ^3 '
to Cww-^aJ Gouk V\^ It *> tJt)

X- /tf-6

-------
The connection between the phytoplankton equations given al?ove
and the P and R in the equation is of particular importance when
the DO response due to changes in phytoplankton population must
be computed.
It can be recognized from the preceding development that the
quantity G P is the yg chlorophyll produced/2, - day. Now every
yg chlorophyll that is produced represents production of phytoplank-
ton carbon to a ratio of about 50-100 yg carbon produced per
yg chlorophyll. The stoichiometric oxygen equivalent of this
carbon (see Chapter 6) is approximately 2.67 yg oxygen. Therefore,
if a is the carbon chlorophyll ratio,
cp
a = 2.67 a	(8-44)
op	cp
where a is the ygDO/yg chlorophyll produced. For a of
50-100 fjlj C/yg Chlor, a is 133-266 yg DO/yg chlor. che average
production of oxygeir ove? a day and over depth is then given "by
p' = a G P	(8-45)
av	op p
which can be used as the source term for the DO balance where
P^v	/4-day) is the average production.
Following the preceding development for the gross growth
rate, G (Eq. 8-29):
P
T- 20
p'  a [G (1.066)	G(I)G(N)]P	(8-46)
op max
av
The maximum oxygen production at saturated light interacting
and excess nutrients is given by:
" 'op^rnax11'066'1"20	
-------
where it can be recalled that D P is the rate of endogenous
respiration of the phytoplanktoS [yg Chlor/5, - day] . If
D cl 0.1/day and a 'Z. .25 mg 0 /yg Chlor, then
p	op	2
R' = .025 P	(8-50)
av
which is the same as Eq. (6- ). Note, however, that Eq. 8-49
is the operative equation and for a range of a and D that
R' as a function of chlorophyll may vary coni?derabl? from
tft simple relationships of Eq. (8-50).
The net production of oxygen is then given by Eqs. 8-46
and 8-49 as
p' = p'	R'
net av av
Eutrophication Control Techniques
The.control of the eutrophication of various water bodies
can take a variety of forms. Perhaps such forms can best be
seen by once again reviewing the mass balance equations for
phytoplankton chlorophyll and a single nutrient, such as phos-
phorus. Thus, for a completely mixed system, Eq. (8-19) can
be repeated here for the phytoplankton
VH - V(Gp - V p " p + Bipin " 5P	(8"51)
and Eq. 8-41 with inputs a!nd flow can	be used for the nutrient,
i.e.
= W + Q, p, + W - (G -D )P	- v A -Q	(8-52)
dt	in in s	P P	si p p
where p is a representative of the controlling nutrient and w is
the nutrient input from the sediment. The engineering control
techniques essentially aim at changing the components of these
equations in the direction of decreasing plant biomass. As with
engineering controls for the dissolved oxygen problem, principal
interest first centers on control of the inputs, in this case,
the nutrient inputs. It can be recalled, however, that there are
really three principal control areas:
1)	control of inputs
2)	alter ation of system kinetics
3)	in-stream treatment and flow control
For the eutrophication problem then, the engineering
techniques include:
=2- i+-S

-------
1) Reduction of nutrient input (W)
2") Changing of internal cycling of nutrients (G and D )
3)	Acceleration of nutrient transport through system p
(QP and Q )
4)	Direct biological and chemical control of plants (dp/dt)
Each of these control techniques have relative advantages
and disadvantages when applied to a specific problem context.
The principal considerations of each will now be reviewed in turn.
Reduction of Nutrient Input
There are five means of reducing the direct input of
nutrients:
1)	Wastewater treatment of municipal and industrial point
sources and CSO, including phosphorus removal by chemical treat-
ment and nitrogen removal by chemical and biological treatment
2)	Alteration of non-point nutrient inputs through land
conservation practices and changes in agricultural use of nutrients.
These practices would include reduction of erosion* testing
of soil before fertilizer application* reduction in winter fertil-
izing, and use of buffer strips.
3)	Diversion of nutrient input to a different water body
where itapact is less
4)	Treatment and control of nutrient at inflow point
including treatment of entire river inflow and building of
'detention basins or storage reservoirs.
5)	Modification of preduct usage to reduce generation of
nutrient at source (e.g. non-phosphate detergents.)
Changing of Internal Cycling of Nutrients
The control options under this approach include :
1)	Dredging of nutrient rich sediments
2)	Hypolimnetic aeration
3)	Chemical precipitation of nutrients
4)	Sealing of sediments to reduce nutrient exchange
5)	Lake or reservoir drawdown
Acceleration of Nutrient Outflow
Techniques under this approach include:
1)	Selective discharge from water body such as lakes
2)	Increased flow through water body.


-------
Direct Biological and Chemical Control
Direct impact on the plant biomass itself can be achieved
1)	Harvesting of plants
2)	Use of aquatic herbicides, e.g. copper sulfate
3)	Dse of organisms (e.g. grossy carp) that graze on
nuisance aquatic plants
1- I iTo

-------
REFERENCES
Chapra, S.C. and S.J. Tarapchak, 1976. A chlorophyll a model and its relation-
ship to phosphorus loading plots for lakes. Water Res. Res., Vol. 12, No. 6,
pp. 1260-126U.
Dillon, P.J. and F.H. Rigler, 197^. The phosphorus-chlorophyll relationship
in lakes. Limnol. Oceanogr., 19(M, pp. 767-773.
Dillon, P.J. and F.H. Rigler, 1975. A simple method for predicting the capa-
city of a lake for development based on lake trophic status. J. Fish. Res. Bd.
Can., 31(9), pp. 1519-1531.
Rast, W. and G.F. Lee, 1978. Summary Analysis of the North American (US Portion)
OECD Eutrophication Project: Nutrient Loading-Lake Response Relationships and
Trophic State Indices. US EPA, EPA-600/3-78-008. Corvallis Environmental
Research Laboratory, Corvallis, Oregon, U5U pp.
Thomann, R.V., 1977. Comparison of lake phytoplankton models and loading plots.
Limnol. & Ocean., Vol. 22, No. 2, pp. 370-373.
Uttormark, P.D. and J.P. Wall, 1975. Lake classification - a trophic character-
ization of-Wisconsin lakes. U.S. Environmental Protection Agency, Corvallis
Environmental Research Laboratory. Report No. EPA-660/3-75-033. 165 pp.
Uttormark, P.D. and M.L. Hutchins, 1978. Input/output models as decision cri-
teria for lake restoration. Tech. Rpt. WIS, WRC, 78-03, Water Res. Center,
Univ. of Wise., Madison, Wise. 62 pp.
Vollen^eider, R-.A., 1968. Scientific fundamentals of the eutrophication of
lakes and flowing waters, with particular reference to nitrogen and phosphorus
as factors in eutrophication. Organ. Econ. Coop. Dev., Paris. Technical Report
No. DA3/CSI/68.27. 159 PP.
Vollenvreider, R.A. and P.J. Dillon, 197^. The application of phosphorus loading
concept to eutrophication research. Tech. Rep. 13690, k2 pp. Nat. Res. Counc.
of Can., Ottawa, Ont.
Vollenveider, R.A., 1975- Input-output models with special reference to the
phosphorus loading concept in limnology. Schweiz. Z. Hydrol. 37:53-83.
Vollenveider, R.A., 1976. Advances in defining critical loading levels for
phosphorus in lake eutrophication. Mem. 1st. Ital. Idrobiol. 33:53-83.
<2 ~/T/

-------
Hydroscience, 1977b National assessment of water quality. Pre-
pared for National Commission on Water Quality. Washington,' D.C.
Bartsch, A.F. and J.H. Gakstatter, 1978. Management decisions
for lake systems on a survey of trophic status, limiting nutrients,
and nutrient landings in American-Soviet Symposium on Use of
Mathematical Models to Optimize Water Quality Management, 1975,
EPA-600/9-78-024, ERL, ORD, USEPA Gulf Breeze, Florida 32561,
pp. 372-394.
Eisenreich, S.J. et al., 1977. Atmospheric loading of phosphorus
and other chemicals to Lake Michigan. J.Grt. Lakes Research, Inter.
Assoc. Great Lakes Research, Vol. 3, No. 3-4, pp. 291-304.
Gakstatter, J.H. et al., 1978. A survey of phosphorus and nitrogen
levels in treated municipal wastewater. JWPCF, Vol. 50, pp. 718-722.
Hydroscience, Inc., 1977 a. The effects of forest management on the
water quality and aquatic .biota of Apalachicola Bay, Florida. Pre-
pared for the Buckeye Cellulose Corp., Perry, Florida, 6 Chap. +
4 Append.
International Joint Commission, 1978. Environmental management
strategy for the Great Lakes system. Final Report of Int. Ref.
Group on Great Lakes Pollution from Land Use Activities; Windsor,
Ontario. 115 pp.
Thoraann, R.V. , 1972. Systems Analysis and Water Quality Managemel.
McGraw-Hill Book Co., N.Y., N.Y. 286 pp.
Omernik, J.M., 1977. Non-point source-stream nutrient level
relationships: a nationwide study. EPA-600/3-77-105, Corvallis
ERL, ORD, USEPA, Corvallis, Oregon. 151 pp. + plates.
Steele, J.H. 1965. Notes on some theoretical problems in
production ecology in primary production in aquatic environments,
C.R. Goldman, Ed., Mem. Inst. Hydrobiology, University of Califor-
nia Press, Berkeley, California, p. 383-98.
Ryther, J.H., 1956. Photosynthesis in the ocean as a function of
light intensity. Limnology and Oceanography, No. 1, pp. 61-70.
Welch, E.B. and M.A. Perkins, 1979. Oxygen deficit-phosphorus
loading relation in lakes. Jour. WPCF. Vol. 51, No. 12, pp 2823-2828.
DiToro, D.M. et al., 1977. Estuarine phytoplankton biomass models-
verification analyses and preliminary applications. In The Sea:
Ideas and Observations on Progress in the Study of the Seas. Ed.
E.D. Goldberg, J. Wiley and Sons, N.Y., N.Y., pp. 969-1020.
DiToro, D.M., D.J. O'Connor and R.V. Thomann, 1971. A dynamic
model of the phytopiankton population in the Sacramento-San
Juaquin Delta. Advances in Chemistry, No. 106. American ChemicaJ
Society, pp. 131-180.


-------
Eppley, R.W. 1972. Temperature and phytoplankton growth in
the sea. Fishery Bulletin. Vol. 70, No. 4, pp. 1063-1085.
Thomann, R.V., R.P. Winfield and D.M. DiToro, 1974. Modeling
of phytoplankton in Lake Ontario (IFYGL) Inter. Assoc. Great
Lakes Research, Proceedings 17th Conference, pp. 135-149.
Fillos, J. and W.R. Swanson, 1975. The release rate of nutrients
from river and lake sediments. Jour. WPCR, Vol. 47, No. 5,
pp. 1032-1042.
DiToro, D.M. and J.P. Connolly, 1980. Mathematical models of
water quality in large lakes. Part 2: Lake Erie. In Press,
U.S. EPA, Duluth, Minn., Grosse lie Lab., Grosse lie, Michigan.
Bannerman, et al., 1975. Phosphorus uptake and release by Lake
Ontario sediments. EPA-660/3-75-006, NERC, ORD, U.S.EPA,
Corvallis, Oregon, 51 pp.
Freedman, P.L. and R.P. Canale, 1977. Nutrient release from
anaerobic sediments. Jour. Env. Eng. Div., ASCE, Vol. 103,
No. EE2, pp. 233-244.
Martens, C.S. et al., 1980. Sediment-water chemical exchange
in the coastal zone traced by in situ Random-222 flux measure-
ments. Science, Vol. 208, pp. 285-288.
Hartwig, E.O. 1975. The impact of nitrogen and phosphorus re-
lease from a siliceous sediment on the overlying water. Third
Int. Estuarine Conf., Galveston, Texas. Paper No. COO-3279-20, 33 p,
Rast, W. and G.F. L-e. 1977. Report on nutrient load-eutrophication
response of Lake Wingia, Wisconsin. In North American project -
a study of U.S. water bodies, L. Seyb and K. Randolph, U.S. EPA
Env. Res. Lab., Corvallis, Oregon, pp. 337-372.
DiToro, D.M. and J.P. Connolly. 1980. Mathematical models of
water quality in large lakes, Part 2: Lake Erie. EPA-600/3-80-
065, ERL, ORD, U.S. EPA, Duluth, Minn. 231 pp.
DiToro, D.M. and W.F. Matystik, Jr. 1980. Mathematical models of
water quality in large lakes, Part 1: Lake Huron and Saginaw Bay.
EPA-600/3-80-056, ERL, ORD, U.S. EPA, Duluth, Minn., 166 p.
Burns, N.M. and F. Rosa, 1980. In situ measurement of the settling
velocity of organic carbon particles and 10 species of phytoplankton,
Limnology & Oceanography 25 ( 5) : 855-864 .
Rast, W. and G. Fred Lee, 1978. Summary analysis of the North
American (U.S. portion) OECD eutrophication project: nutrient
loading-lake response relationships and trophic state indices.
U.S. EPA, EPA-600/3-78-008, ORD, Corvallis, Oregon, 455 pp.
- / i"" 3

-------
Bachmann, R.W. and D.E. Canfield, Jr. 1979. Role of sedimenta-
tion in the phosphorus budget of natural and artificial Iowa
lakes. Project A-063-IA, Iowa State University, Ames, Iowa,
95 pp.
Higgirvs, J.M. and B.R. Kim, 1981. Phosphorus retention models
for Tennessee Valley Authority reservoirs. Water Res. Res.17(3):
571-576.


-------
Waif *of* Voi 14 pp 16)1 to 1663
C Perpmon Ptcm Ltd IW> Pnntcd in Grcal Bnuift
004 j. i is*.*)' i ioi  i o* i Mionr.
A Steady State Eutrophication Model for Lakes
Jerald L. Schnoor1 and Donald J. O'Connor2
lC>vil and Environmental Engineering. The University of Iowa, Iowa City, IA 52242 and
'Environmental Engineering and Science, Manhattan College, Bronx, NY 10471, U.S-A.
(Received May 1980)
INTRODUCTION
The nutrient loading models of Vollenweider (1968,
1969) and Dillon & Rigler (1974) have been used
with success to assess the trophic state of lakes. How-
ever, these models do not quantitatively relate
nutrient concentrations to phytoplankton concen-
trations, a primary concern in water quality manage-
ment More extensive nutrient-phytoplankton models
have been developed which are time and space vari-
able, but also considerably more expensive to utilize
(O'Connor, 1973; Thomann et at, 1975; Di Toro &
ConnoDy, 1979).
In this paper, an alternate approach to eutrophica-
tion modeling is developed via simplifying assump-
tions of the kinetic and transport equations. Both
steady state and non-steady state cases are investi-
gated for a Aort detention time reservoir in Central
Texas, Lake Lyndon B. Johnson (LBJ) and a long
detention time Great Lake, Lake Ontario. Hie steady
cute solution to 81 of the phosphorus limited lakes of
the U.S. National Eutrophication Survey (NES) is
also disnHvd The steady state approach is useful as
a management tool when detailed analyses are not
feasible.
MODEL DEVELOPMENT
A schematic of phytoplankton kinetics is presented in
Fig. 1. Inorganic nutrient is-input by natural and man-
made sources, W,. and is formed by mineralization of or-
ganic nitrogen, JC* It is diminished by washout, 1/r, and
by phytoplankton uptake, Kr via Lotka-Volterra (1956)
kinetics. The phytoplankton-undergo washout and losses
to form organic nutrient via Kt. Phytoplankton also sink
out of the water column at a rate, Kr Organic nutrient is
present due to natural and man-made sources, Wt, as well
as from phytoplankton decay. Particulate organic nutrient
undergoes sedimentation, K, and total organic nutrient
mineralizes with rate constant Ko- If inorganic nutrient is
returned from the sediment, that input must be externally
supplied by Wj.
Only one nutrient is considered limiting to growth, but it
is straightforward to consider others as welL Zooplankton
grazing is immtrrl to be included in the phytoplankton
low rate, #Ct, which converts viable phytoplankton to or-
ganic nutrient
A significant simplification is affected when the system is
considered to be composed of two or more compartments
(e.g. the epilimnion and the hypolimnion or the euphotic
and non-euphotic zones) each of which is assumed to be
completely mixed. In essence, the completely mixed model
represents a spatially averaged concentration within each
compartment Completely mixed compartments are inter-
related via bulk dispersion or an exchange coefficient as by
Imboden (1974).
A further simplification is facilitated if the entire im-
poundment can be considered as a completely mixed sys-
tem or if only the epilimnion is simulated with internal
inputs from the hypo titration. Impoundments of short
detention time (large densimetric Froude number) can
often be considered as completely mixed. Again the simpli-
fication represents a spatial averaging with depth, and the
following equations result
dNi	N, W,
- JCoATo - K,N,P	-+ 
dt	x v
dP P
 - K,N,P -KXP	KJP
Ol	T
(1)
(2)
K,P- JC0No - Jt.No -  +-?T P)
dl	T Y
where
Nt  inorganic nutrient concentration, ML"1
P  phytoplankton nutrient concentration, ML"3
No  organic nutrient concentration, ML" 3
t  mean hydraulic detention time, T
Wt  input rate of inorganic nutrient, MT~1
Ifj  input rate or organic nutrient, MT~1
V  impoundment volume, L\
The addition of equations (l)-(3) yields:
Nt kn WW)
 - K,N9 + 
^1- -1L - K.N0 + ^ - K.P
Of
(4)
where
Nr- N,+ P + N0
dNT _ dN, df dWo
dl ~ d/ + di + dt
WT - Wx + W,
Ws
1
1
Wx 1/r

Nlnorv

Phyio

n,


T

Fig. 1. Kinetics and transport,of nutrient-phytoplankton
system.
<2-/6T

-------
Jerald L Schnoor and Donald J. O'Connor
Noie thai the build up of total nutrient concentration in an
impoundment is determined by only three factors: the
addition of nutrients WT/V. the washout of ouuients Nt/t,
and the net loss of nutrient to the sediment KJ,N0 + P). It
is the kinetic coefficients which determine the partitioning
of the nutrient among inorganic, organic, or planktonic
mass.
Assuming neady state for equations (IH3). the three
nonlinear, ordinary differential equations become a set of
algebraic equations that are easily solvable:
N, -
*, + (1/t) + K,
p_ atN.-N,)+ (*,*<>/*)
- K0)
No -
/> + (N,/tK,)
where
*o + K, + (1/t)
K.
W2 r
N,  ~  average inflow organic nutrient
concentration
N. -
W.t
V
 average inflow inorganic nutrient
concentration
The resulting equations comprise an analytical model
that is easily applied to impoundment situations. It is not
developed empirically, and thus it is applicable to im-
poundments of varying geomorphology and locality. The
principal disadvantage of the model is the need to estimate
the various rate constants required.
It > interesting to note that equations (5H7) are consis-
tent with the Dillon & Rigler (1974) model. Summing the
equations and assuming steady state, one arrives at equa-
(3) after rearranging.
+ Wj, the total nutrient input, MT"1.
surface area, L1.
/  ("o + PVNj, fraction of phytoplankton plus or-
ganic nutrient to total nutrient
NT  P + No + Nk total nutrient concentration, ML"'
H  mean depth, L.
Upon inspection, the term //C,NT<4H/^ is the fraction
of phosphorus retained in the sediment. R. Therefore,
equation (8) is an analytical development of the Dillon and
Rigler plot, log W^r(l  R)/A vs log H. The model equa-
_bons UH3). from which equation (8) is derived, have the
added advantage that they explicitly involve the phyto-
plankton as wdl as nutrient concentration.
ESTIMATION OF COEFFICIENTS
Field data such as those gathered in the U.& National
Eutrophkation Survey may be used to establish average
annual or seasonal concentrations of nutrients in lakes.
For the initancm where reasonable measurements of Nh P,
and N0 are available, it is possible to estimate the kinetic
coefficients. Equations (IH3) contain three state variables
(Nh P, N0) and four coefficients (Kr K K0\ or three
equations with four unknowns. Assuming that K, can be
calculated from productivity measurements or estimated
from similar prototype systems, equations (IH3) were
solved for Kt. Kr K.
(5)
(6)
(7)
K, - K,N, -I - K.
(9)
(10)
<")
Equation (9) states that under steady state conditions,
the gross growth rate minus the washout and sinking rate
is equal to the total loss rate of phytoplankton. X,. Equa-
tion (10) shows that the mass rate of sedimentation,
K(No + PI is equal to the mass rate of total nutrient
input minus outflow. The mass rate of nutrient recycled.
XoNo, increases with primary production (KfltP) and de-
creases with the inorganic input minus the outflow of in-
organic nutrient according to equation (11).
In addition to "back-calculating" the rate constants, it is
possible to determine a range for these constants from field
and laboratory studies. The autocatalytic growth rate con-
stant, Kr can be calculated from light and dark bottle C-14
primary production measurements. Primary production is
equal to K. * N, * P multiplied times a conversion factor
for carbon to phosphorus (40gCg"'.P) and divided by
the photoperiod in hours. For Lake LBJ, the predicted
productivity was 3.0mgCm~' which compared favorably
with depth-integrated primary production field data of
Davenport (1975).
CALIBRATION OF MODEL FOR LAKE LBJ, 1972
1		
. 20.00
10.00
I T97f FliLO OATA l lgTA*O*M0OtVUriO*
 uoott *tsot rs
j'f'm'a'm'j'j'a's'o'n'd
120

-------
A steady state eutrophication model for lakes
The death rate constant, JCt. is actually the sum of the
endogenous decay and predation rales on phytoplankton
Endogenous decay rates of phytoplankton in the dark were
reported as 0.05-0.20 per day by Riley el al (1949) and as
high as (k25 per day for Chlortlla at 3S*C by Sorokin
(1959). Total loss rates of phytoplankton were measured in
Castle Lake by Jassby & Goldman (1974) to be 0.2-0.8 per
day, but this figure includes linking rates.
Literature values for sinking rates, rr of freshwater phy-
toplankton' by Smayda (1974) ranged from (126 to
0.76mdaywhile Tilham & Kilham (1976) reported
0.08-1.87mday"1. Organic matter is the ocean sinks at
0.1813 mday"1 according to McCave (1975). Organic and
phytoplankton sinking velocities must be divided by the
mean depth of the water body to yield the sedimentation
coefficient, Kr It should be noted that the organic sinking
rate coefficient, Km is truly an "effective'* or "apparent"
linking rate since only the particulate fraction would sink
of the total (dissolved + particulate) organic nutrient
present Effective sinking rates or loss rates for total phos-
phorus in lakes have been reported by Chapra (1975) and
others and average 0.1 mday'1 with a range of
0-0.4	mday"1.
Perhaps the least is known about the hydrolysis or
mineralization rate constant, K&. Verhoff & Heffner (1979)
measured K0 to be less than 0.004 per day for three U.&
river waters, while calculations of data by Richey tt aL
(197S) indicate a range of 0.0005-0.11 per day for carbon in
four freshwater lakes. The mathematical models of Tho-
mann (personal correspondence, 1979) and Di Toro &
Connolly (1979) are currently utilizing a Km for phosphorus
of approx. 0.03 per day at 20C in the Great Lakes.
RESULTS AND DISCUSSION
Lake Lyndon B. Johnson
Lake Lyndon B. Johnson (LBJ) is the third of a
series of seven impoundments in the Highland Lakes
chain of Central Texas. It is a mainstream impound-
ment of the Colorado River containing a volume of
1-71	x 10* m1 and a mean depth of 6.7 m. With an
annual average hydraulic detention time of approx. 80
days, it receives no significant wastewater loads but is
dasriffod as eutrophic according to most classification
criteria. Summertime anaerobic conditions do occur
in the hypolimnion of Lake LBJ (Schnoor & Fruh,
1979).
Equations (1M3) were utilized to simulate Lake
LBJ for 1972 and 1973. The euphotic zone of Lake
LBJ occupies greater than 50% of the total volume,
and the model assumption of complete mixing is quite
reasonable over much of the year. The sinking rate of
phytoplankton- was assumed to be negligible relative
to the death rate. Results for the 1972 calibration of
the model are given in Fig. 2. Molybdate reactive
phosphorus (inorganic) and organic phosphorus field
measurements are plotted as vertically averaged con-
centrations. Phytoplankton phosphorus was calcu-
lated from 1972 specie counts and biovolumes per
specie determined by Davenport (1975) during
1973-1974. Phosphorus content of the cell was
assumed to be 1% by dry weight and dry weight was
assumed as 25% of wet weight as per Stumm & Mor-
gan (1970) and Parsons & Takahashi (1973). Error
bars plotted on the data points in Fig. 2 refer to
 1 SD due to spatial variations in measurement
An interesting feature of the calibration in Fig. 2 is
that three of the four model coefficients were held
constant while only the hydrolysis (mineralization)
rate was allowed to vary in a sinusoidal pattern with
temperature. Better fits to the data could have been
achieved with time variable coefficients, but the goal
of this modeling effort was to simplify to as great a
degree as possible. As it is, the general agreement
between model results and measured data shown in
Fig. 2 demonstrates that a simple model can begin to
approximate complex lake dynamics.
A verification of the model was performed by hold-
ing all coefficients constant for another simulation,
1973, an independent data set Results are presented
in Fig. 3. The data of 1973 is a particularly stringent
test for the model since hydraulic and nutrient inflows
were considerably different than in 1972, especially
following a 100 yr recurrence-interval storm which
occurred in October, 1973. Again, the model results
compare favorably to the measured data through Sep-
tember, but during October the growth rate was
nearly extinguished by the effect of a tremendous
amount of debris which carried into the lake: the-sec-
chi disc depth was approx. 2 in, and much of the
surface was covered with floatables. It was necessary
to decrease K, to a fraction of its original value dur-
ing and after the storm, 0.0061 pg~ '-day. Still organic
P does not match the measured data very well during
the last 3 months (Fig. 3). Probably the inflow of
organic phosphorus to the lake was grossly undercsti-
VERIFICATION OF MODEL FOR LAKE LBJ. 1973
uijf 80.00
>3
40.00
"J
uo

-------
Jerald L. Schnook and Donald J. O'Connor
mated, since sampling was too infrequent to accu-
rately gauge the amount of nutrient inflow during
the storm. Secondly, internal scour of organic phos-
phorus from the sediment was not measured.
It is interesting to note that the predicted phyto-
plankton concentration approaches zero during the
1973 storm, day 300. A neighborhood stability
analysis was performed on equations (1H3). It
yields the required conditions necessary to keep the
model numerically stable. The washout condition,
I/t < (N,X,  Ki). was violated in the model during
the storm event which resulted in a near-zero phyto-
plankton standing crop. The measured phytoplankton
standing crop also became near-zero, but nature has
nonlinear mechanisms for keeping systems stable that
are not always included in models (e.g. sheltering,
migration, dispersal, predator-prey switching etc.).
Some advantages of this simplified cutrophication
model for Lake LBJ as compared to the nutrient
loading models of Vollenweider (1969) and Dillon &
Rigler (1974) include: the capability of separating the
effects of organic nutrient inputs from inorganic
inputs (bioavailability), the calculation of nonsteady
state blooms and periodicities, the direct determi-
nation of phytoplankton standing crop, and a better
understanding of the nutrient flux rates via phyto
growth and death, organic nutrient hydrolysis and
sedimentation.
Equations (5H7) are the steady state approxi-
mations of equations (1H3). They may be thought of
as time averages through the year. For Lake LBJ in
1972, the solution of equations (5H7) yields the yearly
average phosphorus concentrations:
inorganic P  9122 pgl"1
phytoplankton P = 1.47/igl-1
organic P  27.7 1"1
As can be seen from Fig. Z these values do indeed
approximate time-averages of the dynamic solution.
The calculated steady state 1973 Lake I Bt concen-
trations (excluding the heavy storm period of October
to December) are:
inorganic P  9-23 pg 1 ~1
phytoplankton P = 1.37/igl-1
organic P = 295 fig l-1
Summer and winter steady-state averages were also
=oximated for Lake LBJ in 1972 and 1973. Since
the original time variable model (equations 1-3) is
n-miiiicar, the steady state solution utilizing time*
coefficients will not precisely equal the time
average of the dynamic solution, but it does provide a
reasonable approximation.
Lake Ontario
Equations (1H3) were also applied	to Lake
Ontario, a Laurentian Great Lake with a	detention
time of approximately eight years. In this	both
diatom and non-diatom populations were simulated
since two distinct peaks in abundance have been
noted, Glooschenko et aL (1974). Only the epilimnion
(the top 17 m) was simulated because below that
depth, the hypoiimnion lacks a viable phytoplankton
population. Nutrient flux from the hypoiimnion to
the epilimnion was externally specified as input data.
The results of the Lake Ontario simulation are
given in Fig. 4. Data are from 1967 to 1973 monitor-
ing cruises by the Canada Centre for Inland Waters.
Chlorophyll a rather than phytoplankton biovolumes
were measured on the cruises, so a conversion factor
for phytoplankton phosphorus to chlorophyll of 1:1
was assumed. [A check was made with biovolumes
from Munawar & Nauwerck (1971) which supported
the assumption.]
Note the agreement between observed data and
computed results. The time-averaged coefficients
used in the simulation were: K, - 0.034 day"l,
K,  0.0059 day"1, K, - 0.00351 pg"'-,
was input as a sinusoidal function which approxi-
mately tracked temperature periodicity (see Fig. 5).
Phosphorus inflows of 35,000 kg day"1 were taken
 IM7-79 FIELD DATA, X 11*
i ii ff
9 Q jo
J'F'M'A'm'J'J'a'S'O'nIO
j'f'm'a'm'j'j'a's'o'n'o'
12

**20
Ro" ^2 - doy-1

Kf  -OOSSl/zfl-doy-'

R |  .03 4 -dojr-'

Rt  J00588-doy-i

.
 ANon-
Ototomy"\^
f ^ diatom
V
j'r'M'A'M'j'j'A1 S'O'n'O
52
1
O a
i/i
10
j'f'm'a'm'j'j'a's'o'n"
Fig. 4. Lake Ontario simulation with two phytoplankton
taxa.
=? - / A"?

-------
A steady stale eutrophication model for lakes
.03
o .02
* .01
.00
>. .0100
"f .0075
^ .0050
~ .0025
**.0000
0.16
"*>. 0.12
o q.08
2 a 04
0.00
_ .006
 .006
\ .004
* .002
.000
j'f'm'a'v'j'j'a's'o'n'o
_  Diatom



n
. Non-

i !
diotom

_j J
i
i


1	
. Diatom
. ---Non-
diatom

n

t 1
1 1
! j
-


J'f'm'a'm'J
J A
s'o lN 'o
j'f'm'a'm'j'j'a's'o'n'.o
Fig. S. Rate constants used in the Lake Ontario
simulation.
from Thomann et aL (1975) including an internal
nutrient flux of 105,000 kg day"1 from the hypolim-
r-aion to the epilinmicHi during the unstable months of
September and October and a smaller flux of
35,000 kg day "1 during January through May. The
September-October flux helps to support the second
peak in phytoplankton chlorophyll, and is trans-
ported from the hypolimnion through the thermocline
by turbulent diffusion. A two layer model, including
the hypolimnion as well as the epilimnion, would
have allowed calculation of this flux rather than
accounting for it as a specified input. It should be
added that the double phytoplankton peak consis-
tently appears in chlorophyll measurements of Lake
Ontario, but the community biovolume measure-
ments of Munawar & Nauwerck (1971) did not indi-
cate the first peak and die-oft
Peak diatom concentrations occurred on or about
July 1 and declined due to an increasing death rate.
The decrease in net production by diatoms may have
been exacerbated by silica limitation at that time of
year. The peak non-diatom population (blue-green
algae, green algae, and phytoflagellates) occurred on
October 1 and declined similarly. Inorganic phos-
phoruj concentrations predicted by the model did not
decline as low in the summertime as has been
observed in field data, possibly due to an erroneously
high" hydrolysis rate constant or due to excessive
phosphorus inputs specified from the hypolimnion.
Organic phosphorus field data was sparse and diffi-
cult to use to draw conclusions. The steady state solu-
tion using time-averaged coefficients. Equations
(5H7X yielded annual mean concentrations of
9.8 jig PI'1 for reactive phosphorus, 3.6 /ig 1 ~1
chlorophyll a, and SJjigl"1 organic phosphorus.
This steady state model could prove very useful as a
management tool for predicting improvements in
water quality as a function of mandate effluent con-
trol.
National eutrophication survey lakes
Shown in Table 1 is the phosphorus nutrient data
from the USEPA National Eutrophication Survey
(1975) of northeastern and north-central United
States Lakes. Only those lakes which were phos-
phorus limited for at least one'sampling period are
listed. Phosphorus limitation is taken to be an in-
organic nitrogen to dissolved phosphorus ratio of
greater than 14:1 and/or a phosphorus limitation in
an algal assay performed in connection with NES.
The column marked PHYTO P is estimated from the
ratio of phytoplankton phosphorus (that phosphorus
associated with phytoplankton) to measured chloro-
phyll a of 0.4 to 1.0. This ratio has not been widely
disnissfd in the literature. However percentages of
phosphorus to algal biomass (dry weight) are nor-
mally (15-3.0 according to Parsons & Takahashi
(1973X while chlorophyll a to algal dry weight bio-
mass range from OJ to 3.0% in Lakes Onondaga
(Murphy & Welter, 1976), LBJ, Erie (Munawar &
Munawar, 1976) and Ontario (Glooschenko et al,
1974). Epply et al. (1977) found that phytoplankton
carbon to chlorophyll ratios fall between 10-100.
These ratios are quite variable, both from lake to lake
.and seasonally, but an average of l.Opgl'1 chloro-
phyll a per pgl~* phytoplankton phosphorus is
typical Organic phosphorus (excluding phytoplank-
ton phosphorus) in Table 1 is calculated as the total
minus the dissolved and phytoplankton phosphorus.
Dissolved phosphorus is the molybdate-reactive phos-
phorus which passes a 0.45 micron Millipore filter.
If the sedimentation coefficient, Km and the nutrient
loading determine the total phosphorus in a lake or
reservoir, then it is the kinetic coefficients Kr K,, and
K0 which determine the nutrient partitioning.
Figure 6 illustrates the phosphorus partitioning in the
NES P-limited lakes. The shaded area of Fig. 6 shows
the region where oligotrophic lakes fall. Oligotrophy
lakes have a small percentage of organic phosphorus
(0-20%), moderate percentages of phosphorus tied up
in phytoplankton (1840%), and large dissolved phos-
phorus fractions (55-80%). Other lakes are described
according to their region on the partition diagram of
Fig. 6.
1 -/?

-------
Nutrient Data fr<
JO
I
o
LAKE
1	LAKE E0AR
2	LIU! HON AH
3	HOUSATONIC
4	LONG
5	MATTAUAMKEAC
6	MOOSEHEAD
7	RANCELEY
6	SEBAGO
9	BAY Of NAPLES
10	HACER POND
11	HARRIS POHD
12	LAKE ALLECAH
1)	BARTON
14	BFLLEV1LLE
13	CHARLEVOIX
16	CHEHUNC
17	PORD
18	JORDAN
19	HACATAUA
20	ROSS RE$.
21	THORNAPPLE
22	UNION
2)	CRYSTAL
24	HIGCINS
2)	HOUCHTON
TROPHIC
STATUS
E
E
E
H
M
0
0
O
0
STATE
CONN
CONN
CONN
MAINE
MAINE
MAINE
MAINE
MAINE
MAINE
MASS
MASS
MICH
MICH
HICH
HICH
MICH
MICH
MICH
MICH
MtCI!
MICH
MICH
MICH
MICH
MICH
t. day
S
17
0.6
4)8
42
1100
1020
1970
26
24
6.2
7
61
2)
1170
mo
IS
304
77
2
11
2
1200
5690
475
Hi
DISS P
462
23
M
31
60
4
11
63
138
68
20
28
22
7
4
6
Tib. ) I
National EutropHlcatton lurvtf
TOT P
p/ _
i
54
39
8
11
1
7
4
1
i)
a
115
121
t
52
111
171
159
)5
4}
47
9
6
It
Chi a
!/ .
It.)
11.1
8.1
3.2
2.0
I.)
2.4
1.)
i.a
198.3
12.9
20.)
27.8
28.)
).0
1J.0
1S.0
20.}
23.6
10.4
14.7
15.7
2.9
1.0
9.2
EST. r
PHTTO r
11.9
).t
8.2
1.6
1.0
1.0
U6
0.98
1.1
198.)
11.9
10.)
17.8
18.)
1.9)
1).0
15.0
10.)
15.6
10.4
14.7
15.7
1.89
0.6)
6.0
1ST.
o
ORG r
M8/*
1.1
0.4
1.8
0.4
1.0
1.0
0.4
0.01
0.8
84)
16
54
1.1
)4.0
0.05
6.0
)).0
13.0
65.0
5.0
1.)
9.)
0.11
1.))
1.0

VOL
Jfl
1.96'
9.15
).86
1.05
4.99
5
3.47
). 59
1.32
1.)
8.64
1.18
8. )4
3.14
1.17
1.06
1.87
1.17
TOT f LOAD
fc/T
H
MLAM
DEPTH
1.66"10
1.79
7.14
1.91
1.1)
). 79
1.87
1)4.7
12).)
118.1
2.7
7.9
1.1
9.2
1.)
1).0
).
101.)
J.O
80,9
.5
1
68.6
1.9
45,70
10.1
15.1
19,6
10
1,0
4.8
10.
)0.

-------
I
N
26	THOMPSON
27	ZUHBftO
20	ST. CROIX
29	rOREST
30	GREEN
31	ANDROSIA
32	BADGER
33	BARTLETT
34	BLACKHOFP
35	CASS
36	EMBARRASS
37	LEECH
38	HADI SON
39	KALMCDAL
40	H1NNET0NKA
41	HINNEUASKA
41	PELICAN
43	SUPERIOR
44	SWAN
43	POVDERHILL POND
46	VINNIPE SAUKEE
47	KELLT PALLS
48	CLEN LAKE
49	CANADICUA
30	CANHONSVILLE RES.
91	CARRTPALLS RES.
32	CASSADACA
53	CATUCA
34	CROSS
HICH
HINN
HINN
HINN
HINN
HINN
HINN
HINN
HINN
HINN
HINN
HINN
HINN
HINN
HINN
HINN
HfKN
HINN
HINN
N.H.
N.H.
N.H.
N.H.
N.T.
N.T.
N.T.
N.T.
N.T.
N.T.
152
IB
23
2080
1330
47
108
694
237
313
22
1900
1200
475
5480
4640
1200
8
876
6.5
1460
1.5
3
5480
210
38
180
4090
t
23
330
36
10
9
10
13
28
24
9
13
9
20
30
18
17
11
 44
9
16
4
13
15
5
22
C
II
8
42
41
11.0
11.0
4.0
1.86"10*
431
<01
11. J
11. J
39.0
3.09"10
103,673
S3
10.1
10.1
9.0
1.91-10*
193,347
11
10.1
6.8}
4.18
l.lfrio'
1,016
1}
4.9
4.9
t.l
1.4"10*
1,036
25.
11.0
13.0
1.0
4.83lo'
14.349
II
1.1
1.1
7.0
1.71-10*
907
lit
49.3
49.3
38.0
3.10-10*
'438
4]
11.a
11.8
6.0
3.16-10*
901
10
8.7
8.7
3.0
4.8-108
11,117
13
4.9
4.9
7.0
3.33-10*
3,301
1)
6.1
4.0
1.0
1.13109
17,964
50
)0.8
10.0
10.0
1.8-107
1,601
11)
41.0
41.0
34.0
1.41-10*
118
;
16.6
16.6
11.0
4.04-10*
	
33
7.6
7.6
10.4
1.73-10*
4,136

11.4
11.4
9.6
1.06108
1,317
79
6.1
6.1
19.0
S.SSMO'
333,031
11
1.8
1.3
1.3
1.18-10*
4.973
]]
6.1
6.1
11.0
3.78-10*
4,683
t
1.1
1.4
0.6
1.41-108
11,317
1*
7.0
7.0
1.0
1.10-10*
13,010
18
1.8
3.8*
9.1
1.07-10*
8,013
9
4.1
1.8
1.1
I.68-I0'
6,041
46
)0.0
19.3
4.3
3.73-I08
81,780
10
3.1
3.1
1.0
I.4I-108
18,639
It
9.7
9.7
3.)
4.67-10*
680
1*
1.1
3.1
1.8
9.39-10*
84,086
76
19.1
19.3
13.0
4.83-lo'
193,110

-------
LAKE
TROPHIC
STATUS
I
-N.
33	REUKA
36	SARATOGA
57	SACANDAGA
38	SCHROON
39	SENECA
60	SV1NCING BRIDGE ACS.
61	CONESUS
62	LOWER ST. REGIS
6)	SLATTERSVILLE RS.
64	CHAMPLAIN
63	CLYDE POND
66	HARRIKAN ICS.
67	LAMOILLE
66	ARROWHEAD
69	UATERBURY IES.
70	TROUT
71	LAU CLAIRE
72	OCONOHOUOC
7)	SHAWANO
74	TAINTER
73	WaPOCASSCT
76	UAUSAU
77	WISCONSIN
78	CENEVA
79	COMO
60	BIG EAi;PUIN> RIS.
81	GRAND
HE - hypcrcutrophlc
E - cutrophic
VT
VI
VI
VI
VI
VI
VI
VI
VI
VI
VI
VI
VI
2830
130
166
133
12)00
92
621
110
3
949
3.6
78
1
1.5
8)
10
209
348
10
194
2
4
10600
401
138
11
HJ
DISS P
_ng/g
3
16
6
1
6
20
1)
8
11
10
6
7
10
9
4
3
38
7
8
81
13
31
J7
6
12
30
130
H - otrophlc
0 - oltgotrophtc
Tahlr I
(cent'd)
TOT F
Chi
PR/>
EST. P
PHYTO P
in/>
EST.
Ho
ORC P
hi/JL
V
VOj,
8
3.7
2.83
0.13
1.07-10
23
11.8
7.7
1.)
1.29-10*
9
4.8
2.4
0.6
9.27-10*
4
2.1
0.9
0.1
2.39-10
10
6.1
3.03
0.93
1.36-10IC
37
28.7
28.7
8.)
4.63-10
20
9.9
6.4
0.6
1.13-10
17
7.9
7.9
1.1
9.34-I06
32
8.1
8.1
13.0
2.02*10
18
11.1
7.2
0.8
2.I9-I01'
21
7.3
7.3
7.3
1.94-10
9
I.I
1.8
0.2
9.19-10*
18
3.3
3.3
4.3
I.03-104
13
8.3
3.3
0.3
1.04-10
7
3.2
2.6
0.4
4.37-10*
9
2.7

1.3
1.8-10
89
19.6
19.6
31.0
1.04-10*
12
).l
3.1
1.9
).03-10*
70
11.9
7.7
4.3
7.97-10*
111
11.7
13.7
16.0
2.81-107
4)
16.6
16.6
11.0
2.54-10
59
3.0
3.0
21.0
1.71-10*
58
31.4
20.6
0.4
6.48-10
13
3.8
3.8
4.2
3.96-10
48
16.4
23.6
12.3
4.98-10
71
33.3
13.3
3.3
i. n-io
190
63.1
J).0
7.0
1.14-10
TOT P LOAD
4,9)9
26,086
21.873
6,340
6.700
24.340
4,923
762
4,698
371,600
4.712
7,791
13.603
) 7.628
4,823
40,884
1,810
1)9,000
).4I3
220,438
347,868
41,116
8,118
H
lir.AN
DEPTH
22
7
7.
14.
88.
I).
8.
3.
2.
19.
).
10.
1.
).
12.
11.
2.
9.
).
4.
3.
2.
1.
18.
1.
4.
1 .

-------
A steady state euirophication model for lakes
INORG N,
VI
IV
PHYTO P
Fig. 6) Phosphorus partitioning diagram and groupings of lakes. Shaded area represents region of
oligotrophy lakes. Roman numerals group lakes of similar kinetic coefficients.
Region
Ihighly	eutrophic,
IIeu	trophic,
IIImesotrophic,	little eutrophic,
IVhighly	eutrophic,
Vlittle	eutrophic,
VIlittle eutrophic
In general there is a rough pattern of increasing
eutrophic tendency as the percentage of organic phos-
phorus increases. Each region on the diagram groups
lakes of roughly similar kinetic coefficients.
Figure 7 gives a plotting of the actual NES phos-
phorus limited lakes for the northeast and north-
Central United States. Considerable scatter exists
among the 81 lakes, which includes lakes of differing
geohydrologies, morphologies and nutrient loadings.
Figure 8 gives the percentage of each nutrient com-
ponent as a function of the total phosphorus for these
same lakes. The dashed lines of Fig. 8 appro*.  1 SD
in percentage. There is a tendency for the organic
fraction to increase as total phosphorus increases. The
percentage of phytoplankton phosphorus first in-
creases and then decreases while the dissolved frac-
tion displays the opposite trend. On the average, phy-
toplankton account for 25-30% of the total phos-
phorus present The wide scatter of data for lakes
with greater than iOOjtgl-1 total phosphorus in Fig.
8 indicates that lakes may operate quite differently in
the highly eutrophic state, either containing a large
INORG N:
100
*	OUGOTROPHIC
*	MESOTROPHIC
 EUTROPHIC
100	100
ORG N0	PHTTO P
Fig. 7. Phosphorus partitioning diagram for the NES phosphorus limited lakes.
A - /4 3

-------
Jerald L Schnoor and Donald J. O'Connor
90
00
70
60
50
40
30
20
.
i
i
\
i 60
90
I
I40
SO
I
:20
to
60
90
40
SO
to
10
DISSOLVED PHOSPHORUS
A  
 /
I I
-L.

9 7 20 90 ro 100 200 900
PMYTOPLANKTON PHOSPHORUS
  
V"' ' ' * . *.	.
^
_i_
S 7 10 20 SO 70 100 200 900
ORGANIC PHOSPHORUS 
 r ,
.f *i.  't
Fig.
9 7 10 20	90 70 CO 200 900
TOTAL PHOSPHORUS, fig I-'
8. Percentage of each phosphorus species vs total
phosphorus.
concentration of organic or else dissolved inorganic
phosphorus.
The method of Dillon & Rigler (1974) does not
relate phosphorus loading to chlorophyll or standing
crop. However, they suggest that their model could be
combined with a total phosphorus to chlorophyll a
correlation, yielding an estimate of standing crop di-
rectly. While the method is quite useful in predicting
total phosphorus levels in lakes, there is some uncer-
tainty (see Table 2). There is also uncertainty involved
in total phosphorus to chlorophyll correlations (cor-
relation coefficient = 0.78 for NES lakes, USEPA
(1974). Combining the two multiples the uncertainty.
Figure 9 shows the results of combining the two re-
lationships for selected phosphorus limited lakes from
the National Eutrophication Survey. The scatter of
data is to be expected, but Fig. 9 illustrates the diffi-
culty in utilizing-this approach for the prediction of
lake recovery in restoration projects. If the predicted
chlorophyll a is significantly less than that measured,
the calculation is in error and the project money
spent will not bring about the desired water quality
objective. A more detailed solution is warranted when
public money is being investigated for lake restora-
tions. The alternative approach suggested here
requires more information and survey data than that
of the nutrient loading models, but it also yields more
information.
The U.S. National Eutrophication Survey Data was
utilized to estimate the kinetic coefficients as given by
equations (9H11) for each lake. Unfortunately, or-
ganic and dissolved phosphorus loadings were not
separately measured, so it was necessary to divide the
total phosphorus loading between inorganic and or-
ganic loadings in proportion to the respective lake
concentrations. Phytoplankton growth coefficients,
Kr were initially assumed and the results of equations
(9H11) ranged from 0.010 to 0.0501 pg" '-day for Kr
0.05-0.50day"1 for /CIt 0.0-0.20day-1 for and
0.0-0.2 dayfor K0. Considerable scatter was evi-
dent in the data, but lakes within each region of Fig. 6
did display central tendencies.
CONCLUSIONS
The modeling approach developed herein has rela-
tive advantages over both the approaches of Vollen-
weider (1968, 1969) and Dillon & Rigler (1974) and
the more complex, multi-variable efforts of Thomann
et al. (1975). It has been shown that steady state sim-
plification of equations (1M3) is consistent with the
Dillon and Rigler method plus it yields estimates of
standing crop directly. The time variable form of the
equations was used successfully to simulate seasonal
variations in Lake LBJ and Lake Ontario.
A relative disadvantage of this approach compared
to the nutrient loading models is the need to estimate
coefficients. However, there are only four coefficients
(the sedimentation, hydrolysis, autocatalytic growth,
and death rate constants), and equations (9H11) can
aid in the initial estimation when coupled with gross
productivity measurements and field survey data.
The sedimentation rate constant controls the
amount of phosphorus lost to the deep sediment and
therefore the total phosphorus concentration in the
lake. It is the hydrolysis, growth and death rate con-
stants which determine the partitioning of nutrients
among the various organic, inorganic, and phyto-
plankton fractions. Among the lakes sampled in the
northeast and north-central United States, it was "3e^
termined that phytoplankton accounted for 10-40%
of the total phosphorus present, while dissolved P was
35-75% and organic 0-40% of the totaL In general,
there was a pattern of increasing eutrophic tendency
as the percentage of organic phosphorus increases.
Ranges on the rate constants for the 81 phosphorus
limited lakes of the U.S. National Eutrophication
Survey were estimated.
AcknowledgementsWe wish to thank the Modeling
Group. Phosphorus Management Strategies Task Force-of
the Great Lakes Research Advisory Board. International
Joint Commission for helpful discussions regarding eutro-
phication modeling, including: Drs Jim Falco," Walter Rast.


-------
Table II
Olllon i Kt|lar Phosphorus Modal Coablnad with NES Chlorophyll Correlation
LAKE
TROPHIC '
STATUS
STATE
t. days
L
*/"J-Yr
R
H

My*)
d/-1
TOT r*
PREDICTED
Pl/t
TOT f
HEASURED
ur/i
Chi 
-------
TROPHIC	L
LAKE STATUS	STATE	t. day	R/*-yr
THOMPSON	K	HICH	1)2	0.41
ZUHBRO	I	HINM	II	03.1
8T. CIOII	I	MIKM	2)	8.89
rORCST	I	HINN	2080	0.1I
CREEM	M	MINN	13)0	0.09
ANDROSU	t	HINN	47	4.02
BADGER	I	HINN	101	0.6)
BA1TLETT	K	HINN	694	0.)7
lUCKHOrr	K	HINN	2)7	1.22
CASS	B	HINN	31)	0.3)
EMBARRASS	E	HINN	22	1.71
LEECH	M	HINN	1900	0.04
KADI SON	B	HINN	1200	0.36
MALMEDAt	E	HINN	47)	0.2B
HINNEUASKA	B	MINN	4640	0.1)
PELICAN	H	tfINN.	1200	0.06
SUPERIOR	E	HINN	8	24.0
SUAN	H	HINN	676	0.47
POUDERMILL POND	E	N.H.	6.)	3.11
VIHNIPE SAUKE	0	N.H.	1460	0.12
KELLY TALLS	E	N.H.	1.)	28.8
CLEN LAKE	E	N.H.	3	13.1
CANADICUA	0	N.T.	)480	0.14
CANNONSVILL RES. B	N.T.	210	4.26
CARRYPALLS RES.	H	N.T.	38	0.71
Table
tl (cont'd)
1
H

t(l-)
1
/.
TOT r*
mEDlCTCD
M/l
TOT r
HEASUUD
im/
<0.0
1.7
0.169
62.6
41
o.t
>.J
1.30
416
330
o.n
6.6
0.373
42.6
33
<0.0
1.4
0.633
167
21
0.67
6.4
0.114
17.1
13
0.37
7.9
0.326
41.3
23
<0.0
1.1
0.166
133
22
0.57
1.6
0.301
116
136
0.84
4.4
0.137
31.1
43
0.63
7.6
0.111
14.6
20
<0.0
1.6
0.103
39.6
23
0.34
4.7
0.096
20.4
13
0.76
4.0
0.763
71.2
30
<0.0
1.6
0.364
202
123
0.10
6.0
0.191
31. a
33
0.46
1.4
0.107
44.6
32
0.39
i.a
0.216
36.S
79
0.79
ii.i
0.237
19.6
13
O.Oi
2. J
0.032
20.6
33
0.77
11.1
0.110
6.4
6
0.31
i.)
0.079
34.4
24
O.JJ
).4
0.073
21.3
26
0.6)
39.0
0.733
16.9
9
0.71
19.1
0.711
37.0
46
0.21
3.4
0.033
9.6
10
Chi d*
PREDICTED
hk/4
22.9
216
14.)
Chi
HEASU
83
5
14
67
47
10
4
1)
6
26
91
10
1)
20
)
6
2
11
6
)
12
2
12.
12.
10.
10.
4.
13.
2.
49.
12.
8.
4.
6.
30.
41
16
11
6
3
6
2
7
3
4
30
3

-------
J]
CAYUGA H
H.Y.
401
s*
CROSS E
N.Y.
7
33
UUKA 0
N.Y.
: t
It
SA1AT0CA 1
N.Y.
liO
37
SACANDACA N
N.Y.
166
3a
SCHROON 0
N.Y.
133
39
SENECA N
N.Y.
11100
60
5VINCIMC IRIDCE,
RES. 1
N.Y.
92
61
CONISUS E
N.Y.
611
61
LOVER IT. REC1S E
N.Y.
110
6)
SLATTERSVILLE RES. 1
R.I.
3
64
CHAMP LAM H
VT.
949
63
CLYDE rOHD E
VT.
1
66
HARRIKAN US. H
VT.
?a
t;
LAMOILLE E
T.
l
68
ARROMIEAD E
VT.
i
69
WATERBURY RES. H
VT.
BJ
71
EAUCLAIRE E
Wt.
10
71
(KAUANO E
Wl.
34a
74
TAtNTER E
UI.
10
73
WAfOGASSET E
HI.
194
76
WASAU E
UI.
2
77
WISCONSIN E
UI.
4
0
RIC EAU FLEINE
RES. 1
UI.
136
SI
CRAND E
UI.
11
kiLil,
tH
tot F prad
cttd
,OI10 ',.1.1  0 Mt ,o10 chl a - 1154
0.49
0.32
34.6
2 . i .
48.2
14
16
33.3
0.23
3.3
..H>
90.0
76
33
0.10
0.33
22.6
0.367
16.2
8
4
1.60
0.33
7.9
0.309
39.1
23
13
0.18
0.26
7.6
0.061
8.0
9
2
0.39
<0.0
14.3
0.163
11.4
4
3
0.38
0.80
88.7
2.36
28.9
10
9
7.07
0.39
13.4
0.731
34.6
37
19
0.38
0.31
8.9
0.278
31.2
20
10
0.41
0.11
3.1
0.110
21.6
17
6
3.39
0.17
2.4
0.064
27
32
8
0.31
0.48
It.4
0.684
33
18
11
8.27
0.13
1.4
0.06*
20.3
21
6
0.88
0.17
10.4
0.136
13
t
4
25.2
0.10
1.7
0.033
32
18
10
11.)
0.27
3.1
0.079
23
13
7
1.34
0.24
12.7
0.232
18
7
3
9.04
<0.0
2.1
0.248
108
89
4)
0.07
0.23
1.2
0.081
23.)
20
7
20.3
0.12
4.1
0.489
119
111
49
0.71
0.43
3.3
0.213
40.6
4)
1)
28.4
<0.0
2.2
0.136
70.9
39
26
13.2
0.03
1.8
0.138
87.8
38
34
1.49
0.24
4.8
0.490
102
71
40
8.37
0.16
1.2
0.217
181
190
. 80
L  Cot phosphorus loading
K  fraction o! phoaphorua retained
t  itan annual hydraulic detention tlM
H  scan depth

-------
Jerald L Schnook and Donald J. O'Connor
70
IT,
 5
>0
60
uj 50
40
so
30
o
20
41/ TS
'if V
T*
r
O
10
60
20
50
30
40
CHLOROPHYLL a PREDICTED
Fig. 9. Measured vs predicted chlorophyll for the Dillon & Rigler (1974) model combined with the NES
total phosphorus to chlorophyll correlation, USEPA (1974).
Frank VerhofT and Mr John MancinL The calculations of
Table 2 were provided by Mr Frank Murphy, Environ-
mental Engineering and Science Graduate Program, Man-
hattan College, Bronx, New York. The financial support of
the National Science Foundation and an NSF Postdoc-
toral Fellowship to Dr Schnoor is gratefully acknowl-
edged.
REFERENCES
Chapra S. C (1977) Total phosphorus model for the Great
Lakes. J. environ. Engn. Die. Am. Soc. civ. Ergrs 103,
147-161.
Davenport J. B. (1975) Phytoplankton succession and the
productivity of individual algae species in a central
Texas reservoir. M.S. Thesis. University of Texas, Austin,
TX_
Dillon P. J. & Rigler *F. H. (1974) A test of a simple
nutrient budget model predicting the phosphorus con-
centrations in lake water. J. Fish. Res. Bd Can. 31.
1771-78.
Di Toro D. M. & Connolly J. P. (1979) Mathematical
models of water quality in Urge lakes, Part 2: Lake Erie.
U.S. Environmental Protection Agency, in prr%y.
Washington, DC.
Eppley R. W, Harrison W. G_ Chisholm S. W. & Stewart
E. (1977) Particulate organic matter in surface waters off
southern California and its relationship to phytoplank-
ton. J. mar. Res. 35, 671-696.
Glooschenko W. A, Moore J. E^ M una war M. & Vollen-
wader R. A. (1974) Primary production in lakes Ontario
and Erie: a comparative study. J. Fish. Res. Bd Can. 31,
253-263.
Imbodea D. M. (1974) Phosphorus model of lake eutrophi-
cation. Limnol. Oceanogr. 297-304.
Jassby A. D. A Goldman C R. (1974) Loss rates from a
lake phytoplankton community. Limnol. Oceanogr. 19,
618-627.
Lotka A. J. (1956) Elements of Mathematical Biology.
Dover. New York.
McCave I. N. (1975) Vertical flux of particles in the ocean.
Deep-Sea Res. 22, 491-502.
Munawar M. & Nauwerck A. (1971) The composition and
horizontal distribution of phytoplankton in Lake
Ontario during the year 1970. Proc. Conf. Great Lakes
Res. 14, 69-78.
Munawar M. & Munawar L F. (1976) A lakewide study of
phytoplankton biomass and its species composition in
Lake Erie. J. Fish. Res. Bd Can. 33. 581-600.
Murphy C. B. Jr & Welter G. J. (1976) Indices of algal
biomass and primary production in Onondaga Lake.
National Conference of Environmental Engineering
Research Development and Design, ASCE En v. Eng.
Div Seattle, WA.
O'Connor D. J. (1973) Dynamic water quality forecasting
and management. U.S. Environmental Protection
Agency, EPA-660/3-73-009. Washington, DC
Parsons T. R. & Takahashi M. (1973) Biological Oceano-
. graphic Processes. Pergamon Press, New York.
Richey J. E-, Wissmar R. G, DeVol A. H_, Likens G. E,
Eaton J. S, Wetzel R. G Odum W. E, Johnson N. M,
Loucks O. L, Prentki R. T. & Rich P..H. (1978) Carbon
flow in four lake ecosystems. Science 202, 1183-1186.
JLiley G. A, Stommel & Bumpus (1949) Ecology of plank-
ton. Bull. Bingham Ocean. ColL 12, 3.
Schnoor J. L. & Fruh E. G. (1979) Dissolved oxygen model
of a short detention time reservoir with anaerobic hypo-
bmnion. Wat. Resour. BulL 15, 506-518.
Smayda T. J. (1974) Some experiments on the sinking
characteristics of two freshwater diatoms. Limnol.
Oceanogr. 19, 628-635.
Sorokin C (1959) Tabular comparative data for the low
and high temperature strains of chlorella. Nature 184,
643-644.
Stumm W. A Morgan J. J. (1970) Aquatic Chemistry.
Wiley-InteTscience, New York.
Thomann R. V, DiToro D. M Winfield R. P. & O'Con-
nor D. J. (1975) Mathematical modeling of phytoplank-
ton in Lake Ontario. U.S. Environmental Protection
Agency, EPA-660/3-75-005. Washington. DC.
2 - / 4 
-------
A Dynamic Model of Phytoplankton Populations
in Natural Waters*
Introduction
The quality of natural waters can be markedly
influenced by the growth and distribution of phytoplankton.
Utilizing radiant energy, these microscopic plants assimi-
late inorganic chemicals and convert them to cell material
which, in turn, is consumed by the various animal species
Ln the next tropic level. The phytoplankton, therefore,
aeS the base of the food chain In natural waters, and
.i-ir existence is essential to all aquatic life.
The quality of a body of water can be ad-
versely affected if the population of phytoplankton
becomes so large as to interfere with either water
~Dominic M. Di Toro, Donald J. O'Connor, Robert V. Thomann
Environmental Engineering and Science Program
Manhattan College


-------
use or the higher forms of aquatic life. In .particular, high concentrations
of algal biomass cause large diurnal variations in dissolved oxygen which
can be fatal to fish life. Also, the growths can be nuisances in themselves,
especially when they decay and either settle to the bottom or accumulate
in windrows on the shoreline. Phytoplankton can cause taste and odor
problems in water supplies and, in addition, contribute to filter clogging
in the water treatment plant.
The development of large populations of phytoplankton and, in some
cases, larger aquatic plants can be accelerated by the addition of nutrients
which result from man's activities or natural processes. The resulting
fertilization provides more than ample inorganic nutrients, with the re-
sulting development of excessive phytoplankton. This sequence of events
is commonly referred to as eutrophication.
Generally, the management of water systems subjected to accelerated
eutrophication because of waste discharges has been largely subjective.
Extensive programs of nutrient removal have been called for, with little
or no quantitative prediction of the effects of such treatment programs.
A quantitative methodology is required to estimate the effect of proposed
treatment programs that are planned to restore water quality or to predict
the effects of expected future nutrient discharges. This methodology
should include a model of the phytoplankton population which approxi-
mates the behavior of the phytoplankton in the water body of interest
and, therefore, can be used to test the effectr of the various control pro-
cedures available. In this way, rational planning and water quality man-
agement can be instituted with at least some degree of confidence that
the planned results actually will be achieved.
This paper presents a phytoplankton population model in natural
waters, constructed on the basis of the principle -of conservation of mass.
This is an elementary physical law which is satisfied by macroscopic
natural systems. The use of this principle is dictated primarily by the
lack of any more specific physical laws which can be applied to these
biological systems. An alternate conservation law, that of conservation
of energy, can also be used. However, the details of how mass is trans-
ferred from species to species are better understood than the correspond-
ing energy transformations. The mass interactions are related, among
other factors, to the kinetics of the populations, and it is this that the bulk
of the paper is devoted to exploring.
Conservation of mass has been successfully applied to the modeling
of'the dissolved oxygen distribution in natural waters as well as the dis-
tribution of salinity and other dissolved substances. The resulting models
have proved useful in guiding engineering and management decisions
concerned with the efficient utilization of water resources and the pro-
tection of their quality. It is felt that the phytoplankton model presented
5-/7 o

-------
herein can serve a similar purpose by providing a basis for predicting
the effects of nutrient control programs on the eutrophication of natural
waters.
Thus, tne primary purpose of this paper is to introduce a,quantitative
model of phytoplankton population dynamics in natural waters. If.,is
within this problem context that the simplifications, assumptions, an$
generally the structure or,.the model is formulated.. An.attempt is made
to make,the equations representative of the biological mechanisms^ while
still retaining a sufficient, simplicity so that the result is tractable and
useful.
Review of Previous Models
The initial attempts to model the dynamics of a phytoplankton* popu-
lation were based on a version of the law of conservation of mass in which
the bydrodynamic transport of mass is assumed to be insignificant 'Let
P(t) be the concentration of phytoplankton mass at timei in a suitably
chosen region of water. The principle of conservation of mass ran be
expressed as a differential equation
where S is the net source or sink of phytoplankton mass within the region.
If hydrodynamic transport is not included, then the rate at -Which P in-
creases or decreases depends only on the internal sources and sinks 6f
phytoplankton in the region of interest.
The form of the internal sources and sinks of phytoplankton is dic-
tated by the mechanisms which are assumed to govern the growth' and
death- of phytoplankton. Flenung (1939),' as described by Riley (I),
postulated that spring diatom 'flowering iri the English' Channel is de-
scribed by the equation
^ = la  (6 + ci)]P
where P is the phytoplankton concentration, a is a constant growth'fare,
and (b ct) is a death rate resulting from the grazing of zoopTanJcton.
The zooplankton population, which is increasing owing to its grazing,
results in an increasing death rate which is approximated by the linear
increase ot the death rate as a function of time.
A less empirical model has been proposed by Riley (1946) (-2) based
on the equation
d-t = [P. - R -
2 -I 7 /

-------
where P* is the photosynthetic growth rate, R is the endogenous respira-
tion rate of the phytoplankton, and G is the death rate owing to zooplank-
ton grazing. A major improvement in Riley's equation is the attempt to
relate the growth rate, the respiration rate, and the grazing to more
fundamental environmental variables such as incident solar radiation,
temperature, extinction coefficient, and observed nutrient and zooplank-
ton concentration. As a consequence, the coefficients of the equations
are time-variable since the environmental parameters vary throughout
the year. This precludes an analytical solution to the equation, and nu-
merical integration methods must be used. Three separate applications
(2, 3, 4) of these equations to the near-shore ocean environment have
been made, and the resulting agreement with observed data is quite
encouraging.
A complex set of equations, proposed by Riley, Stommel, and Bumpus
(1949) (5) first introduced the spatial variation of the phytoplankton
with respect to depth into the conservation of mass equation. In addi-
tion, a conservation of mass equation for a nutrient (phosphate) was also
introduced, as well as simplified equations for the herbivorous and car-
nivorous zooplankton concentrations. The phytoplankton and nutrient
equations were applied to 20 volume elements which extended from the
surface to well below the euphotic zone. In order to simplify the calcu-
lations, a temporal steady-state was assumed to exist in each volume ele-
ment. Thus, the equations apply to those periods of the year during
which the dependent variables are not changing significantly in time.
Such conditions usually prevail during the summer months. The results
of these calculations were compared with observed data, and again the
results were encouraging.
Steele (1956) (6) found that the steady-state assumption did not
apply to the seasonal variation of the phytoplankton population. Instead,
he used two volume segments to represent the upper and lower water
levels and kept the time derivatives in the equations. Thus, both temporal
ar'5 "patial variations were considered. In addition, the differential equa-
tion for phytoplankton and zooplankton concentration were coupled so
that rhe interactions of the populations could be studied, as well as the
uutrient-phytoplankton dependence. The coefficients of the equations
were not functions of time, however, so that the effects of time-varying
soUi radiation intensity and temperature were not included. The equa-
tions were numerically integrated and the results compared with the ob-
served distribution. Steele applied similar equations to the vertical
distribution of chlorophyll in the Gulf of Mexico(7).
The models proposed by Riley et al. and Steele are basically similar.
Each consider the primary dependent variables to be the phytoplankton,
zooplankton, and nutrient concentration. A conservation of mass equa-
4 - I 7-2.

-------
tion is written for each species, and the spatial variation is incorporated
by considering finite volume elements which interact because of vertical
eddy diffusion and downward advective transport of the phytoplankton.
Their equations differ in some details (for example, the growth coefficients
that were used and the assumptions of steady state) but the principle
is the same. In addition, these equations were applied by the authors to
actual marine situations and their solutions compared with observed data.
This is a crucial part of any investigation discussion wherein the assump-
tions that are made and the approximations that are used jure difficult
to justify a priori.
The models of both Riley and Steele have been reviewed in greater
detail by Riley (I) in a discussion of their applicability and possible
future development. The difficulties encountered in formulating simple
FLOW
TEMPERATURE
SOLAR
RADIATION
-L-t
HOOPLANKTON
PREY
GRAZING
PHYTQPLANKTON
NUTRIENT
LIMITATION
NUTRIENT
USE
NUTRIENTS
MAN MADE
INPUTS
Figure 1, Interactions of environmental variables and the phyto-
plankton, zooplankton, and nutrient systems
- / 73

-------
theoretical models of phytoplankton-zooplankton population models were
discussed by Steele (8).
Other models have been proposed which follow the outlines of the
equations already discussed. Equations with parameters that vary as a
function of temperature, sunlight, and nutrient concentration have been
presented by Davidson and Clymer (9) arid simulated by Cole (10). A
sst of equations which model the population of phytoplanlcton, zooplank-
ton, and a species of fish in. a large lake have been presented by Parker
(II). The application of the techniques of phytoplankton modeling to
the problem of eutrophication in rivers and estuaries has been proposed
by Chen (12). The interrelations between the nitrogen cycle and the
phytoplankton population in the Potomac Estuary has been investigated
using a feed-forward-feed-back model of the dependent variables, which
interact linearly following first order kinetics (13\.
The formulations and equations presented in the subsequent sections
are modifications and extensions of .previously presented equations which
incorporate some additional physiological information on the behavior
">f phytoplankton and zooplankton populations. In contrast to tKe ma-
jority of the applications of phytoplankton models which have been made
previously, the equations presented in the subsequent sections are applied
to a relatively shallow reach of the San Joaquin River and the estuary
further downstream. The motivation for this application is an investiga-
tion of the possibility of excessive phytoplankton growths as environ-
mental conditions and nutrient loadings are changed in this area. Thus,
the primary thrust of this investigation is to produce an engineering tool
hich can be used.in the solution of engineering problems to protect the
./iter quality of the region of interest.
Phytoplankton System Interactions
The major obstacle to a rigorous quantitative theory of phytoplankton
population dynamics is the enormous complexity of the biological and
physical phenomena which influence the population. It is necessary, there-
fore, to idealize and simplify the conceptual model so that the result is a
manageable set of dependent systems or variables and their interrelations.
The model considered in the following sections is formulated on the basis
of three primary dependent systems: the phytoplankton population, whose
behavior is the object of concern; the herbivorous zooplankton popula-
tion, which are the predators of the phytoplankton, utilizing the available
phytoplankton as a food supply; and the nutrient system, which repre-
sents the nutrients, primarily inorganic substances, that are required by
the phytoplankton during growth. These three systems are affected not
only by their interactions, but also by external environmental variables.
a - n V-

-------
The three principal variables considered in this- analysis are temperature,
which influences all biological and chemical reactions,, dispersion and
advective flow, which are the primary mass transport mechanisms in a
natural body of water, and solar radiation, the energy source for the
photosynthetic growth of the phytoplankton.
In addition to these external variables, the effect of man's activities
on the system is felt predominately in.the nutrient system., .Sources of. the
necessary nutrients may be the result of, for example, inputs of waste-
water from municipal and industrial discharges or agricultural runoff.
The man-made waste loads are in most cases the primary control variables
which are available to affect changes in the phytoplankton and zooplank?
ton systems. A schematic representation of these systems and their, inter-,
relations is presented in Figure 1.
In addition to the conceptual model which isolates the major inter-
acting systems, a further idealization is required which -sets the lower
and upper limits. of the temporal and spatial scales being considered.
Within the context of the problem of eutrophicatiop and its control, the
seasonal distribution of the phytoplankton is of major importance, so. that,
the lower limit of the temporal scale is on the order of days. The spatial
scale is set by the hydrodynamics of the water body being considered,.
For example, in a tidal estuary, the spatial scale is on the order of miles
whereas in a small lake it is likely a good deal smaller. The upper limits
for the temporal and spatial extent of the model are dictated primarily'
by practical considerations such as the length of time for which adequate
information is available and the size of the computer being used for the
calculations.
These simplifying assumptions are made primarily on the basis of
an intuitive assessment of the important features of the systems being
considered and the experience gained by previous attempts to address
these and related problems in natural bodies of water. The basic prin-
ciple to be applied to this conceptual model, which can then be translated
into mathematical terms, is that of conservation of mass.
Conservation of Mass
The principle of conservation of mass is the basis upon, which the
mathematical development is structured. Alternate formulations, such
as those based on the conservation of energy, have been proposed. How-
ever, conservation of mass has proved a useful starting point for many
models of the natural environment.
.The principle of conservation of mass simply states that the mass of
the substances being considered within an arbitrarily selected volume
must be accounted for by either mass transport into and out of the volume
* -/7S~

-------
or as mass produced or removed within the volume. The transport of
mass in a natural water system arises primarily from two phenomena:
dispersion, which is caused by tidal action, density differences; turbulent
diffusion, wind action, etc.; and advection owing to a unidirectional flow
for example, the fresh water flow in a river or estuary or the prevailing
currents in a bay or a near-shore environment. The distinction between
the two phenomena is that, over the time scale of interest, dispersive
mass transport mixes adjacent volumes of water so that a portion of the
water in adjacent volume elements is interchanged, and the mass trans-
port is proportional to the difference in concentrations of mass in adjacent
volumes. Advective transport, however, is transport in the direction'of
the advective flow only. In addition to the mass transport phenomena,
mass in the volume can increase resulting from sources within the volume.
These sources represent the rate of addition or removal of mass per unit
time per unit volume by chemical and biological processes.
A iftathematical expression of conservation of mass which includes
the' terms to describe the mass transport piKenomena and the'source term
is a partial differential equation of the following form
^ = V -:EyP - y'  QP + SP	(1)
where P (x, y, z, t) is the concentration of the substance of intereste.g.,
phytoplankton biomassas a function of position and time; E is the
diagonal matrix of dispersion coefficients; Q is the advective flow rate
vector; SP is the vector whose terms are the rate of mass addition by the
sources and sinks;.and.V is the gradient operator. This partial differen-
tial equation is too general to be solved analytically, and numerical
techniques are used in its solution.
An effective approximation to Equation 1 is obtained by segmenting
the water body of interest into n volume elements of volume Vj and rep-
resenting the derivatives in Equation 1 by differences. Let V be the
n X n diagonal matrix of volumes VA, the n X n matrix of dispersive
and advective transport terms; S/>, the n vector of source terms SP), aver-
aged over the volume V}; and P, the n vector of concentrations Fjt which
are the concentrations in the volumes. Then the finite difference equations
can be expressed as a vector differential equation
VP = AP + VSP	(2)
where the dot denotes a time derivative. The details of the application
of this version of the dispersion advectioii equation to natural bodies of
water has been presented by Thomann (14) and reviewed by O'Connor'
et al.~(15).
J-/74

-------
The main, interest in this report is centered on the source terms S/>;
for the particular application of these equations to. the phytoplankton
population in natural water bodies. It is convenient to express the source
term of phytoplankton, S/;, as a difference between the growth rate, Gpf,
of phytoplankton and their death rate, DPj, in the volume Vj. That is
Srj = (GP] - D?j)Pj	(3)
where GPJ and Drj have units [day"1]. The subscript P identifies the
quantities as referring to phytoplankton; the subscript ; refers to the ^vol-
ume element being considered. The balance between the magnitude..of
the growth rate and death rate determines the rate at which phytoplank-
ton mass is created or destroyed in the volume element Vj. Thus, the
form of the growth "and death rates as functions of environmental param-
eters and dependent variables is an important element in a. successful
phytoplankton population model.
Phytoplankton Growth Rate
The growth rate of a population of phytoplankton in a natural en-
vironment is a complicated function of the species of phytoplankton
present and their differing reactions to solar radiation, temperature, and
the balance between nutrient availability and phytoplankton require-
ments. The complex and often conflicting data pertinent to this problem
have been reviewed recently by Hutchinson (1967) (16), Strickland
(.1965) (17), Lund (1965) (18), and Raymont (1963) (19). The avail-
able information is not sufficiently detailed to specify the growth-kinetics
for individual phytoplankton species in natural environments. Hence,
in order to accomplish the task of constructing a growth rate function, a
simplified approach is followed. The problem of different species and
their associated nutrient and environmental requirements is not addressed.
Instead, the population is characterized as a whole by a measurement of
the biomass of phytoplankton present. Typical quantities used are the
chlorophyll concentration of the population, the number of organisms per
unit volume, or the dry weight of the phytoplankton per-unit volume
(20). With achoiee of biomass units established, the growth rate ex-
presses the rate of production of biomass as a function of the important
environmental variables. The environmental variables to be considered
below are light, temperature, and the various nutrients which are neces-
sary for phytoplankton growth.
 Light and Temperature. Consider a population of phytoplankton,
either a natural association or a single species culture, and assume that
the optimum or saturating light intensity for maximum growth rate of
biomass is present and illuminates all the cells, and further that all' the
2.-/77

-------
4jO
~* 10
20
15
U
JO
to
3
0
TEMPERATURE C
Figure 2. Phytoplankton saturated growth rate (base e)
as a function of temperature
necessary nutrients are present in sufficient quantity so that no nutrient
is in short supply. For this condition, the growth rate that is observed
is called the maximum or saturated growth rate, K\ Measurements of K'
(base e) as'a function of temperature are shown in Figure 2 and listed
in Table I. The experimental conditions under which these data were
collected appear to meet the requirements of optimum light intensity and
sufficient nutrient supply. The data presented are selected from larger
groups of reported values, and they represent the maximum of these
reported growth rates. The presumption is that these large values reflect
the maximum growth rates achievable. From an ecological point of view,
it is necessary to consider the species most able to compete, and, in terms
of growth rate, it is the species with the largest growth rate which will
predominate. A straight-line fit to this data appears to be a crude but
reasonable approximation of the data relating saturated growth rate K'
to temperature, T
K' = KXT	(4)
where Kx has values in the range 0.10 . 0.025 day'1 CM. This coefficient
indicates an approximate doubling of the saturated growth rate for a
temperature change from 10 to 20 C, in accordance with the generally
reported temperature-dependence of biological growth rates. The opti-
mum temperature for algal growth appear? to be in the range between
20 and 25C, although thermophilic strains are known to exist (27). At
higher temperatures, there is usually a suppression of the saturated growth
rate, and the sfraight-line approximation is no longer valid. It should
a - / 7?

-------
also be noted that the scatter in the data in Figure 2 is sufficiently large
so that the linear dependence on temperature and also the magnitude
of K' can vary considerably in particular situations.
In the natural environment, the light intensity to which the phyto-
plankton are exposed is not uniformly at the optimum value but it varies
as a function of depth because of the natural turbidity present and as a
function of. time over the day. Thus, the phytoplankton in the lower
layers are exposed to intensities below the optimum and those at the
surface may be exposed to intensities above the optimum so that their
growth rate would be inhibited. Figure 3b,c,d from Ryther (28) are
plots of the photosynthesis rate normalized by the photosynthesis rate at
the optimum or saturating light intensity vs. the light intensity, 7, incident
on the populations. Figure 3a is a plot of function
for I, = 2000 ft-candles, proposed by Steele (8) to describe the light-
dependence of the growth rate of phytoplankton.
The similarity between this function and data from Ryther is suffi-
cient to warrant the use of this expression to express the influence of
nonoptimum light intensity on the growth rate of phytoplankton. Other
workers have suggested different forms for this relationship (29, 30).
Table I. Maximum Growth Rates as a Function of Temperature
Ref.	Organism
Saturated Growth Rate,
Temperature, K'(Base Day1)
21	Cklorella ellipsaidea
; (green alga)
22	Nannochloris utomus
(marine flagellate)
23	NitzscJiia closierium
(marine diatom)
25
15
20
10
27
19
15.5
10
4
2.6
25
25
25
25
25
25
10
15
20
25
3.14
1.2
2.16
1.54
1.75
1.55
1.19
0.67
0.63
0.51
1.96
2.02
2.15
1.8
1.52
2.64
0.2
1.1
2.4
3.9
5 Natural association
24	Chlorella pyrenoidosa
24	Scenedesmus quadricavda
25	Chlorella pyrenoidosa
25	Chlorella mdgaris
25	Scenedesmus obliquus
25	Chlamydomonas reinhardti
26	Chlorella pyrenoidosa
(synchronized culture)
(high-temperature strain)
^ ~/7f

-------
(a) Pi^ 0.3

55
w	.o
-
> lb) P/ps oj
V)	
o
h-
O	o
0.
U.
O
LJ
tr (c) P/pg oj
o
111
N
Zj
<
2
tr
o
z
Chlorophyta
Diatoms
Flagellates
(d) P/p, o J
LIGHT INTENSITY (FOOT CANDLES x 10s)
Limnology and Oceanography
Figure 3. Normalized rate of photosynthesis vs. incident
light intensity: (a) Theoretical curve after Ste_ele (8); (b,c,d)
Data after Ryther (28)
These variations approximately follow the shape of Equation 5 for low
Vght intensities but differ for the region of high light intensities, usually
by not decreasing after some optimum intensity is reached. In particular,
Tamiya et al (21) have investigated the growth rate of Chlorella ellip-
?oidea to various light and temperature regimes. The saturated growth
iiies as a function of temperature are included in Figure 2. The influence
of varying light intensity fits the function 		
F(I) =
I + K'/a
(6)
where K' is the saturated growth rate and a is a constant (a 0.45 day"1
kilolux"1). However, since K' is a function of temperature, the saturating
light intensity for Equation 6 is also a function of temperature. Similar
data obtained by Sorokin et al. (26) using a high-temperature strain of
Chlorella pyrenoidosa support the temperature-dependence of the satu-
2 - / 2o

-------
rating light intensity for chlorella. Therefore, in .using Equation 5, a
temperature-dependent light saturation intensity may be warranted.
At this point in the analysis, the effect of the natural environment
on the light available to the phytoplankton must be included. Equation 5
expresses the reduction in the growth rate caused by nonoptimum light
intensity. This expression can therefore be used to calculate the reduction
in growth rate to be expected at any intensity. However, this is too
detailed a description for conservation of mass equations which deal
with homogeneous volume elements, V,, and the growth rate within these
elements. What is required is averages of the growth rate over the vol-
ume elements.
In order to calculate the light intensity which is present in the
volume Vj, the light penetration at the depth of water where V/is located
must be evaluated. The rate at which light is attenuated with respect to
depth is given by the extinction coefficient, kt. That is, at a depth z, the
intensity at that depth, 7(z), is related to the surface intensity, I0, by the
formula
I(z) = J0 exp (- k
-------
where f is the daylight fraction of the day (i.e., the photo period) and 70
is the average incident solar radiation intensity during the pkoto period.
Let fj be the reduction in growth rate attributed to Bonoptimum
light conditions in volume V}, averaged over depth and time. Then f/ is
given by
1. C"' 1 f	j, j
Tjt -n-^lr- + ,rdt
(10)
where T  1 day, the time-averaging interval,  Hj  the depth of
segment Vj, and kej is the extinction coefficient in V}. The result is
rt = jr^g- -e-*	(11)
vhere
"" = T. (12)
/.
~ r.
The integral given by Equation 10 is a form of an integral used by
Steeman Nielson (1952), Tailing (1957), and Ryther and Yentsch
(1957), as described by Vollenweider (1958) (30), and, in particular,
Steele (8), for the purpose of relating an instantaneous rate (e.g., growth,
photosynthesis, etc.) to an average day rate and an average depth rate.
The reduction factor rf is a function of the extinction coefficient krj
of the volume V. However, ihe extinction coefficient is a function of the
phytoplankton concentration present if their concentration is large. Thus,
an important feedback mechanism exists which can have a marked effect
on the growth rate of phytoplankton. As the concentration of phyto-
plankton in a volume element increases, the extinction coefficient, par-
ticularly at the green wavelengths, starts to increase. This mechanism
is called self-shading. The most straightforward approach to including
this effect into the growth rate expression is to specify the extinction
coefficient as a function of the phytoplankton concentration
kti = k'.j + h(Pj)	(13)
where kfcS is the extinction coefficient attributable to other causes and kej
includes the phytoplankton's contribution. The function h(Pj) has been
investigated by Riley (31), who found that it can be approximated by
3. ~ / s a

-------
h(Pj) = 0.0088 Pi + 0.054 PjVi
(14)
where ?s has the units ^g/liter chlorophyll, concentration and h has
units m"1. A more recent investigation (32) shows that this relationship
applies to coastal waters of Oregon for a range in chlorophylla concen-
tration of from 0 to 5.0 mg Chla/m3.
A theoretical basis for this relationship is the Beer-Lambert law,
which expresses the extinction coefficient in terms of the concentration of
light-absorbing material. For dense algal cultures, this law has been
experimentally verified (33). A similar relationship based on this law
has been proposed by Chen (12) from the data of Azad and Borchardt
(34)
h(Pj) = 0.17 Pi	(15)
For h in m"1 and P>, the phytoplankton concentration is mg/liter of dry
weight This expression gives values comparable with Equation 14 for a
reasonable conversion factor for the units involved.
To summarize the analysis to this point, the saturated growth rate
K' has been estimated from available data and its temperature depend-
ence established. The reduction to be expected from nonoptimum light
intensities has been quantified and used to calculate the reduction in
growth rate, rJt to be expected in each volume element V} as a function
of the extinction coefficient and the depth of the segment. The mechanism
of self-shading has been included by specifying the chlorophyll depend-
ence of the extinction coefficient. It remains to evaluate the effect of
nutrients on the growth rate.
Nutrients. The" effects of various nutrient concentrations on the
growth of phytoplankton has been investigated and the results arie quite
complex. As a first approximation to the effect of nutrient concentration
on the growth rate, it is assumed that the .phytoplankton population in
question follow Monod growth kinetics with respect to the important
nutrients. That is, at an adequate level of substrate concentration, the
growth rate proceeds at the saturated rate for the temperature and light
conditions present. However, at low substrate concentration, the growth
rate becomes linearly proportional to substrate concentration. Thus, for
a nutrient with concentration Nj in the fu segment, the factor by which
the saturated growth rate is in the /',u segment reduced is: N}/(K, -f Nj).
The constant, K which is called the Michaelis or half saturation con-
stant, is the nutrient concentration at which the growth rate is half the
saturated growth rate. There exists an increasing body of experimental'
evidence to support the use of this functional form for the dependence of
the growth rate on the concentration of either phosphate (35), nitrate,
or ammonia (36) if only one of these nutrients is in short supply. An
SL- / ?3

-------
- yU* 200
BO	130	200
NO, (mo-N/I)
A ><3J
^m"30
POi (^40-P/ll
Figure 4. Nutrient absorption rate as a function of nutrient
concentration: comparison of Michaelis Menton theoretical
'curve with data from Ketchum (37)
example of this behavior, .using the data from Ketchum (37), is shown
in Figure 4a for the nitrate uptake rate as a function of nitrate concentra-
tion and in Figure 4b for the phosphate uptake as a function of phosphate
concentration. These result"; are from batch experiments. Similar results
from chemostat experiments, which seen^ to be more suitable but more
lengthy for this type of analysis, have also been obtained. Table II is a
listing of measured and estimated Michaelis constants for ammonia,
nitrate, and phosphate. The estimates are obtained by talcing one-third
the reported saturation concentration of the nutrients. These measure-
ments and estimates indicate that the Michaelis constant for phosphorus
is approximately 10 /ig P/liter and for inorganic nitrogen forms in the
range from 1.0 to 100 ^g N/liter, depending on the species ^nd its previ-
ous history.
The data on the effects of the concentration of other, inorganic nutri-
ents on the growth rate is less complete. Since algae use carbon dioxide
as their carbon source, during photosynthesis, this is clearly a nutrient
which can redijce the growth rate at low concentrations (43). .Reported
saturation concentration for Chlorella is < 0.1% "atm (24).
Z-i ZH-

-------
The silicate concentration is a factor in the growth rate of diatoms
for which it is an essential requirement. The saturated growth rate con-
centration is in the range of 50-100 /ig Si/liter (17).
There are a large number of trace inorganic elements whidi have
been implicated in the growth processes of algae, among which are iron
[for which a Michaelis constant of 5 /ig/liter for reactive iron, has been
reported (39)], manganese, calcium, magnesium, and potassium (18).
However, the significance of these elements in the gr*owth of phyto-
plankton in natural waters is still unclear. Trace organic nutrients have
also been shown to be necessary for most species of algae: 80% of the
strains studied require vitamin Bi2, 53% require thiamine, and 10%
require biotin (44). Presumably, these nutrients,are.available in sufficient
quantities "in natural waters so that their concentration does not appre-
ciably affect the growth rate.
In the preceeding discussion of nutrient influences ,on the growth
rate, it is tacitly assumed that only one nutrient is in short supply and
all the other nutrients are plentiful. This is sometimes the case in a
natural body of water. However, it is also possible that more than one
nutrient is in short supply. The most straightforward approach to formu-
lating the growth rate reduction caused by a shortage of more than one
nutrient is to multiply the saturated growth rate by the reduction factor
for ea.ch nutrient. This approach has also been suggested by Chen (12).
Table II. Michaelis Constants for Nitrogen and Phosphorus
Michaelis Constant,
y.g/Liter as N or F
25
-l50
10
6a.
10"
10
1.4-7.0
1.4-5.6
6.3-28
7.0-120
8.4-130
7.0-77
2.8
1.4-8.4
14
18':
* Estimated.
Ref.
Organism
Nutrient
38
Chaetoceros gracilis
P04

(marine diatom)

39
Scenedesmus gracile
total N

total P
40
Natural association
PO,

Microcystis aeruginosa
P04

(blue-green)

41
Phaeodaclylum tricornutum
PO<
36
Oceanic species
NO,

Oceanic species
NH,
36
Neritic diatoms
NO,

Neritic diatoms
NH,
36
Neritic or littoral
NO,

Flagellates
NH,
42
Natural association
NO,

Oligotrophic
NH,
42
Natural association
NO,

Eutrophic
NH,
5 - / 2 S~

-------
As an example, the data from Ketchum (37) for the rate of phosphate
absorption as a function of both phosphate and nitrate concentration can
be satisfactorily fit with a product of two Michaelis-Menton expressions.
The resulting fit, obtained by a multiple nonlinear regression analysis, is
shown in Figure 5. The Michaelis constants that result are 28.4 /ig
N08-N/Iiter and 30.3'>ig PO-P/liter, with a saturated absorption rate
of 151 X 10"s /g P04-P/cell-hr. This approximation to the growth rate
behavior as a function of more than one nutrient must be regarded as
only a first approximation, however, since the complex interaction re-
ported between the nutrients is neglected.
The result of the above investigation is the following growth rate
expression. For the case of one limiting nutrient, N, with Michaelis con-
stant Km, the growth expression for the rate in the fb. segment is
" K'T' (j$t ("" - <-*") (icrhr) 
-------
form that is used subsequently in the applications, of these equations to
natural phytoplankton populations.
Comparisons with Other Growth Rate Expressions
The most extensive investigation of the relationship between the
growth rate of natural phytoplankton populations and the. significant
environmental variables, within the context of phytoplankton models, is
that of Riley et al. (1949) (5). The expression which results from their
work is
log [g7fl 0 1 = 22-884 + log , - log /. -
6573.8
T'
(17)
where GP is the growth rate (day*1), K' = 7.6, J0 = average daily inci-
dent solar radiation (ly/min), T' = temperature in K, and vp is the
nutrient reduction factor for phosphate concentration, Np, defined as
Vp  1.0	Np > 0.55 mg-at/m3
vp = (0.55)~lNp Np < 0.55 mg-at/m3
(18)
In order to compare this expression with that in the previous section,
let the nutrient reduction factor be replaced by a MichaelisMenton
expression.
v. =
K
mp~ I Np
(19)
where Kmp is the Michaelis constant for phosphate. To be comparable with
Equation 16, Kmp should equal approximately 0.20 mg-at/m3 (6.2 mg
P/m3). Using Equation 19 for v, the growth rate expression becomes
- *'' yrhil
where
N,
logio r,(T) =
Km[r,{T) V /.] ^ N'
22.9 (T) - 336.4
T + 273
(20)
(21)
and T is temperature in degrees centigrade. To compare this expression
with that proposed in the previous section, consider first the nutrient
saturated growth rate as a function of solar radiation intensity and tem-
perature. The equations are compared in Figure 6a as a function of total
daily solar radiation for three temperatures. The dotted line is Equation
a-17i

-------
Id
1.0
M
.	.20
SOLAR RAOIATION (LANGLEYS/MIN)
.30
UJ
 J
1.0
hi
to
.20
0
SOLAR RADIATION (LANGLEYS/MIN)
Figure 6. Comparison of phytoplankton growth
rates as a function of incident solar radiation intensity
and temperature
20, and the solid line is the product of Equations 4 and 5. The rate expres-
sions are comparable, although two differences are apparent. In Riley's
expression the effect of temperature is less pronounced in the 15 to 25 C
range, and the effect of higher daily average solar radiation intensities is
opposite (i.e., tends to increase the rate) to that of Equation 5 based
on Steele's expression. The growth rate equations averaged Over depth
are compared in Figure 6b. The depth average rate resulting from Riley's
expression is
Gr = T3T ln [; +	<22>
which is compared with Equation 16. The differences are now more
pronounce.d In particular, the higher growth rates at lower light intensi-
ties given by Equation 16 are reflected in the increased depth average
growth rate. This is not unexpected since the majority of the population
is exposed to low&r light levels at the lower depths. Also, the dependence
<2- / 2 2

-------
on temperature is quite different, being linear in the case of Equation 16
but practically suppressed in Equation 22.
An interesting feature of Riley's Equation 20 is the multiplication
of the Michaelis constant by an expression which depends on temperature
and light intensity. The effect is to lower the Michaelis constant at high
temperatures and at high light intensity levels, which seems to be a
reasonable behavior for a phytoplankton population.
More elementary growth rate formulations ha,ve been proposed
which do not span the range of conditions.attempted in Equations 16 and
20. In particular, a common proposal is to make the growth rate linearly
proportional to the various environmental variables. For example, David-
son and Clyroer (1966) (9) assumed that the growth rate is proportional
to phosphate concentration and photo period and a temperature factor
given by exp [  (T  18}VIS], This temperature factor is quite dif-
ferent from all others proposed and greatly magnifies the effect of tem-
perature on the growth rate. For example, at T = 18 C, the factor equals
1.0, whereas at T = 9C, the factor drops to 0.01, a 100-fold decrease,
compared with approximately a 2-fold decrease predicted by Equations 16
and 20. This exaggerated effect seems to be unrealistic.
A complete investigation of the environmental influences on the
growth rate, is still to be made. In particular, it has been-emphasized
that there is an interaction between nitrogen and phosphorus limitations
as well as other effects which influence the phytoplankton growth rate.
Also, these effects are .different for differing species. The species-
dependent effects are important in the problem of the seasonal succession
of phytoplankton species.
For any particular application, it iff advisable to investigate the
growth rate of the already-existing population, as the resulting expression
may differ significantly from the general over-all behavior as described
by Equations 16 and 20. "Also, in dealing with natural associations of
species of phytoplankton, the various constants which result from such
an investigation can be considered to be averages over the population,
and so they represent in some average way the population behavior as
a whole.
P^yhoplankton'Death Rate
Numerous mechanisms have been proposed which contribute to the
death rate of phytoplankton: endogenous respiration rate, grazing- by
herbivorous zooplankton, a sinking rate, and parasitization (27). The
"first three mechanisms have been included in previous models Jor phyto-
plankton dynamics, and they have been shown to be of general' impor-
tance.
A- IS J

-------
Endogenous Respiration. The endogenous respiration rate of phyto-
plankton is the rate at which the phytoplankton oxidize their organic
carbon to carbon dioxide per unit weight of phytoplankton organic car-
bon. Respiration is the reverse of the photosynthesis process and as such
contributes to the death rate of the phytoplankton population. If the
respiration rate of the population as a whole is greater than the photo-
synthesis or growth rate, there is a net loss of phytoplankton carbon, and
the population biomass is reduced in size. The respiration rate as a func-
tion of temperature has been investigated, and some measurements are
presented in Figure 7 and Table III. A straight line seems to give an
adequate fit of the data; that is, Respiration Rate  K2T. For the respira-
tion rate in days"1 and T in C, the value of K2 is in the range 0.005 
0.001. The lack of any more precise data precludes exploring the respira-
tion rate's dependence on other environmental variables. However, an
important interaction has been suggested by Lund (18). During nutrient-
depleted conditions, "many algae pass into morphological or physiological
resting stages under such unfavorable conditions. Resting stages are ab-
sent in Asterionella formosa, and this is why a mass death occurs in the
nutrient-depleted epilimnion after, the vernal maximum." In terms of the
respiration rate, the resting stage corresponds-to a lowering of the respi-
ration rate as the nutrient concentrations decrease. Thus, a Michaelis-
Menton expression for the respiration rate nutrient dependence may also
be required, and this dependence should be investigated experimentally.
This mechanism is quite significant from a water quality point of view
since the deaths of algae after a bloom is of primary concern in protecting,
1 u-
u
<
s
1
g

UJ
8
a
z
bJ
10
23
3
0
TEMPERATURE C
Figure 7, Endogenous respiration rate of phytoplankton vs.
temperature; after Riley (5)
?o

-------
Table III< Endogenous Respiration Rates of Phytoplankton (5)
Endogenous Respiration
Organism	Temperature, C . Rate, Day'1 {Base,)
Niizschia dosterium
6
0.035

35
0.170
Niizschia dosterium
20
0.08
C
-------
aspect of phytoplankton mortality is such that the use of one grazing
coefficient to represent the process must be viewed as a first approxima-
tion. However, since this mathematical expression does represent a
-physiological mechanism that has been investigated and for which re-
ported values of Cu are available, this approximation is a realistic first
step. Also, it is difficult Jto see, aside from refinements as to temperature
and phytoplankton concentration dependence, what further improve-
ments could be made in the formulation so long as the phytoplankton
and zooplankton population are represented by a biomass measurement
which ignores the species present and their individual characteristics.
For simplicity in this investigation, the grazing rate is assumed to be a
constant. The death rate of phytoplankton resulting from the grazing of
zooplankton is given by the expression C^Zj, where Z; is the concentration
of herbivorous zooplankton biomass in the fb volume element.
For models of the phytoplankton populations in coastal oceanic wa-
ters and in lakes, the sinking rate of phytoplankton cells is an important
contribution to the mortality of the population. The cells have a net
downward velocity, and they eventually sink out of the euphotic zone
to the bottom of the water body. This mechanism has been investigated
and included in phytoplankton population models (5, 12). However, for
the application of these equations to a relatively shallow vertically well
mixed river or estuary, the degree of vertical turbulence is sufficient to
eliminate the effect of sinking on the vertical distribution of phyto-
plankton.
Table IV. Grazing Rates of Zooplankton



Grazing Rate,



Liter/Mg Dry
Ruf.
Organism
Reported Grazing Rate
Wt.-Day

Rotifer


16
Brachionus calyciflorus
0.05-0.12a
0.6-1.5

Copepod


5
Calanus sp.
67-2086
0.67-2.0
45
Calanus finmarchicus
27
0.05
46
Rhincalamus nasutvs
98-670
0.3-2.2
47
Qentropages hamatus

0.67-1.6

Cladocera


48.
Daphnia sp.

1.06
49
Daphnia sp.

0.2-1.6
50
Daphnia magna
81
0.74
51 
 Daphnia magna
57-82
0.2-0.3

National Association


5
Georges Bank
80-110*
0.8-1.10
*	Ml/ animal-day.
*	Ml/mg wet wt-day.
JL-ifSi

-------
Therefore, considering only 'the phytoplankton respiration and the
predation by zooplankton, the death rate of phytoplankton is given by the
equation
Dpj = KzT + CuZj	-<23)
and.for a zooplankton biomass concentration ZJt the mortality rate-can
be calculated from this equation.
2-0]
U
 ,.o
UJ
5
(E
O
a '
<
tr
o
* baphnia Magna
p
/ 
x D. Schodteri
/
~ 0. pule*
.v
_ v 0. gaieala

 Acartia clausi
.V
/V
o A. tonso
.v
e Centrapages hamatus
 C. typicus
A'
:/ ,/
 _#
..	
. . 


  
/ / /
0
*
0,~	 1
	!	1	L.
10	IS	20
TEMPERATURE t

Figure 8. Crazing rates of zooplankton vs. tem-
perature
This completes the specification of the growth and death- rates of
the phytoplankton population in terms of the physfcal variables: light
and temperature, the nutrient concentrations, and the xobpJankt'on pres-
ent. With these variables known as a function of.time,,H is possible'to
calculate the phytoplankton population resulting throughout the ypar.
However, the zooplankton population and the nutrient, concentrations
are not known a priori since they depend on the phytoplanktoh popula-
tion which develops. That is, these systems are interdependent' &nd can-
not be analyzed separately. It is therefore necessary to characterize both
the zooplankton population and the nutrients in mathematical terms in
order to predict the phytoplankton population which would develop in
a given set of circumstances.
a.-/

-------
The Zooplankton System
As indicated in the previous section, the zooplankton population
exerts a considerable influence on the phytoplankton death rate by its
feeding on the phytoplankton. In some instances, it has been suggested
that this grazing is the primary factor in the reduction of the concentra-
tion of phytoplankton after the spring bloom." In the earlier attempts to
model the phytoplankton system, the measured concentration of zoo-
plankton biomass was used to evaluate the phytoplankton death rate
resulting from grazing. However, it is clear, that.the same arguments used
*o develop the equation for the conservation of phytoplankton biomass
can be applied directly to the zooplankton system. In particular, the
source of zooplankton biomass SZj within a volume element Vj can be
given as the .difference between a zooplankton. growth rate GXj and a
-zooplankton death rate DZj. Thus, the equation for the source of zoo-
plankton biomass, which is analogous to Equation" 3, is
Szj = {G/.j  Dzi)Zj	(24)
where GZJ and DXj have units day"1 and Zj is the concentration of zoo-
plankton carbon in the volume element VThe magnitude of the growth
rate in comparison with the death rate determines whether the net rate
of zooplankton biomass production in Vj is positive, indicating net growth
rate, or negative, indicating a net death rate.
As in the case of the phytoplankton population, the growth and death
rates, and In fact the whole life cycle o individual zooplankters, are com-
plicated affairs with many individual peculiarities. The surveys by Hutch-
inson (16) and Raymont (19) give detailed accounts of their complex
biology. It is, however, beyond the scope of this paper to summarize all
the differences and species-dependent attributes of the many zooplankton
species. The point of view adopted is macroscopic,, with the population
characterized in units of biomass. The resulting growth and death rates
can be thought of as averages over the many species present. These
simplifications are made in the interest of providing a model which is
simple enough.to be manageable and yet representative of the over-all
behavior of the populations.
Growth Rate. The grazing mechanism of the zooplankton provides
the basis for the growth rate of the herbivorous zooplankton, CZj- For a
filtering rate Cu% the quantity of phytoplankton biomass ingested is CaPj,
where.?; is the phytoplankton biomass concentration in V}. To.convert
this "rate to a zooplankton growth rate, a parameter which , relates, the
phytoplankton biomass ingested to zooplankton biomass produced, a
utilization efficiency, aZP, is required. However^ this utilization efficiency
or yield coefficient is not a constant. At "High phytoplankton cbncentra-
Jl -/ ? 4-

-------
tions, the zooplankton do not metabolize all the phytoplankton that they
graze, but rather they excrete a portion of the phytoplankton in undi-
gested or semidigested form (55)." Thus, utilization efficiency is a func-
tion of the phytoplankton concentration. A convenient choice for this
functional relationship iiazrKmr/'( Kp + P>) so that the growth rate for
the zooplankton population is
C" = {kJ+ p)	<2S)
The resulting growth rate has the same form as that postulated for the
nutrientphytoplankton relationship, namely, a MichaelisMdntori ex-
pression with respect to phytoplankton biomass. In fact, the argument
which is used to justify its use in Equation 16 can be* repeated ih this
context. The'difference is that ih this case the substrate or -nutrient is
phytoplankton biomass, and the microbes are the zooplankton. The
Michaelis constant KmP is the phytoplankton biomass concentration !at
which the growth rate G-zj is one-half the maximum possible growth rate
Or.pCgKmp. The fact that at high phytoplankton- concentrations the zoo-
plankton growth rate saturates was incorporated by Riley .{191?) (55)
in the first model proposed for a zooplankton population.
The assimilation efficiency of .the zooplankton at low phytoplankton
concentrations, a7.P, which is the ratio of phytoplankton organic carbon
utilized to zooplankton organic carbon produced has been estimated by
Conover (56) for a mixed zooplankton population. The results of 2J5
experiments gave an average of 63% arid a standard deviation of 20%.
Other -reported values are within this -range- -Experimental values for
KmP, which in effect set the maximum growth rate of zooplankton, are not
available and would probably be highly species-dependent. Perhaps a
more effective way of estimating KmP is first to estimate' the maximum
growth rate at saturating phytoplankton' concentrations, azPCgKmp, and
then calculate KmP. Growth rates for copepods through'their life cycle
average 0.18 day"1 (46). For the Georges Bank population, Riley used
0.08 day"1 (55) for the maximum zooplankton growth rate. For a value
of the grazing coefficient C of 0.5 liter/mg-dry wt-day arid an assimila-
tion coefficient of 65%, the Michaelis constant for zooplankton assimila-
tion, KmP, ranges between 0.25 and 0.55 mg-dry wt/liter of phytopl&nkton
biomass. However, these values should only be taken as an indication of
the order of magnitude of Kmp. It is probable that its value can' vary
substantially in different situations.
The fact that the growth rate reaches a maximum or saturates is an
important feature of the formulation of the zooplankton growth rate since
z - / 75-

-------
in some cases the phytoplankton concentration during part of .jfre year
exceeds that which "tKe zooplankton can Effectively metabolize: If the
zooplankton growth rate is not limited in some way and, instead, is
assumed simply to be proportional to the phytoplankton concentration,
as proposed in simpler models, the resulting zooplankton growth rate
during phytoplankton blooms can be very much larger thin is'physio-
logically possible for zooplankton, an unrealistic result. The saturating
growth rate also has implications in the mathematical properties of the
resulting equations. In particular, the behavior differs significantly from
the classical Volterra Preditor-Prey equations (57). This, is discussed
further in a subsequent section.
The growth of the zooplankton population as a whole, of which the
herbivorous zooplankton are a part,.is complicated by the fact that some
zooplankters are carnivorous or omnivorous. Thus, the nutrient for the
total'population should include not only'phytoplankton but also organic
detritus as a food source since this is also available to the grazing zoo-
plankton. However, for cases where the phytoplankton are abundant and
the growth rate saturates for the significant growing periods, the simpli-
fication introduced by ignoring the detritus is probably acceptable!
Death Rate. The death rate of herbivorous zooplankton is thought
to be caused primarily by' the same mechanisms that cause the death of
the phytoplankton, namely, endogeneous respiration and predation by
higher trophic levels. The endogeneous- respiration rate of zooplankton
populations has been measured and the results of some of these experi-
ments ate,presented in Figure 9 and Table V.
0.30
0.20
0.10
UJ
20
23
5
10
0
TEMPERATURE C
Figure 9. Endogenous respiration rat$ of zooplankton vs.
temperature
a-/ 76

-------
Table V. Endogenous Respiration Rate of Zooplankton
Respiration Rate,
Ml Ot/Mg Dry
Ref.
Organism
Plotting Symbol
Temp., C
Wt-Day
58
Cladocerans
X
18
14.2



4
2.7
58
Copepods
+
18
12.2


4
.3.8
58
Copepods
~
18
8:2


16
6.5



12
5.2



8
4.1



4
3.4
1
Calanus
~
20
4.2

Jinmarchicus

15
2.3


10
1.4



4
1.3
59
Diaptomus
~
25
12.1'

leptopus

20
7.4


15
5.8



10
2.8



5
2.5
59
D. clavipes

25
12.5


20
8.5



15
5.1



10
2.4



5
1.8
59
D. siciloidea
~
25
21


20
13.5



15
7.8



10
5.5



.5
4.8
59
Diaptomus sp.
o
25
4.3


20
3.0



15
2.1



10
1.7



5
1.1
It is clear from these measurements that the respiration rate oF
zooplankters is temperature-dependent. It is also dependent on the
weight of the zooplankter in question and its life cycle stage (59). As a
first approximation, a straight line dependence is adequate, and the
endogeneous respiration rate is given by the equation,* respiration rate =
K:iT where K*'= 0.2 rt 0.1 (day 0C)-1.. The conversion from.the reported
units to a death rate is made by assuming that 50% of the zooplankton
2-'77

-------
dry weight represents th carbon weight and that carbohydrate (jCH.O)
is being oxidized. The data are somewhat variable and serve only to
establish a range of values within which the respiration rate of a natural
zooplankton.association might be expected.
. The death rate attributed to predation by the higher trophic levels,
specifically the carnivorous zooplankton, has been considered by previous
models ig.a more or less empirical way. The complication resulting froip
another equation and the uncertainty as to the. mechanisms involved (are
quite severe, at this trophic level. In particular, it is probable that an
equatipn for organic detritus is necessary to describe adequately thq
available fqod, ' Hence, it is expedient to break the causal chain at .this
poiqt:and. assume that the herbivorous zooplankton death rate .resulting
from all other causes is given by a constant, the magnitude of which is
to be determined empirically. The severity of this assumption can be
tested by examining the sensitivity of the solutions of the phytoplankton
and zooplankton equations to the magnitude of this constant. Hence, the
resulting zooplankton death rate is given by
Dzj  KiT -+ K 4	(26)
where K| is empirically determined.
With the growth and death rates given by Equations 25 and 26,
respectively, the source term for - herbivorous zooplankton biomass is
given by Equation 24. The conservation of mass equation which describes
the behavior of Z, is given by Equation 2, with Zj as the dependent
variables replacing Pj and SZj replacing as the source terms.
This completes the formulation of the equations which describe the
zooplankton system. The equations for the nutrient system remain to be
formulated.
.The Nutrient System
The conservation of mass principle is applied to the nutrients "being
considered in the same way as it has been previously applied to' the
phytoplankton and zooplankton biomass within a volume siegment. The
number of mass conservation equations required is equal to the number
of nutrients that are explicitly included in the growth rate formulation
for the phytoplankton. For the sake of simplicity, the formulation for
only one nutrient is discussed below.
The source term S.v; in the conservation of mass equation for the.con-
centration of the nutrient Nin the fb volume segment Vf is. the-sum of.
all .sources and sinks of the nutrient within. V,. The primary interaction
between the nutrient system and the phytoplankton system is .the. reduc-
tion or sink of nutrient connected with phytoplankton .growth. The rate
A-/9?

-------
of increase of phytoplankton biomass is G^Pj. To convert thir assimila-
tion rate to the rale of utilization of the nutrient, the ratio of biomass
production to net nutrient assimilated is required. Over a long time
interval, this ratio approximates the nutrient-to-biomass ratio of the
phytoplankton population. For example, if the nutrient being considered
is total inorganic nitrogen and the phytoplankton biomass is characterized
in terms of dry weight, then this ratio is the ni trogen-to-diy-weight ratia
of the population. For both nitrogen and phosphorus, these ratios have
been studied for a number of phytoplankton species and natural associa-
tions. An example of this information is presented in Table VI, condensed
from Strickland (27). If aH? is the nutrient-to-phytoplankton biomass ratio
of the population, then the sink of the nutrient owing to phytoplankton
growth is CvpCpjPj.
A secondary interaction between the biological systems and the
nutrient systems is the. excretion of nutrients by the zooplankton jancl the
release of nutrients in an organic form by the death of phytoplankton
and zooplankton. The excretion mechanism has been considered by Riley
Tabic VI. Dry Weight Percentage* of Carbon, Nitrogen,
and Phosphorus in Phytoplankton *
% Carbon % Nitrogen % Phosphorus
Phyloplankier Average Range Average Range Average Range
Myxophyceiae	36	(28-45)	4,9	(4.5-5.8)	1.1	(0.8-1:4)
Chlorophyceae	43	(35-48)	7.8	(6.6-9.1)	2.9	(2.4-3.3)
Dinophyceae	43	(37-47)	4.4	(3.3-5.0)	1.0	(0.6-1.1)
Chrysophyceae	40	(35-45)	8.4	(7.8-9.0)	2.1	(1.2-3.0)
Bacillariophyceae	33	(19-50)	4.9	(2.7-5.9)	1.1	(0.4-2.0)
	The units are (mg of carbon, nitrogen, or phosphorus)/(mg dry weight of phr-
toplankton) X 100%.
*	Condensed from Strickland (77).
(40) in a generalization of the equations of Steele. The rate of phos-
phorus excretion has also been measured experimentally (60). Using the
formulation for zooplankton growth rate proposed herein, the rate of
nutrient excretion is the rate grazed, aXPCtP^Zh minus the rate metabo-
lized, aypGz^Zj; that is, the excretion rate is

(27)
At high phytoplankton concentrations, almost all the grazed phytoplank-
ton is excreted since the bracketed term in Equation Tt approaches unity.
There is a difficulty, however, in usirtg this term directly as a source
of nutrient. To illustrate this difficulty, assume that the nutrient is inor-
z -/ f ?

-------
ganic nitrogen. A part of the excreted nitiogen, however, is jn .organic
fojto, and 4 bapterial decomposition into the inorganic forms must pre-
cede, utilization by the phytoplankton. The same is true for the nutrient
released by the death of phytoplankton, fl.V7K2TP>, and that released by
the death of zpoplankton, aszK3TZj, where aNZ is the nutrient-to-zoo-
plankton biomass raUo. Therefore, strictly speaking, a conservation of
mass equation for the organic form of the nutrient is required. The
organic form is then converted to the inorganic form. For the case of
nitrogen, the kipetics of this conversion have been investigated and
applied to stream and estuarine situations- (13). If the conversion rate is
large by comparison with the other rates in the phytoplankton and zoo-
pkrikton equations, then the direct inclusion of these sources is approxi-
matey correct.
The sources of nutrients arising from man-made inputs,such as-waste-
water, discharges and agricultural runoff, are included explicitly into the
source term since these sources are usually the major Control variables
available to influence the biological systems. An extensive review of the
magnitude and relative importance of these, sources of nutrients, pri-
marily nitrogen and phosphorus, has recently Tseen made (61). A useful
distinction is made between diffuse sources such as agricultural runoff
loads, and ground water infiltration, which are difficult to measure and
control, and point sources such as wastewater discharges from municipal
and industrial sources, for which more information is available. The
nitrogen and phosphorus loads from agricultural runoff are quite Variable
and depend on many variables such as soil type, fertilizer application,
rainfall, and irrigation practice. The nutrient sources from point loads
can be estimated more directly. For example, the nutrient load from
biologically treated municipal wastewater is in the order of 10 g/capita-
day total nitrogen and 2 g/capita-day total phosphorus. The ratio of per
capita phosphorus to physiologically-required phosphorus is approxi-
mately 2 to 3, the excess being primarily the result of detergent use.
Industrial loads can also be important, especially effluents from food
processing industries. If the required loading rates are available, their
loads should be included in the nutrient mass balance equations. In
particular, if the investigation of the phytoplankton population is directed
at the probable effects of increasing or decreasing the nutrient load, these
loads must be explicitly identified and their magnitude assessed.
Let Win be the rate of addition of the nutrient to the fh volume
element. This source is then included as a component in the nutrient
source term in the mass balance equation.
An important.additional source of inorganic nutrients which may
influence the availability of nutrients is the interaction of the overlying


-------
water either with the underlying mineral strata if exposed or with what-
ever sediment is present. These interactions can complicate the source
term but they should be included if they add significantly to the available
nutrient.
The source term which results from the inclusion of the phytoplanfc-
izz utilization sink, the zooplankton excretion and the mortality sources,
auu the man-made additions is
Ssj =	 aypGpjP> 4- aypCgZjPs ^1  ^
+ aNpKtTPj + aszK&Zi	(28)
Any additional sources and sinks that contribute can be added to the
source term as needed. With the source term formulated, th-conserve
tion of nutrient mass equation is given by Equation 2 with Nj asthe.
dependent variable replacing P} and S.v; replacing SPJ.
The Equations- of the Model
In the previous sections, the equations for phytoplankton and zpp-
plankton biomass and nutrient concentration within one volume element
have been formulated. The resulting equations are an attempt to describe
the kinetics of the growth and death of the phytoplankton and zooplank-
ton populations and their interaction with the nutrients available. The
form of the equations for the volume Vj are as. follows:
Pi = [Gi'j(Pit Njf t) - Dpj(Zj, t)\Pj + Srj(Pj, Zh Nh t) (29)
Zj = [G2i(Ps, 0 - Dzj{t)]Zj + Szj(Pj, Zj, t)	(30)
Ni = Ss-j(P Zjt t)	(31)
where G/y and DP} are given by Equations 16 and 23, G*/and DZI are
given by Equations 25 and 26, and SXi by Equation 28. The dependence
of the growth and death rates on the concentration of the three dependent
variables and time is made explicit in this notation.
These equations describe only the kinetics of the populations in a
single volume element V,. However, in a natural water body there exists
significant mass transport as well. The mass transport mechanisms can be
conveniendy represented by the matrix A with elements aih If for par-
ticular segments i and / the matrix element at) is nonzero, then the
volume segments V and Vj interact, and mass is transported between
the two segments. Letting P, Z, and N be the vectors of elements
Pj, Zh and Nj arid letting Sr, Sx, Sz be the vectors of elements SPj, SZj,
A-Zo /

-------
and Syj, the conservation of mass equations for the three systems includ-
ing the mass transport and kinetic interactions are
VP = AP + YSp	(32)
VZ = AZ + YSz	(33)
T'iV = AN + VS*	(34)
where V is the diagonal matrix of the volumes of the segments. These
are the equations which form the basis for the phytoplankton population
model. The detailed formulation and evaluation of the mass transport
matrix has been discussed elsewhere (14,15, 62).
The form of Equations 32-34 makes explicit the linear and nonlinear
portions of the equations. In the equation for P, the phytoplankton
biomass; the concentration PJf in the volume element V;, is linearly
coupled to the other Pi's through the matrix multiplication by A. How-
ever,. there is no nonlinear interaction between Pj and any other Pk, k
The reason is that the transport processes are described by linear
equations. It is usually the case, however, that the*A matrix is a function
of time, since at least the advective terms usually vary in time. The
nonlinear terms in the vector SP involve Pj itself and the corresponding Zj
and Nj. Hence, the P equation is coupled to the Z and N equations
through tHis term. Note, however, that Pj is not coupled to the Zk, k ^ j,
in any other segment, so that the coupling .takes place only within each
volume segment.
Therefore, the nonlinearities provide the coupling between the. phy-
toplankton, zooplankton, and nutrient systems. This coupling is accom-
plished within each volume and does not extend beyond the volume
boundary. The coupling among the volumes is accomplished by the
linear transport interaction represented by the matrix A. This matrix
may be time-varying but its elements are not functions of the phytoplank-
ton^. zooplankton, or nutrient concentrations! Hence, in many ways these
equations behave linearly. In particular, their spatial behavior is un-
affected by the nonlinear source terms. However, the temporal behavior
and the relationships between each Ph Z and N;- are distinctly nonlinear.
Comparison with Lotka-Vol-terra Equations
The classical theory of predatorprey interaction as formulated by
Volterra involves two equations which express the growth rate of the
prey and the predator (57). Within the context of phytoplankton and
zooplankton population, the prey is the phytoplankton and the predator
the zooplankton. In the notation of the previous sections, for a one-
volume system, the Lotka-Volterra equations are:
A -^o <5.

-------
^ = (C,F - Dp')P - C,PZ	(35)
at
*1 = - DzZ + azrC,PZ	(36)
at
where all the coefficients, Gp, D'p, Ce, Dz, and dzp are assumed to be
constants and GP > D'p. This is a highly simplified situation since, as
indicated previously, the growth and death rates are functions of time
and, in the case of the phytoplankton growth rate, of the phytoplankton
and nutrient concentrations as well. However, for a situation with ade-
quate nutrients and low initial phytoplankton concentration, the non-
linear interaction is small initially, and the time variation of Gp can be
small during the summer months. In any case, the analysis of this sim-
plified situation is quite instructive.
Although no analytical solution is available for these simplified
equations, their properties are well understood (63). In particular, the
equations have two sets of singular points corresponding to the solutiqn
of the righthand side of Equations 35 and 36 equated to zero: the trivial
solutions ?* == 0, Z" = 0, and
P* =	Z* = c" ~ D'P	(37)
azpL, a	Is 0
A perturbation analysis of Equations 35 and 36 about this singular point
shows that the solutions whose initial conditions are close to P*, Z*,
oscillate sinusoidally about this singular point. Hence, no constant solu-
tion is possible. The prey and predator populations continually oscillate
and are out of phase with each other. When the .predator predominates,
the prey is reduced, which in turn causes the predator to die for lack of
food, which allows the prey to proliferate for lack of predator, which then
causes the predator to grow because of the prey available as a food sup-
ply, and so on. The interesting feature is that these oscillations continue
indefinitely.
The -classical LotkaVol terra equations assume an isolated popula
tion with no mass transport into or out of the volume being considered.
To simulate the effect of mass transport into the volume, assume that an
additional source term of phytoplankton biomass exists and has constant
magnitude P0. For this situation, the equations become
f4r = (Gj. " D',.)P -CUPZ + P0	(38)
dt
dt
dZ
-TJ = Dz'A + aZpC gPZ	(39)
2.- 3lo3

-------
The nontrival singular point for these equations is
p* =	z* =	+ {Gp c D'p)	(40)
azj>L g	uz	t(
A perturbation analysis about this singular point yields a second order
linear ordinary differential equation whose characteristic equation has
the roots Ai and k2 where
^i.j  
clzpPqC t
2 Dz
ayfA - azpC.P, - (G, - D',) Or
(41)
Since for Pp > 0, these roots have negative real parts, this singular point
is a stable focus, and the steady state values given by Equation 40 are
approached either by a damped sinusoid or an exponential (63). Note
that for Po  0, the classical case, the roots are purely imaginary, and
the oscillation persists indefinitely.
This analysis suggests that the effect of transport into the system
stabilizes the behavior of the equations and in particular allows the
solutions to achieve a constant solution. This is in marked contrast to the
behavior of the classical Lotka-Volterra equations.
Another modification, which has been introduced into the zooplank-
ton equations, changes the behavior of the proposed equations in contrast
to the Lotka-Volterra equations. It has been argued that the zooplankton
growth rate resulting from grazing must approach its maximum value
when the phytoplankton population becomes large since the zooplankters
cannot metabolize the continually increasing food that is available. Thus,
the growth rate aZPCg?Z is replaced by aZpCffZP KmP/{? + Kmp) where
Kmp is a Michaelis constant for the reaction. The equations then become
~ = (GP- D'p)P - GaPZ + Po	(42)
dZ . r> l azpC JZPKmp	. -v
Tt - ~~ DzZ + P+ Kmp	C43)
The nonzero singular points are
DzKmp
P* =  CK D	0 + ~ ^ ^	(45)
CgP* + Cg	{ }

-------
This solution reduces to the previous situation, Equation 40, for large
K^p. This is.expected since for KmP large with respect to P, the expression
KmP/(P + Kmp) approaches one. However, an interesting modification
from classical predatorprey behavior occurs if the following condition
is met
azpC fKmP = Dz + 	(46)
where c is a small positive number. For this condition, P* is large and
positive. What happens in this case is that the zooplankton population,
although it continues to grow exponentially, cannot grow quickly enough
to terminate the phytoplankton growth by grazing, and the phytoplankton
continue to grow exponentially until P* is reached. Of course, in the
actual situation, for which GP is not a constant, other phenomena such as
nutrient depletion and self-shading exert their effect, and the growth may
be stopped sooner. However, if the growth rate of zooplankton at a
phytoplankton concentration equal to the Michaelis constant K^p is only
slightly larger than their death rate Dz, then the zooplankton alone do
not rapidly terminate the bloom.
This condition is an important dividing line for the possible behavior
of the phytoplankton-zooplankton equations set forth in the previous
sections. In particular, it indicates what must be true for a system
wherein the zooplankton are a significant feature in the resulting phyto-
plankton solution. However, if Equation 46 is satisfied, then the zoo-
plankton are not the dominant control of the phytoplankton population.
Application-San Joaquin River
As an "example of the application of the equations proposed herein,
consider the phytoplankton and zooplankton population observed at
Mossdale Bridge on the San Joaquin River in California during the two
years 1966-1967. Mossdale is located approximately 40 miles from the
confluence of the San Joaquin and the Sacramento Rivers. The data
presented below have been supplied to the authors by the Department
of Water Resources, State of California (S4), as part_o.an ongoing
project to assess the effects of proposed nutrient loads and flow diversions
on the water quality of the San Francisco Bay Delta. A more complete
report of this investigation is forthcoming (62).
In order to simplify the spatial segmentation and the calculations, a
one-volume segment is chosen for the region of the San Joaquin for which
Mossdale is representative. The volume of this segment is, of course,
somewhat arbitrary, and a more representative spatial segmentation,
would remove this uncertainly. However, it is instructive to consider
the behavior of the solution of this simplified model.


-------
UJ
~-
120
240
360
120
240
960
2(1000
6,000
12,000
8,000
4,000
800
K >
S
600
51 "
360
240 360
TIME - DATS
360-
Figure 10. Temperature, flow, and mean daily solar radiation;
San Joaquin River, Mossdale, 1966-1967
The- nutrient data available indicate that phosphate, bicarbonate,
silicate, calcium, and magnesium are available at concentrations" well
above the levels for which it has been suggested that these 'nutrients
limit growth. Only the ammonia and nitrate concentrations are low, and
they both decrease markedly during the 1966 spring bloom. Hence, these
nutrients must be considered explicitly. To simplify the computations,
the ammonia and nitrate nitrogen are combined, and the nutrient' con--
sidered is total inorganic nitrogen.
There is some uncertainty concerning the magnitude and the tem-
poral 'variation of the inorganic nitrogen load being discharged to the
system during the time interval of interest. For lack of a better assump-
tion, the inorganic nitrogen load WN being discharged into, the volume
is assumed to fce a constant, the magnitude-of which is determined by

-------
comparison with the observed inorganic nitrogen concentration data at
Mossdale.
The variation of the environmental variables being considered
namely, temperature, solar radiation, and advective flow in the San
Joaquin during the two-year period of interestand the straight line
approximations that are used directly in the numerical computation are
shown in Figure 10. The influent advective flow, which is assumed to
have constant concentrations of phytoplankton and zooplankton biomass
and inorganic nitrogen, is routed through the volume. Since Mossdale is
located above the saline portion of the San Joaquin, no significant dis-
persive mass transfer is assumed to exist by comparison Math the advective
mass transfer.
The equations which represent this one-segment model are
P = 7,'- DP)P + ^ (P0 - P)	(47)
Z = (Gz - Dz)Z + ^ (Z0 - Z)	(48)
N = - asPGPP + ^ | (No - N)	(49)
where Q  Q(t) is the advective flow entering and leaving the volume;
V is the volume of the segment; P0, Zo, and N0 are the phytoplankton,
zooplankton, and inorganic nitrogen concentration of the flow entering
the volume. The remaining terms have been defined previously by
Equations 16, 23, 25, and 26. In the nutrient equation, only the direct
source of inorganic nitrogen, Wy, has been included; the organic feed-
back terms representing excreted nitrogen, etc., Equation 28, have been
dropped. Since the magnitude of W*- is uncertain and is .assigned by
comparison with observed data and computed model output, these feed-
back terms can be thought of as being incorporated in the value obtained
for WK.
The solution of Equations 47, 48, and 49 requires numerical tech-
niques. For such nonlinear equations, it is usually wise to employ a
simple numerical integration scheme which is easily understood and pay
the price of increased computational time for execution rather than using
a complex, efficient, numerical integration scheme where unstable be-
havior is a distinct possibility. A variety of simple methods are available
for .integrating a set of ordinary first order differential equations. In par-
ticular, the method of Huen, described in Ref. 65, is effective and stable.
It is self-starting and consists of a predictor and a corrector step. Let
y  /(*!/) he the vector differential equation and let h be the step size.
2. - 207

-------
The predictor is that of Euler: with yo the initial condition vector at to,
the predictor value of y at f0 + ^ ^
y* = 2/0 + V(fo, Vo;	(50)
The corrector value is simply
Vi = Vo + ~ [/(*o, yo) + /(
-------
Notation
Kx
I.
k'm
H
Km
f
K,
n
^ o
Po
azp
KmP
Dz
Zq
o.vr
C/Chl
No
Ws-
V
Table VII. Parameter Values for the Mostdale McxTel
Description	Parameter Value
0.1 day-' C
300 ly/day
Saturated growth
rate of phytoplankton
Light saturation intensity
for phytoplankton
Extinction coefficient
Depth
Michaelis constant for
total inorganic nitrogen
Photoperiod
Endogenous respiration
rate of phytoplankton
Zooplankton grazing rate
Influent phytoplankton
chlorophyll concentration
Zooplankton conversion
efficiency
Phytoplankton Michaelis
constant
Zooplankton death rate
Influent zooplankton carbon
concentration
Phytoplankton nitrogen-
. carbon ratio
Phytoplankton carbon tctotal
chlorophyll ratio
Influent total inorganic
nitrogen concentration
Direct discharge rate of
nitrogen
Segment volume
Phytoplankton total cell
count/phytoplankton
Zooplankton count/'
zooplankton carbon ratio
4.0 m~l
1.2 m
0.025 mg N/liter
0.5 + sin [0.0172 (t - 165)] day
0.005 day-1 'C"1
0.13 liter/mg - C - day
5.0 vtg Chl/liter
0.6 mg C/mg - C
60 jig Chl/liter
0.075 day-1
0.05 mg C/liter
0.17 mg N./mg - C
50 mg C ''mg - Chi
0.1 mg X/ liter
12500 lbs'day
9.7 X 10 ft'
100 cells/ml = 1.75 iig Chl/liter
104 No./liter = 1.30 mg C liter
trarily. However, the carbon-to-chlorophyll ratio which results (sec
Table VII) is within the range reported in the literature. The same
problem exists with the rotifer counts to rotifer carbon conversion: the
value used is given in Table VII.
The comparison of the model output and the observed data for the
two-year period for which data are available is shown in Figure 11. The
parameter values used in the equations are listed in Table VII.
It is clear from both the data and the model results that a classical
predator-prey situation is observed in 1966: the spring bloom of phyto-
plankton resulting from favorable temperature and light intensity pro-
vides the food for zooplankton, which then reduce the population during
<2 - AO J

-------
o
t-
ICO.OOO
60,000 [
I
j 60,000 !-
<\ I
_j -SO,000 |-
O UJ	1
>  2Q000j-
c.
6.C00
12.000
z -I
"S 8,000
^ 
St 2
ru
120
120
240
360
' as
I
o 2 0 6
cc	
O 2
z uj
-o ,0.4
it
Oz 0.2
120
120
J966
240
360
TIME
0AYS
1967
Figure 11. -Phytoplankton, zoovlankton, and total inorganic ni-
trogen; comparison of theoretical calculations and observed data;.
San Joaquin River, Mossdale, 1966-1967.
the summer. The decrease of the zooplankton and the subsequent slight
secondary bloom-of phytoplankton complete the cycle for the year. It Is
not clear, however, from a casual inspection of the data; whether' the
zooplankton population terminated the phytoplankton growth, as in
classical predaFor-prey situations, whether the nutrient cbriCentration
dropped to a limiting value that reduced the growth rate, or a1 combina-
tion of the two. This point is elaborated in the next section.
The situation in 1967 is quite different. No significant phytoplankton
growth is observed until late in the year. The controlling variable in this
case is the large advective flow during the spring and summer of 1967
(see Figure 10) which effectively washes out the population in the region.
Only when the flow has sufficiently decreased so that a population .can
2.-2./0

-------
develop do the phytoplankton show a slight increase. However, the
dropping temperature and light intensity level terminate the growth for
the year.
Growth Rate-Death Rate- Interactions
The behavior of the equations which represent the phytoplankton,
zooplankton, and nutrient systems in one volume can be interpreted in
terms of the growth and death rates of the phytoplankton and zooplank-
ton. The equations are as before
^ - (G, - Dp)P + |(P. - P)	(84)
^ = (C2 - Dz)Z + |(Z. - Z)	(55)
where F0 and Zo are the concentrations of phytoplankton and zooplankton
carbon in the influent flow, Q. A more useful form for these equations is
^ = IC, - (Dp + |)]P +	(58)
^ = [C2 - (Dt + |)]Z + |z.	(57)
A complete analysis of the properties of these equation is quite difficult
since the coefficients of P and Z are time variables and also functions of
F and Z. However, the behavior of the solution becomes more accessible
if the variation of these coefficients is studied as' a function of time. The
expressions GP  (DP -f- Q/V) and Gz  (Dz -f Q/V) can be con-
sidered the net growth rates for phytoplankton and zooplankton. The
advective or flushing rate, Q/V, is included in these expressions since it
acts as a death rate in one segment system.
The sign and magnitude of the net growth rate controls the behavior
of the solution. For a linear equation, for which the net growth rate is
not a function of the dependent variable (i.e., P or Z), the type of solu-
tion obtained depends on the sign and magnitude of the net growth rate.
That is, for the equation
^ = aP + 2.P,	(58)
where a'Q, and V are constant, the solution is
2.-2. I (

-------
P{t) = P(o) e + Po ^ (ea< - 1)
(59)
For a negative, that is, for a negative net growth rate, the solution tends
to the steady state value P0 Q/|a|V. However, for a positive, the solution
grows exponentially without limit. Thus, for a negative but |a| small, or
for a positive, the solution'becomes large; whereas for a negative but jaj
large, the solution stays small. -Hence, the behavior of the solution
can be inferred from the plots of the net growth rates. Figure 12a is a
plot of the following terms from the 1966 Mossdale calculation: GP with-
out the MichaelisMenton multiplicative factor includedi.e., the growth
rate at nutrient saturation denoted by GP (I,T); GP itself denoted by GP
(NJ,T)i.e., the growth rate considering the nutrient effects. The net
growth rate GP  (DP Q/V) is also plotted. Similarly, in Figure 12b,
the growth rate of zooplankton Gz, the mortality rate Dz, the flushing rate
Q(t)/V, and the net growth rate Gz  (D2 4* Q/V) aTe plotted.
0.6
>-
<
(E
0.4
z
-
0.2
2v
o*
t- a
x
z
3
a.
o
h-
>'
X
.a.
-0.2
180 240 300 360
120
TIME-DAYS
1966
0.2
-0.1
120 ISO 240 300 3 60
TIME-OAYS
60
Figure 12. Theoretical growth rates for phytoplank-
ton and zooplankton populations

-------
The analysis of the 1966 model calculations can now be made by
inspecting these figures. The net growth rate for the phytoplankton
GP  (Dp 4- Q/V) becomes positive at t = 85 days owing to an increase
in Gp, the result of rising temperature and light intensity, and a decrease
in O/V as the advective flow decreases. The positive net growth rate of
the population causes their numbers to increase exponentially fast until
th nutrient begins to be in short supply. This is evidenced by the de-
parture of the Gp curve from the Gp at nutrient saturation curve. At the
same time, the DP curve is showing a marked increase because of the
increased zooplankton population and their grazing. The result Is that
the net growth rate becomes zero and then negative as the zooplankton
reduce the phytoplankton population by grazing. The growth of the
zooplankton can be analyzed in a similar fashion using Figure 12b. The
net growth rate becomes positive when the phytoplankton population is
large enough to sustain the zooplankters. Then the zooplankton grow
until they have reduced the phytoplankton population to a level where
they are no longer numerous enough to sustain the zooplankton. The net"
zooplankton growth rate then becomes negative and the population
diminishes in size. This small zooplankton population no longer exerts a
significant effect on the death rate of the phytoplankton, DP, and its value
decreases, causing the net phytoplankton growth rate to become positive
again, and the smaller autumn bloom results. The decreasing tempera-
ture and light intensity and the increasing advective flow then effectively
terminate the bloom as the year ends.
Summary and Conclusions
A model of the dynamics of phytoplankton populations based on the
principle of conservation of mass has been presented. The growth and
death kinetic formulations of the phytoplankton and zooplankton have
been empirically determined by an analysis of existing experimental data.
Mathematical expressions which are approximations to the biological
mechanisms controlling the population are added to the mass transport
terms of the conservation-equation for phytoplankton, zooplankton, and
nutrient mass in order to obtain the equations for the phytoplankton
model. The resulting equations are compared with two years' data from
the tidal portion of the San Joaquin River, California. Similar compari-
sons have been made for the lower portion of Delta and are reported
elsewhere (62).
It is recognized that certain parameters in the model have been
estimated from the data which are then used to demonstrate the veracity
of the model. The parameters used in the verification were either ob-
tained from prototype measurements or estimated from the range of
2.-H3

-------
values reported in the literature. The refinement of the later set of param-
eters was made by comparing the observed 1966 data and calculated
results. The model was further verified by applying the parameters ob-
tained in the 1966 analysis to the c ata of the following year. The parame-
ter values finally used were all within the ranges of reported literature
values. The agreement achieved between the available data _ and the
model calculations is sufficiently encouraging to prompt further effort
in this direction.
The primary aim of this investigation, presenting a useful model
as a component in solution of the eutrophication problems, in our opinion,
has been achieved. The resulting equations are admittedly complex and
require numerical methods for solution. It is anticipated as with all model-
ing activities that the structure presented herein will be expanded and
modified in the future to incorporate additional features of the eutrophi-
cation phenomena. In particular, the model as it is presently structured
does not address the species changes that, might result as the environment
is changed. This is a problem of some consequence, and refinements and
expansion of tlae number of species considered is an area for future work
(12). However, the initial application of these equations to. an actual
problem; area with specific eutrophication problems has been sufficiently
successful to .support, its engineering use as a preliminary step in the
assessment of a potential or actual eutrophication. problem.
Acknowledgment
The authors are pleased to acknowledge the participation of John L.
Mancini of Hydroscience Inc. in the research reported herein, as .well as
the assistance of Gerald Cox and Jack Hodges of the Department of
Water resources and Harold Chadwick of the Department of Fish and
Game, State of California.
The research was sponsored in part by a research grant to Manhattan
College from the Federal Water Quality Administration and in part from
research funds made available by Hydroscience, Inc.
The application of the phytoplankton. model to;.the San Joaquin
River was sponsored by the California Water Resources Commission and
carried out by Hydroscience Inc.
Literature Cited
(1)	Riley, G.. A., Theory of Food-Chain Relations in the Ocean, "The Sea,"
p. 438-63, M. N. Hill, Ed., Interscience, New Yorkt 1963.
(2)	Riley, G. A., "Factors Controlling Phytoplankton Populations on Georges
Bank," /. Marine Res. (1946) 6 (1), 54-73.
(3)	Riley, G. A., "Seasonal Fluctuations of the Phytoplankton Populations in
New England Coastal Waters," J. Marine Res. (1947) 6 (2), 114-25.
a-sli +

-------
(4)	Riley, C. A., Von Arx, R., 'Theoretical Analysis of Seasonal-Changes in
the Phytoplankton of Husan Harbor, Korea," J. Marine Res, (1949) 8
(1), 60-72.
(5)	Riley, C. A., Stommel, II., Rumpus, D. F., "'Quantitative Ecology of the
Plankton of the Western North Atlantic," Bull. Bingham Oceanog, Coll,
(1949) 12 (3),1-169.
(6)	Steele, J. H., "Plant Production on Fladen Cround," J. Marine Biol, Assoc.
U.K. (1956) 35, 1-33.
(7)	Steele, J. H., "A Study of Production in the Culf of Mexico," J, Marine
Res. (1964 ) 22,211-22.
(8)	Steele, J. H., Notes on Some Theoretical Problems in Production Ecology,
"Primary Production in Aquatic Environments," C. R. Goldman, Eo.,
Mem. Inst. Idrobiol., p. 383-98, 18 SuppL, University of California
Press, Berkeley, 1965.
(9)	Davidson, R. S., Clymer, A. B., "The Desirability and Applicability of
Simulating Ecosystems," Ann.'N. Y. Acad. Sci. (1966) 128 (3), 790->4,
(10)	Cole, C. R., "A Look at Simulation through a Study on Plankton Popula-
tion Dynamics," Report BNWLt485, p. 1-19, Battelle Northwest Labo*
ratory, Richland, Washington, 1967.
(11)	Parker, R. A., "Simulation of an Aquatic Ecosystem," Biometrics (1968)
24 (4), 803-22.
(12)	Chen, C. W., "Concepts and Utilities of Ecologic Model," J. Sanit, Eng.
Dio., Am. Soc. Civil Eng. (Oct. 1970) 96, 1085-97.
(13)	Thomann, R. V., O'Connor, D. J., DiToro, D. M., "Modeling of the Nitro*
gen and Algal Cycles in Estuaries," 5th Intern. Water Pollution Res,
Conf., San Francisco, Calif., July 1970.
(14)	Thomann, R. V., "Mathematical Model for Dissolved Oxygen," J, Sanit,
Eng. Div., Proc.Am. Soc. Civil Eng. (October 1963) 83, SA5, 1-30.
(15)	O'Connor, D. J., Thoinann, R. V., "Stream Modeling for Pollution Con-
trol," Proc. IBM Sci. Computing Symp. Environ. Sci November 14-16,
1966,	p. 269.
(16)	Hutchinson, G. E., "A Treatise on Limnology Vol. II. Introduction to
Lake Biology and the Limnoplankton," p, 30&-54, Wiley, New York,
1967.
C7) Strickland, J. D. H., Production of Organic Matter in the Primary Stages
of the Marine Food Chain, "Chemical Oceanography," Vol, 1, p. 503,
J. P. Riley and C. Skivow, Eds., Academic, New York, 1965,
(18)	Lund, J. W. C., 'The Ecology of the Freshwater Phytoplankton," Biol,
Rev. (1965) 40, 231-93.
(19)	Raymont, J. E. G., "Plankton and Productivity in the Oceans," p. 93-406,
Pergainon, New York, 1963.
("20) Vollenweider, R. A., Ed., "Manual on Methods for Measuring Primary
Production in Aquatic Environments," Ch. 2, p. 4-24, Blackwell Sci'
entific Publications, Oxford, England, 1969.
(21)	Tamiya, H., Hase, E., Shibata, K., Mituya, A., Iwamura. T., Nihei, T.,
Sasa, T., Kinetics of Croicth of (Jhlorefla with Special Reference to Its
Dependence on Quantity of Available Light and on Temperature,
"Algal Culture From Laboratory to Pilot Plant," p. 204-34, ]. S. Burlew,
Ed., Publ. 600, Carnegie Institute of Washington, D. C., 1964.
(22)	Yentsch, C. S., Lew, R. W., "A Study of Photosvnthetic Light Reactions,"
J. Marine Res. (1966) 24 (3).
(23)	Spencer, C. P., Studies on the Culture of a Marine Diatom," J. Marine
Biol. Assoc. U.K. (1954) 28; quoted by Harvey. H. W 'The Chem-
istry and Fertility of Sea Waters,' p. 94, Cambridge University Press,
2. -2LJ S~

-------
(24) Myers, J., Growth Characteristics of Algae in Relation to the Problem
of Moss Culture, 7Algal Culture From Laboratory to Pilot Plant,"
p. 37-54, Publ. 600, J. S. Burlew, Ed., Carnegie Institute of Washing-
ton, D. C., 1964.
Sorokin, C., Krauss, R. W., "The Effects of Light Intensity on the Growth
Rates of Green Algae," Plant Physiol. (1958) 33, 109-13.
Sorokin, C., Krauss, R. W., "Effects of Temperatures and Illuminance on
Chlorella Crowth Uncoupled from Cell Division," Plant Phusiol. (1962)
37, 37-42.
Fogg, G. E., "Algal Cultures and Phytoplankton Ecology," p. 20, Univer-
sity of Wisconsin Press, Madison, Wis., 1965.
Ryther, J. H., "Photosynthesis in the Ocean as a Function of Light In-
tensity," Limnol. Oceanog. (1956) 1, 61-70.
Shelef, G., Oswald, W. J., McGauhey, P. H., "Algal Reactor for Life Sup-
port Systems," J. Sanit. Eng. Div., Proc. Am. Soc. Civil Eng. (February
1970) 96, SA1.
Vollenweider, R. A., Calculation Models of PhotosynthesisDepth
Curves and Some Implications Regarding Day Rate Estimates in Pri-
mary Production Measurements, "Primary Production in Aquatic
Environments," C. R. Goldman, Ed., Mem. Inst. Idrobiol., p. 425-57,
18 Suppl./ University of California Press, Berkeley, 1965.
Riley, G. A., "Oceanography of Long Island Sound 1952-1954. II. Physi-
cal Oceanography," Bull. Bingham Oceanog. Coll. (1956) 15, 15--46.
Small, L. F., Curl, H., Jr., 'The Relative Contribution of Particulate Chlo-
rophyll and . to the Extinction of Light, off the Coast of Oregon,"
Limnol. Oceanog. (1968) 13 (l), 84.
Oswald, W. J., Gotaas, H. B., Ludwig, H. F., Lynch, V., "Photosynthetic
Oxygenation," Sewage Ind.. Wastes (1953) 25 (6), 692.
Azad, H. S., Borchardt, J. A., "A Method JFor Predicting the Effects of
Light Intensity on Algal Growth and Phosphorus Assimilation," ]. Wa-
ter Pollution Control Federation (1969 ) 41 (11), part 2.
Dugdale, R. C., "Nutrient Limitation in the Sea: Dynamics,' Identifica-
tion, and Significance," Limnol. Oceanog. (1967) 12 (4), 685-95.
Eppley, R. W., Rogers, J. N., McCarthy, J. J., "Half Saturation Constants
for Uptake of Nitrate and Ammonium Dy Marine Phytoplankton," Lim-
nol. Oceanog. (1969) 14 (6), 912-20.
Ketchum, B. H., "The Absorption of Phosphate and Nitrate by Illumi-
nated Cultures of Nitzschia Closterium," Am. J. Botany (June 1939) 26.
Thomas, W. H., Dodson, A. N., "Effects of Phosphate Concentration on
Cell Division Rates and Yield of a Tropical Oceanic Diatom," Biol. Bull.
(1968) 134 (1), 199-208.
Lake Tahoe Area Council, South Lake Tahoe, Calif., "Eutr&phipation of
Surface WatersLake Tahoe, May 1969," p. 33, 95705; Report for
Federal Water Pollution Control Adm., Dept. of Interior, WPD 48-02.
Riley,.G. A., "Mathematical Model of Regional Variations in Plankton,"
Limnol. Oceanog. (1965) 10 (Suppl.), R202-R215.
Gerloff, Skoog, "Nitrogen as a Limiting Factor for the Growth of Micro-
cystis Aerugmosa in Southern Wisconsin Lakes," Ecology (1957) 38,
556-61.
Maclsaac, J. J., Dugsdale, R. C., "The Kinetics of Nitrate and Ammonia
Uptake by Natural Populations of Marine Phytoplankton," Deep Sea
Res. (1969) 16, 415-22.
Kuentzel, L. E., "Bacteria, Carbon Dioxide, and Algal Blooms," ]. Water
Pollution Control Federation (October 1969) 41 (10).
Droop, M. R., Organic Micronutricnts, "Physiology and Biochemistry
of Algae," p. 14]-60, R. A. Lewin, Ed., Academic, New York, 1962.
A - A / (c

-------
(45)	Adams, J. A., Steele, J. H., Shipboard. Experiments on the'Feeding of
Calanus Finmarchicus, "Some Contemporary Studies in Marine Sci-
ence," p. 19-35, H. Barnes, Ed., C. Allen and Unwin Ltd., London,
1966.
(46)	Mullin, M. M., Brooks, E. R.t "Laboratory Culture, ^Growth Rate, and
Feeing Behavior of a Planktonic Marine Copepod," Limnol. Oceanog.
(1967)	12 (4), 657-66.
(47)	Anraku, M., Omori, M.t "Preliminary Survey of the Relationship Between
the Feeding Habits and the Structure of the Mouth Parts of Marine
Copepods," Limnol. Oceanog. (1963) 8 (1), 116-26.
(48)	Wright, J. C.t "The Limnology of Canyon Ferry Reservoir. I. Phytoplank-
ton-Zooplankton Relationships," Limnol. Oceanog. (1958) 3 (2),
150-9.
(49)~Burns,	C. W., "Relation between Filtering Rate Temperature and Body
Size in Four Species of Daphnia," Limnol. Oceanog. (1969) 14 (5),
693-700.
(50)	Ryther, J. H., "Inhibitory Effects of Phytoplankton upon the Feeding of
Daphnia Magna with Reference to Growth, Reproduction and Sur-
vival," Ecology (1954 ) 35, 522-33.
(51)	McMahon, J. W., Riglerj F. H., "Feeding Rate of Daphnia Majgna Straus
in Different Foods Labeled with Radioactive Phosphorus, Limnol.
Oceanog. (1965) 10 (1), 105-13.
(52)	Conover, R. J., "Oceanography of Longjfeland Sound, 1952-1954. VI.
Biology of Acartia Clausi and A. tonsa," Bull. Bingham Oceanog. Coll.
(1956) 15, 156-233.
(53)	Mullin, M. M., "Some Factors Affecting the Feeding of Marine Copepods
of the Genus Calanus," Limnol. Oceanog. (1963 ) 8 ( 2), 239-50.
(54)	Bums,.C..W., Rigler. F. H., "Comparison of Filtering Rates of Daphnia
in Lake Water and in Suspensions of Yeast," Limnol. Oceanog. (1967)
12 (3), 492-402.
(55)	Riley, G. A.. "A Theoretical Analysis of the Zooplankton Population of
Georges bank," J- Marine Res. (1947) 6 (2), 104-13.
(56)	Conover,A. J., "Assimilation of Organic Matter by Zooplankton," Limnol.
Oceanog. (1966) 11,338-45.
(57)	Lotka, A. J., "Elements of Mathematical Biology," p. 88-94, Dover, New
York, 1956.
(58)	Bishop, J. W., "Respiration Rates of Migrating Zooplankton in the Natural
Habitat," Limnol. Oceanog. (1968) 13 (1), 58-62.
(59)	Comita, G. W.. "Oxygen Consumption in Diaptomus," Limnol. Oceanog.
(1968)	13 (1), 51-7.	,	:
(60)	Martin, J. H., "Phytoplankton Zooplankton Relationships in Narragansett
Bay III," Limnol. Oceanog. (1968) 13 (1).
(61)	Vollenweider, R. A., "Scientific Fundamentals of the Eutrophication of
Lakes and Flowing Waters, with Particular Reference to Nitrogen and
Phosphorus as Factors in Eutrophication," p. 117, Organization for Eco-
nomic Cooperation and Development Directorate for Scientific Affairs,
Paris, France, 1968.
(32) O'Connor, D. J., DiToro, D. M., Thomann, R. V., Mancini, J. L., "Phyto-
plankton Population Model of the Sacramento-San Joaquin Delta Bay,"
Technical Report to Department of Water Resources, State of Cali-
fornia, by Hydroscience. Inc., Westwood, N. J., 1971.
(63)	Davis, H. T., "Introduction to Nonlinear Differential and Integral Equa-
tions," p. 99-109, Dover, New York, 1962.
(64)	Department of Water Resources, State of California, private communica-
tion, 1966.'
A-3./7

-------
(65)	Stiefel, E. L., "An Introduction to Numerical Mathematics," p. 163, Aca-
demic, New York, 1966.
(66)	Hamming, R. W., "Numerical Methods for Scientists and Engineers," p.
194-210, McGraw-Hill, New York, 1962.
(67)	Levy, H., Baggott, E. A., "Numerical Solutions of Differential Equations,"
p. 91-110, Dover, New York, 1950.
Received May 27, 1970.
Z-3L it

-------
SIMPLIFIED PHYTOPLANKTON MODELING FOR STREAMS1
Introduction
It is becoming increasingly apparent that as more advanced degrees of
waste treatment are installed, the water quality of streams may shift into
more difficult problem contexts. For example, when primary or poorly
treated secondary effluent was discharged to a stream, the principal water
quality effects were sludge deposits, low or anaerobic dissolved oxygen
conditions, high turbidity and an aquatic ecosystem dominated by pollution
tolerant organisms. As the treatment level increases, light penetration
is enhanced, there is a shift to an aquatic ecosystem that may be dominated
by the primary producers - the phytoplankton and the periphyton as well as
rooted aquatic macrophytes. The nutrient balance then becomes more important
since the biomass may be stimulated by excess nutrient discharges. High
concentrations of phytoplankton or periphyton can result in marked diurnal
variations in dissolved oxygen. Therefore, as the mean value of D.O. is
improved, the diurnal range may Increase due to the stimulated presence of
the primary producers. It is important then to analyze the potential im-
pacts of nutrient discharges on resulting plant biomass. In these notes,
phytoplankton are considered as the principal plant form resulting from
the discharge of nutrients.
The Principle of the N/p Ratio
Considerable progress has been made in recent years in describing the
basic mechanisms of phytoplankton dynamics in lakes and estuaries. The
models that have been developed usually involve complicated interactions
between nutrients and phytoplankton growth and hence do not generally lend
themselves to simplified computations. Other simplified models for total
phosphorus in lakes have also been developed but the applicability to
streams is not direct. In order to provide a first and very simplified
approach to a nutrient balance in a stream, the ratio of the nitrogen to
phosphorus concentration is useful.
1 Robert V. Thomann and John Mueller
-2 - 1 / J

-------
The N/p ratio can be examined especially where there is a tradeoff to
be made between nitrogen removal or phosphorus removal. One can see this
tradeoff by examining the total nitrogen (TN) or inorganic nitrogen (IN)
to total phosphorus (Tp) or inorganic phosphorus (Ip) ratios under differ-
ent levels of treatment. When TN/Tp or IN/Ip are less than about 7-10,
nitrogen will often be the limiting nutrient, while if the ratio is greater
than about 7-10, phosphorus is considered as the limiting nutrient. The
use of these bounds on the ratio can be easily seen by the following calcu-
lation.
Consider that a certain percentage of the inorganic nutrient forms
(the forms available for plant uptake) will be ultimately converted to
plant biomass. A good estimate is about 50-75%. With the cell stoichio-
metry of 1 yg P/yg chlorophyll and 7 yg N/yg chlorophyll, the maximum amount
of biomass that would result can be estimated.
Figure 1 shows the basic principle. For an effluent concentration of
22 mg Inorganic N/i. and 5 inorganic p/, (representative of high rate acti-
vated sludge (HRAS), without any phosphorus removal), the following maximum
chlorophyll concentrations can be computed using a 75% conversion:
IN: 22 Sf^^S)  1 ^ Ch^T  1000 ^ = 2357 ghlr
I	7 ygN	mg	
Ip: 5 HfP(.75)  1 M Ch^r  1000 = 3750 flor
	ygP	g	I
Applying the notion of a limiting nutrient, the total amount of phos-
phorus would not be converted to the 3750 yg chlor/Z because the nitrogen
then would be totally exhausted. Therefore, nitrogen would run out first,
would limit growth and the maximum biomass would be 2357 yg chlor/Z. Of
course, there may be many reasons (.e.g. length of river) that would prevent
this maximum level from being reached. The reasoning underlying the .boun-
dary of TN/Tp of 7-10, is therefore founded on the cell stoichiometry of
the phytoplankton and a conversion of available nutrient forms. At high
(> 7-10) TN/Tp, the phosphorus concentration would run out before nitrogen
and hence would limit growth..
k - J. Jo

-------
UjJo Pj)i. <>w^/
V?
jT
l-. V. V
r?
i
zz
VI
Z*.,
NA.
pome

22ro
>
^Va> A
tklo*-
2L2r7

Ihffyg /t//'/.
LI **i'i-i
tful. ckh*.
fAa* chl$r* phy Jl I\j "h
Xnj j. I """J
k) H.j)i r aU	jbly.
e^.)uvi4 i>\> i4^k P hti. t Vk (VJ
J?
Z.Z
r r
-EZEL
Tw 0 rgA h/c

xxxx:
ZZ7
771
%

Tyflrj,
7i"0	*n I hi
fit**, Chi:'.
M&H. cUljrt P^yll 1 tr$.	1**'$.
Figure 1. Illustration of principle of nitrogen - phosphorus
ratios in controlling phytoplankton biomass
S.-a. 2. /

-------
Figure 1(b) shows the situation where HRAS with phosphorus removed
is applied. Now the IN/Ip ratio is 22, the maximum biomass possible (at
75% inorganic phosphorus conversion) is 750 yg/Ji chlor and phosphorus
limits the maximum production.
At different levels of treatment, the ratio of TN/Tp in the stream
at the point of discharge will vary depending on the ratio of river flow
to effluent flow. Table 1 summarizes this ratio for streams that are
dominated by the plant effluent (i.e., approximately 50% or greater of
the river flow is effluent flow). Note that under higher rate activated
sludge and HRAS plus nitrification, nitrogen would be limiting. But if
a biomass problem exists and some nutrient control is necessary, then
HRAS and phsophorus removal will shift the system from nitrogen to
phosphorus removal. Again, under certain conditions of effluent flow
to river flow, phosphorus may be the limiting nutrient under different
levels of treatment.
Figure 2 shows the relationship between the ratio of TN/TP for
different ratios of the plant effluent flow to the total river flow. The
upstream flow is assumed to have the followin-g nutrient characteristics:
TN = 1.45 mg N/J,
Tp = .052 mg P/A
TN/Tp = 28
Note that in general, runoff from non-point sources will tend to have
high TN/Tp ratios indicating that phosphorus is the limiting nutrient for
non-point source situations. Figure 2 shows that when the effluent flow
is less than about 2% of the total river flow, phosphorus would tend to be
the limiting nutrient (TN/Tp > 10). For effluent/river flow ratios greater
than about 2%, the limiting nutrient depends on the treatment process. For
all ratios, HRAS and P removal results in phosphorus a limiting situation.
Table 2 shows some N/P ratios for various sources. It can be seen that
non-point source runoff tends' to have high N/p ratios while marine waters
tend to have low N/p ratios.

-------
TABLE 1
N/p and Limiting Nutrient for Different Treatment Levels
Treatment Level''
Eff.
TN
Cone
IN
.. mg/Jl-/
Tp Ip
TN
Tp
IN
IP
Max. .,
chlor.
VR/*
Limiting
Nutrient
Raw
t
40
25
10
7
4
.3.6
2678
N
HRAS
27
22
8
5
3.4
4.4
2357
N
HRAS + Nitrif.
26
22
7
5
3.7
4.4
2357
N
HRAS + P removal
27
22
1
1
27.0
22.0
750
P
HRAS + N removal
3
2
8
5
0.4
0.4
214
N
HRAS + P rem. + N rem.
3
2
1
1
3.0
2.0
214
N
^HRAS - High rate activated sludge
2/
 TN, IN - total and inorganic nitrogen respectively; Tp, Ip - total and inorganic
phosphorus, respectively
3/
Calculated from .75 conversion of inorganic nutrient, 1 yg chlor/yg P
and 1 yg chlor/7 yg N; i.e. min {.75 (Ip)  1000; .75 (IN)  1000}
7
Jl - 2.2 3

-------
TABLE 2
1/
N/p Ratios for Point Source, Non-Point Source and Marine Waters
Source
Point - HRAS w/o P removal
HRAS w P removal
Non-Point - 50% Agric.
& Urb.
Marine Waters
TN
IN
Limiting
IE
IE
Nutrient
3
4
ft
27
22
P
28
25^
P

2
N
Reference
Omernik (1977)
Goldman et al.(1973)
^TN/Tp - Total nitrogen/Total phosphorus; IN/Ip - Inorganic nitrogen/inorganic phosphorus,
both on mg/Jl/mg/i, basis
2/
	For IN = 0.53 mg N/ and Ip = .021yng P/Jl in non^point surface runoff
3/
	For IN = 33 yg N/i. and Ip = 15 yg P/


-------
RATIO
TP
...L -
001
^	Figure 2. TN/TP a9 a function of plant effluent flow/total river flow for different levels of treatment.
Treatment effluent concentrations from Table 1, river concentrations: TN = l.A5mg N/; TP = .052 mg P/.
*1

-------
The N/p ratio is therefore a useful first approximation to determining
the significance of each nutrient in controlling phytoplankton biomass. One
should not however necessarily conclude that because nitrogen is the limiting
nutrient in a given situation that nitrogen is the nutrient to be controlled.
As the point source example indicated if a system were controlled by nitrogen,
the installation of HRAS + P removal would shift the system to phosphorus
limitation.
A Simple Stream Model Using the Principle of N/p Ratio
For streams there are several aspects of the above discussion that
should be recognized.
1)	The distance and hence the time of travel for stream nutrient
problem contexts generally tend to be short, perhaps on the order of
less than 10 days. This would be equivalent to distances of less than
about 100 miles for streams moving at 1 ft/sec. Most stream stretches
of interest would be shorter than this so that the travel time would be
less than the 10 day period. As a result, the chlorophyll biomass may
not have enough time to grow to the maximum level calculated from the N/p
ratio approach discussed above. The rate of growth of the phytoplankton
and the travel time of the stream length are therefore of specific im-
portance .
2)	Phytoplankton growth dynamics indicate that the concentrations
of nitrogen and phosphorus that limit growth are relatively small compared
to normal ambient levels of nutrients in streams subject to point source
discharges. This can be seen by considering Eq. 8-22 of these notes-, i.e.
G = G(T)  G(I) * GO!)	(1)
P
where G^ is the growth rate of the phytoplankton (day ), G(T), G(I) and
G(N) are the effects of temperature, light and nutrients respectively
on the growth rate. From Eq. 8-28, the nutrient effect is given by:
GCN) = Min	(2)
At concentrations of the nutrient greater than about 5 times the half
saturation concentration, the effect of the nutrient on the growth rate G(N)
is less than 10%. That is, at IN and Ip at five times and , G(N) = 0.83


-------
and therefore has a relatively small effect on the overall growth rate of
phytoplankton as seen from Eq. (1) above. Table 8-6 of these notes shows
that the Michaelis concentration (the concentration at which growth rate
is reduced by 1/2) for nitrogen is about 10 - 20 Vg N/ and for phosphorus
is about 1 - 5 vg P/L Therefore, for IN and Ip greater than about 0.1 mg
N/& and .025 mg P/, respectively, these nutrients will not have any effect
on the growth rate. Considering Tables 1 and 2, it is seen that, depending
on stream dilution, the concentrations of IN and Ip will generally be sig-
nificantly above thse levels. Figure 3 shows this fact for upstream IN
and Ip of 0.53 mg N/i and 0.21 mg P/I respectively (Omernik, 1977). As
indicated, for nitrogen, the concentration at the outfall never reaches
limiting levels simply because the upstream IN concentrations alone is above
the maximum limiting concentration of about 0.1 mg N/2,. For phosphorus, when
the effluent flows are greater than about 5 - 10% of the total river flow,
then the Ip at the outfall will be above maximum limiting phosphorus con-
centration. It should be stressed however that these considerations are
meant as a guide only since limiting nutrient concentrations may be reached
at some downstream location from the outfall. As a general rule however,
Figure 3 indicates that for ratios of effluent flow to total river flow of
greater than about 10%, both phosphorus and nitrogen will tend to be present
in excess concentrations. For "small" streams where effluent flow is equal
to greater than upstream flow especially at drought conditions, then it is
almost certainly true that the nutrients will be in excess' and will not limit
phytoplankton growth for a given stretch, of river.
A simple model can now be constructed using the above considerations
and the principle of the N/p ratio. Assume that a steady-state condition
prevails. The analysis is therefore representative of a given flow and
temperature regime that has held steady long enough for conditions to have
reached an equilibrium state. Consider the phytoplankton equation at steady-
state as:
u " = CGp - DP - VH)P  V	>
where P is phytoplankton chlorophyll Oj chlor/Jt) G is given by Eq. (1).
-1	P
0^ is respiration rate {day ], vg is net settling from water column (m/day).
a - a a i

-------

X
@

HQfiS

	 	 	 	 ?- .0 ar - tftH. I>'+', /;~j
.0/ 0.1
w ^ P7a ur*
w
Jw4",, /Vc/
^ a /M
, .
4 J ^ I
Htffls
hlftflS f /V
/;~*(/ }
. u \
 00^
,0 I
X A/r 6ily*
-------
*
H is stream depth, u is stream velocity, x is distance and t is travel
time (day) and:
G = G -D -v/H	(4)
n p p s
If G # f(IN,Ip) then G is a function only of temperature, light, extinc-
P	n
tion coefficient and net settling velocity. Figure 4 shows the behavior of
G as a function of several environmental variables representative of con-
n
ditions in smaller shallow streams. Thus the assumption of excess nutrients
permits solution of Eq. (3) as:
P = P exp (G )t	(5)
o	n
where P is the phytoplankton chlorophyll at the outfall,
o
Figure 5 shows the possible forms of Eq. (.5). Because of light limitations
and settling effects, G^ may be less than zero in which case there will be an
exponential decrease of phytoplankton with travel time. G^ may also be zero
where growth is just balanced by respiration and settling. The biomass then
remains constant with distance. Finally, G^ may be positive resulting in ex-
ponential growth of the phytoplankton. The ultimate biomass then results from
conversion of the IN or Ip at the outfall as discussed previously.
The inorganic nutrient equation can now be examined in the light of the
preceding N/p discussion. Assume that a given fraction of IN or Ip will
constitute the nutrient pool from which the growth of the phytoplankton will
draw nutrients. Let the inorganic pool nitrogen = and the inorganic pool
phosphorus = p^. A fraction of 0.75 used earlier is a good approximation,
i.e. 75% of the total inorganic nutrient is available for conversion to
phytoplankton. The residual 25% of the nutrient recycles into the detrital
pool and less available forms and is also lost by settling.
Therefore, the nutrient equation is for phosphorus:
dpi
J" - -aG P	(6)
dt P P
and for nitrogen:
dNi
t7)


-------



T

v

4

T7



4J
mg

w


VP

1

ui

V-

<

tc

X

-

i

o

ec





X
1
a.
Xj

O)
h
0
Ul

z
o.a-
-o.z-
-0.+-

^/h 0*^0
rKeH=I.O
K-H= 10.0
-0.6-

-l.o-
Fob laotK plotsl
Ta = laoo jUn^Uy/jUy (o^t^-p)
Ty a 300
f c 0.6"
F <-
VARIATION of H6T PHYTO. GRovdSU RATC witH TEMP, LIGHT j SBTTL/A/G

-------
?oi > 4-
5o^*t 

a i	i
L**y
$t*tr

-------
where a^ = 1 yg phos/y chlor and a^ = 7 yg N/yg chlor. The chlorophyll
is given by Eq. (.5) and substituting into Eqs. (6) and (7) and solving
gives:
a G P	G t*
Pi = "V"2 (1 " 6 11 ) + Pio	C8)
n
for pi > 25 yg P/l
and
aG P	G t*
Ni = V  CI " e n ) + Nio	(9)
n
for N > 100 yg N/A
where piQ and are phosphorus and nitrogen at the outfall in the river
and note that the equations are only applicable for the inorganic nutrients
above the maximum limiting concentration of p^ = 25 yg/i. and of 100 yg/.
If estimates of G^ and Gn are obtained from previous expressions and Pq
and initial conditions at outfall are available, then the travel time to
reach the maximum nutrient concentration can be computed. This will then
fix the maximum biomass to be expected over that reach. Solving Fig. (8)
k
for t^^ at = 25 yg P/Ji gives:
_ !_ o P' + P , " 25
25 G 			CIO)
n
P
a G P
where	P' = p p 	(10a)
o G
n
k
Figure 6 shows t^ for various conditions on the parameters. Using G^ = 1/day
and Gr = 0.1/day, and for Poi the initial available phosphorus concentration
of greater than 1000 yg P/H, (see Figure 3), which covers small effluent domin-
k
ated streams with HRAS and w/o P removal, Figure 5 indicates that t^ is gener-
ally greater than 5-10 days. Therefore, for small effluent dominated streams,
if the study length is less than about 5-10 days, the phosphorus will still be
above 25 yg P/& and therefore in excess. At average velocities of 0.5 - 1 ft/sec,
this is equivalent to about 40 - 160 miles, well within the study reaches usually
under investigation. Note however from Figure 6 that the phytoplankton concen-
tration at the outfall is an important parameter to be specified. At high initial
chlorophyll levels at the outfall the time of travel to reach the ultimate con-
2 - A 3 J

-------
t
IS.
(days)
10.0
1.0
O *1
> -'
_/
XX
Jin I I'lJ

/o	^0O	/ooo
Figure 6. Relationship between t^, the travel time to pt of 25 \ig/l and
nutrient and phytoplankton parameters.

-------
centration of phytoplankton is of course markedly reduced since a sufficient
"seed" biomass already exists at the outfall. For small streams however one
would not normally expect upstream concentrations to be greater than 100
Ug chlor/JL
In this simple model then, the only way in which the maximum phytoplankton
biomass will decrease as a function of nutrient removal at a point source is to
reduce the time to reach the maximum limiting nutrient concentration. Figure 7
A	it
shows this effect. If t?(. remains greater than t , the actual stream length
/ j	3
after phosphorus removal then there will be no reduction in biomass. This is
because the stream is simply not long enough for a given net growth, rate to
result in a nutrient limitation.
To summarize this simple model then, the following procedure is suggested.
1)	Compute G from Eq. (4) and Eqs. 8-29 and 8-30, or
n
estimate from available phytoplankton data on the
stream using Eq. (5).
2)	For a given inorganic phosphorus concentration at the outfall
estimate percent available for phytoplankton growth, say 75%.
*
3)	Calculate t_s from Eq. (10) and compare actual stream length
* * * * *
t to t,t, If t is less than toc, then P = P exp G t .
a 25	a	25	max o	n a
* *
If t is greater than t,- then the biomass is at least P =
a	25	max
*
Pq exp 6^25 and is probably slightly greater than this amount.
4)	Estimate the new p^^ under a phosphorus removal program.
*
5)	Calculate the new t^ under the removal program.
* * * ~
6)	Compare (.t-,-) to t . If (tnc) < t then a biomass reduction
25 new a	25 new a
will occur and the maximum biomass is given approximately by P = P
* * * 
exp G Ct-c) . If Ctc) > t then no reduction in biomass will
r n 25 new	25 new  a
occur as a result of the treatment program.
The case where G = 0 is an interesting one. For this case, P = P , a
n	o
constant. Therefore,
dpi
T " "a-G_p-	(ID
dt
*	p p o
2 -2 3V-

-------
JU ?
-  
clh'"r-
[/^thhr
Figure 7. Relationship between phytoplankton chlorophyll and travel time
showing reduction in biomass due to reduction in time of travel
to limiting nutrient.
a - a 3 a"

-------
which is also a constant. The inorganic phosphorus would therefore decline
linearly with travel time as:
p. = -a G P t + p	(12)
ri p p o	io
*
The distance to t^ therefore:
* pi'25
25 a G P
p p o
However, it can be noted that for this case, reduction of nutrients at the source
will not alter the biomass. Again this	only applies for the excess nutrient
* *
region. If p, is reduced such that t	> Ct~c) then it can be presumed that
 io a 25 new
a reduction in biomass will occur but the actual reduction cannot be computed
since it will represent the limiting nutrient region.
Extension of Simple Stream Model
One of the more sensitive assumptions made in the preceding simple model
is the specification of the amount of inorganic nutrient available for con-
version. Since this can result in a 25-50% reduction of outfall nutrient
available for phytoplankton growth, it is an assumption that can be further
examined. Consider again the reach of the stream where the nutrients are
considered to be in excess and examine two nutrient forms: pQ as the organic
or less available form of phosphorus and p^ as the inorganic phosphorus form
available for uptake by the phytoplankton. In this context, p^ is operationally
defined as total phosphorus biomass the sum of phytoplankton phosphorus and
dissolved inorganic phosphorus. The three equations then that describe this
interaction are:
dp	v
;-DP-K p - Hr P	<14)
, *	oi o H ro
at
dpi
r = K p - a G P	(15)
dt* oi o p p
* - G P	(16)
dt n
2 ~ 3 3 (o

-------
where K . is the hydrolysis or biodegradation of organic forms to inorganic
01
phosphorus and v is the net loss rate of the organic phosphorus. Since
so
nutrients are in excess, Eq. (16) is decoupled from Eqs. (.15) and (14) and
the solution is given by Eq. (5). Substitution of this equation into Eq.
(14) gives the following:
dp	*
r + K p = DP exp G t	(17)
_ * o o o	n
at
where K K . + v /H. The solution is:
o oi so
DP G t* -K t*	-K t*
0/11	0\.	O	/ion
po= infr(e -e > + pooe	C18)
o n
where pqq is the organic phosphorus at the outfall.
Substitution of this equation and Eq. (5) into Eq. (15) permits solution of
the inorganic nutrient form as:
* *
G t	-K t
pi = PilCe n " 15 + Pi2a " e  ) + pio	C19)
where
i K 
-------
by high chlorophyll concentrations. However, the relationship between the
resulting phytoplankton biomass and the dissolved oxygen resources may be
of significant concern. This is especially true for the diurnal variations
in D.O. occasioned by the phytoplankton. The basic D.O. equation including
only sources and sinks due to phytoplankton is:
dc
u -rr*- - K (c - C ) + P' - R'	(20)
dx asp	av av
where c is the D.O. variation due to photosynthetic effect K is the re-
P	a
aeration coefficient and P'av and R'av are the average daily phytoplankton
D.O. production and respiration respectively. Now:
P' = a G P	(21)
av op p
R' = a DP	(22)
av op
where a^ = 0.133 - 0.266 mg DO/yg chlor. If now is designated as the
deficit resulting from photosynthesis, i.e.
then
D = c - c ,
P s P
<*D-
= -a (G - D) P (t ) - K D	(23)
	no n	a
dt	op p	a p
*
Several possibilities now can be examined on P(t ). These would be
*
cases where data were available on P(t ) and inferences can be drawn of the
*
effect of P(t ) on the average D.O. regime.
*
Case I: P(t ) = constant = P
		o
For this case, = 0 and CG^ - D) = (vs/H). Thus if vg/H / 0, then
Gp > D and there is a positive production of D.O. given by:
a (G - D)P	-K t*
Dp = " P PK	2 a - e 3 )	C24)
a. - a. 3 2

-------
If however it is determined that v = o, then growth just balances res-
s
piration (to maintain P ) and G - D = o. Therefore, there is no net produc-
o	p
tion of D.O. If then from the data, the phytoplankton is a constant with
distance, then either there is a net production of oxygen for vg/H # o, or
the production is zero for vg = o.
*
Case II: P = p exp G t ; G > o
		ro	n n
For this case growth exceeds respiration and settling and there is a net
production of oxygen. Substitution into Eq. (23) gives:
dD	G t*
H. =, -a (G - D)P e n - K D	(25)
dt* opv p	o	a p
The solution then is:
a (G - D)P G t* -K t*
p = " ''k G  " -e ' >	(26)
r	an
which is approximately exponential. It should be recalled that this case can
k
only apply to the "excess nutrient" region which is less than t ^ (for phos-
phorus) as discussed earlier.
*
Case III: P = p exp G t : G < D.
		ro	n n
With net growth less than zero, these data would show phytoplankton de-
clining with distance downstream. In such a case, respiration and net set-
tling exceed growth and there may or may not be a net utilization of oxygen.
If v = o, then D > G, and a net utilization occurs. For v ^ o however,
s	s
Gp may still exceed D and a net production could occur. This can only be
determined by a specific analysis of the actual stream. Substitution into
Eq. (23) gives:
dD	-G t*
_ = -a (G - D)P e n - KD	(27)
dt	op p	o	a p
and the solution is:
3 - A 3 J

-------
*
D
P

e
-K t
a
)
(28)
These D.O. equations coupled to the simplified phosphorus-phytoplankton model
discussed earlier permit the model analyst to analyze the response due to
nutrient reduction on both the phytoplankton as well as the D.O.
An example of the impact of phosphorus reduction on ambient chlorophyll <1
concentrations follows.
A - 3. V o

-------
REFERENCES
Goldman, J.C., D.R. Tenore, H.I. Stanley. 1973. Inorganic nitrogen removal
from wastewater: effect on phytoplankton growth in coastal marine waters.
Science, Vol. 180:955-956.
Omernik, J.M. 1977. Non-point source-stream nutrient level relationships:
a nationwide study. EPA-600/3-77-105, Corvallis, ERL, USEPA, Corvallis,
Oreg., 151 pp. + plots.


-------
EXAMPLE - SIMPURje* PH OJp80ftUS_ftNAi^JSjN,_JTBEAM3 *
DATA
Qu.
W(STP)
o	~9t

TRIBUTARY
4
2Q ftii.
MAIM STB M
V+


Ce n<
it 10 K

Item
Present
} esioh


FLow - upstteq.^ c-P-s
- ST? M6D
\
20
0 .IS
11
0.3 0


Stream - "Depth 00 t
-	Velocity (u.) -fps
-	Wok.'te-r TehpeKtt un? (t) C
3.0
o.s
23
Q.a
0.4-
IS


5lA-h 1 \aily Sol<\> Real iV.tlOh iah
- Pho"topeMocL (f)
~ 3"troit f Co n ce n't recti n
	Uprt)~eaii
-	STP e-fflufeht
0. 0-2
3*
0. oz
t


Chlorophyll Ol Concer>"fc-ejtion /Wi.
-	U.p5trecT_lttoh betkvee/i
*X = 0  2.0 Mlej^ Coh f I r.
^ O"0HN A MUELLER
A - 3 V-J.

-------
tj0  lo	Q.S- fp> Xic.^ r*fl ^ a 7.44 d&ys
p10 = P0 eG"ito , 6>5- = as eG*,xa'^ j
zr |Xw	= 0.391/oky
1. Estimate- Ne-t P/iyto Sett)L*\j ft<Vj/h ; ^ - H ( Gp - bp ~^/n)
Gp = G(t) . G(x)
(l3-2o)	. ,
G (t) = l.S- X l.OCt	= 2.\*/d*y
G(x) =_aJL[exf (-*,) - ex p (-<.)[
He H
"/tS = ^0 V^/O-^/sdo iy/cUy =? ^'0
fs than
ho Lno>*jihic pkojjtomj h."tni"fc I Unit a/tioh occukt f"oh	CLKoL
pht>f^lnj anal yri\t LS a CC.lAng.t-tt .	


-------
B. Issiqw con bin oni
, x	ft
I. Ert:irhft.te N^t Pbyto Growth Rwt'e (6*)
A*** iKe^t Met settling rate of pkyto ls s^he ai
p^eseht conjti't'ioh ( ." -ATj =. 0. 3n/cl.y^ ahd	I ("t" extinction
Coefficient wi II be	ai present (y. Ke = 0.33/ft}.
=< o ~ 4", 00 CU pK; vi.*jly ^ a 1".00 CXf '0. 33 X 1.2.} "1,935"
G(-x) - i.tia x o,.r [ejcpf-I.13J-) - ep = 0.1 X l.Oi-^5""20^ = 0.1 + 7/lay
G/k = O.-T^- O.fl-7 - ( 0.3X7 A. 2. J = O. ^3"? /day
*.. Co.lc^t'vte MftXjKuin Possible Ptiyto Cone. im T"m b t*.t y the ihorje-nic. yhosfhatKi rnA.tn~
11 kvi 11" Cvit I o Ki ioeyohd "X. * II fhi/ei ^sii&-e f>*e j H>e hiaxi/hniv* p ky"to p !<*,/fte>, covCPhth tA e
twenty toil* l"ac/, ur*n.M be i.* the- r^ivfe o "f5
/*j/-t ^ C^-i^ax) < Q 0
Z- 2 * 4-

-------
B.frgsiGN ConfrmoNJ font.
74
4-.	"Foh Original Loading
Po' = ^0. t
ffio = [03 {l^O.O^i- 0.3x l,SSxs)/(I'L+o.yxi.ss^
ttr a ' 0 ( 3-D.C, + 10S.5-2S' \ - ^ 1 Q Jftyj
0.2Jf5-0. fc	)
Notre tWt t"he lo^ct reduction haj decreaje ft.O^+O.JxI^Ta 0.3 Xl^rjs <2
"ttr=I L ( JMJ^L^l^SL-X ^ 0.11+ cU/s
o.zr? v ^d.6 y
^Ot* "fchf-S . low CJ-p-p ) M.e/i"tr Co hoe/ft nibi on j uh^tre-a>*
pky "to plfi-nffttM wd*,|L Ijg. Oct; <*. % M t**u
-------
EFFECT OF 3lNU.S0tbAL LoA* VARIATION OKI 3TRSAM
tlJJOLVg^ OxygFN CONCfeWTRATlOMi *
EAT A
W
pq	p %
100 cfj	K(.a 0,15/otfcy
U = 4- foe/day	= 0.15/(fee/
Cs = ?. 0 Kj/l	Kc. a O.ns/iy
PRC B
C<*.|cul concehtro.toh
L.Ct)= L + ft. ii-h [C^X^'^i]
Lo = Wo/q=r loooo Ji/oky/O00 cfsA5.^ - \S.55 *]/l
<*o = A0/9 - 5T>oo/(u<, x5:34l) = S.lf h^/X
Mv) =tti L0(t) (e~K'V*- e **/*)
wkeh 1) = dissolved oxy^^i deflect
C(x,t) ~ Cs-}>(:*, tr)
wlre C(*yt) = dissolved oxygen concenti-ation
CPM
CAM
0	6	IX IS 1+ "t
*> JOHN A MUELLER

-------
w.fck -Xc- U	,	%
ke," Kh
/xc=	J* lo-15/o.is)  y.7S niLlef ,
(o/is-- o.i-s')
t c m nyj
0.5" S.SS + <*.1* J/#[tirtt-^.le)]^e"0XS*l^ -	^
- 3.51 + 1.7? sin[l/n(t- 1. *<>)]
C(xcyt)= *.G - ^SI+uH Jn["X0
- +.1-3- 1.79 Sin	<	
S^iloWy fr K* C W If *ile*}
C(C/ *) = "* Uiodc ha-'tufe of5- the- t>. 0,
A,lxo note tlie time Ua f 0.1d^wfn, 11 Hood, "the tnaxi*** ka<[,
"to tke *.*	d*.ily ae-Ficifc ft.t Kc.N^-.y
Spccti^,! pioti cf b.o. ett C-AM  II- Noo/v are sho*n t#
J*-?1* i'ct.l/y cj <* play _ expect e< hejuftj". 5pct(ccl 5Ai>>f)iA^ "? "tfc?
J J - -+- wW +- "I 5aj ,
a-a47

-------
"7 i
DISSOLVED
oxyGEN r _
CONl C i
f 4i? i

 		/
12 k*

|tf k

	
>
"I	
C
noon
I
II
C fM
-I1I
\f	14-
MtbN.	CAM

to*)
G- -AM
I	11
X- MILES
l.j\G 
\

\7 Moon
(t4)
MAX LbG e WhN
1-14-f

-------
THE WICOMICO RIVER ESTUARY
AN ESTUARINE EUTROPHICATION EXAMPLE
Background
The purpose of modeling the Wicomico River, a tributary to Chesapeake
Bay, was to illustrate the general methodology of applying mathematical
models to determine waste load allocations for a eutrophied estuary. Eutro-
phied conditions, upstream of Chesapeake Bay in the vicinity of major out-
falls, as observed in the Wicomico River, are typical of many Maryland
rivers. The Wicomico River analysis also incorporates most of the complexi-
ties encountered in a modeling study.
The Wicomico River study area is shown in Figure W-l, and extends from
the dam on Johnson's Pond in Salisbury, Maryland to the mouth of Ellis Bay,
a distance of approximately 22 miles. The river is tidal to the dam with a
mean daily tidal range at Salisbury of 3.0 feet. The salinity generally
varies from about 10 ppt at the mouth to less than 1 ppt throughout the
upper 1/3 to 1/2 of the estuary length depending on tidal stage, season and
weather factors. The maximum salinity observed in the vicinity of Salisbury
is reported CWebb and Heidel, 1970) to be about 0.1 ppt at U.S. Highway 50
(MP 21). As such, the river is essentially fresh water throughout its upper
reaches.
At mean low tide, the average depths in the tidal portion of the Wicomico
River vary from 6 feet at the mouth, increasing to 20 feet midway up river,
and decreasing to 8 feet at Salisbury. A center channel provides for some
water-borne commerce and is used principally by oil tankers and barges.
The total drainage area of the Wicomico River basin is 239 square miles.
Approximately 90 percent of the Wicomico River watershed is rural - about
equally divided between farm, forest and marsh. The population of this area
is about 50,000 of which about 70 percent is concentrated in the vicinity of
Salisbury. The raising of chickens, related feed and processing industries,
^ Abstracted from Salas and Thomann, (J.975).
3 -/

-------
and the production and processing of other farm products are an important
part of the economy. Several industries which specialize in manufactured
products are located at Salisbury.
The major waste source in the tidal portion of the Wicomico River is the
Salisbury Sewage Treatment Plant (STP) (refer to Figure W-l) which receives
both domestic (40 percent of volume), and industrial (60 percent of the volume)
waste (Pheiffer and Donnelly, 1972). This secondary treatment plant discharged
an average of about 4 million gallons per day with a BOD^ of approximately
3,000 lb/day.
Hydrology
The United States Geological Survey (JJSGS) maintains one gaging station
on a continuous basis in the Wicomico River watershed. This station is located
on Beaverdam Creek (drainage area = 19.5 square miles) (Figure W-l) which is a
tributary to the tidal Wicomico River near Salisbury. Average stream flow in
the creek for the 38 years of record is 23.9 cfs with, maximum and minimum re-
corded discharges of 1,480 cfs and 0.4 cfs, respectively. The 7 day-10 year
low flow is 1.4 cfs (Walker, 1971). Low flows, however, are affected by regu-
lation at the dam in Beaverdam Creek.
The North Prong of the Wicomico River above the dam (which separates the
tidal and non-tidal portions of the Wicomico River) at Salisbury crosses the
Naylor Mill Paleo channel Can ancient filled river channel). This paleo chan-
nel has been reported (Boggess and Heidel, 1968) to highly influence the low
flow conditions in the upper Wicomico River resulting in high yields. This
may be contrasted to probably lower yields in the lower Wicomico River where
groundwater infiltration is not as pronounced. As such, the freshwater flow
is disproportionate to the drainage area under low flow conditions with the
majority of the freshwater flow emanating from within the upper reaches of
the watershed.
Correlations were developed with measured discharge data to estimate the
freshwater flow in the Wicomico River for the periods of analyses.
3-X

-------
v,	\--~*
5> Ik
LEONARI
JOHNSOI
POND>
U.S. 50
SALISBURY
STP OUTFA
SALISBURY
WHITEHAVEN
U.S.G .5s
GAGING
STATION
ELLIS
BAY
MONIE BAY
SCALE
0	12	3
MILES
FIGURE Wl
LOCATION MAP - WICOMICO RIVER

-------
General Description and Analysis of Available Data
Major water quality sampling efforts in the Wicomico River were conducted
by the Federal Water Pollution Control Administration (FWPCA) during the summer
of 1967 under relatively high flow periods. Spatial coverage extended from
above the Johnson Pond Dam at Salisbury to the mouth, of the Wicomico River as
shown in Figure W-2. Tributaries to the Wicomico River were also monitored.
Measurements were taken at high and low water slack during August, Parameters
that were most frequently measured were temperature, secchi disk, total and
fecal coliform, chlorides, dissolved oxygen, BOD, and suspended and volatile
solids. Dissolved oxygen and BOD were measured at both the surface and mid-
depth at many stations. Nutrient and chlorophyll 'a' measurements were limited
to three stations. The highest chlorophyll 'a' levels were observed at Quantico
Wharf (Station 5). The average was about 9.2 yg/1 with values often greater than
100 yg/1. Review of subsequent data indicated that this was insufficient spa-
tial coverage and that peak concentrations for these parameters were probably
missed.
Daily precipitation records in the area for the month of August 1967 indi-
cate that substantial rainfall of greater than 6.2 inches fell during the three
days just prior to the August 7 survey and about 5.5 inches fell during the
second survey as measured at Salisbury. The impact on dissolved oxygen levels
was significant. Figure W-3 presents the spatial profiles of dissolved oxygen
for high and low water slack during August 7 to 11. As can be seen, the dis-
solved oxygen in the upper reaches in the vicinity of Salisbury progressed from
at or near saturation (= fcJ mg/1). on August 7 to dissolved oxygen levels of less
than 5 mg/1 from MP 20 to 8 during August 10 and 11. Precipitation with conse-
quent cloud cover was observed during these latter two days.
For the survey periods, low and high water slack generally occurred during
mid-morning and late afternoon, respectively. As such, the dissolved oxygen
data taken during the slack water runs serve to partially indicate the extent
of diurnal variation in dissolved oxygen concentrations. As can be seen in
Figure W-3, during the latter two days, dissolved oxygen throughout the day was
generally the same in the upper Wicomico River. This indicates a suppression
of photosynthetic activity probably due to the reduction of available sunlight
by cloud cover,.
3-H-

-------
SCALE
Zjl S. PRONG
MILES
STP
SALISBURY
SALISBURY
3A
* NUTRIENT AND CHLOROPHYLL 'A'
MEASUREMENTS AVAILABLE
CREEK
a,
WHITEHAVEN
ELLIS
BAY
SCALE
9A
MILES
MONIE BAY
FIGURE WX
WICOMICO RIVER
SAMPLING STATION LOCATIONS - FWPCA SURVEYS SUMMER 1967

-------
AUGUST 7, 1967
D.O. SATURATION
10
O
2
z
LU
o
>
X
o
Q
Ui
>
_1
O
CO
C/)
a
AUGUST 8, 1967
0.0. SATURATION
22
20
18
IS
14
12
10
 (0
O
2
Z
UJ
o
>
X
o
o
Ui
>
o
to
<>
a
AUGUST 9, 1967
0.0. SATURATION

LEGEND:
 LOW WATER ( A.M.)
 HIGH WATER (P.M.)
1
!
18 16 14 12 10 8 6 4 2 0
MILES ABOVE MOUTH OF WICOMICO RIVER
0AM SALISBURY
STP
FIGURE W 3
DISSOLVED OXYGEN - WICOMICO RIVER
AUGUST 7 TO II, 1967
3

-------
AUGUST 10, 1967
0.0. SATURATION
12
3
\
O 10
2
5 8
o
>
X g
o 6
a
ui
> 4
_1
O
tn
cn 2
AUGUST n, 1967
-aa SATURATION
LEGEND:
 LOW WATER (A.M.)
 HIGH WATER ( P. M.)
I I I I
J.
DAM
18 16 14 12 10 8 6 4 2
MILES ABOVE MOUTH OF WICOMICO RIVER
SALISBURY
STP
FIGURE W3 '( Cont'd)
DISSOLVED OXYGEN WICOMICO RIVER
AUGUST 7 TO II, 1967

-------
The State of Maryland also conducted extensive monitoring of water quality
in the Wicomico River in July and August 1971. The stations sampled by the
State are, in most cases, essentially identical to those used by the FWPCA in
1967 as presented in Figure W-2. Parameters measured included secchi disk,
temperature, total and inorganic phosphorus, TKN, ammonia, nitrite-nitrate,
chlorophyll 'a1, total and fecal coliform, dissolved oxygen, total organic car-
bon, conductivity, and salinity. BOD was a notable exception. Sampling during
these surveys was conducted once a day generally during the morning hours.
During the July survey sampling was initiated after predicted low water slack,
whereas during the August survey sampling was completed prior to predicted low
water slack. Both surveys were conducted under relatively dry weather condi-
tions when compared to the 1967 surveys. A steady state modeling framework was
utilized in the analysis of the Wicomico River which implies a constant flow
regime. Therefore, the critical summer period of July 1971 was chosen for cal-
ibration of the model. The data taken during August 1971 were utilized for
verification of the model. Due to the transient conditions caused by the heavy
rainfall during the surveys conducted in 1967, these periods could not be ana-
lyzed in a steady state modeling framework.
The dissolved oxygen data observed during the two surveys conducted in the
summer of 1971 are presented in Figure W-4. Dissolved oxygen levels were gen-
erally high with the standard of 5 mg/1 generally met throughout the estuary.
Supersaturition is encountered at times over a large portion of the upper
river, especially in the vicinity of the Salisbury STP discharge. The dissolved
oxygen was progressively measured later in the day during each of the days in
the July survey. Therefore, the difference in dissolved oxygen at stations
during the July survey period partially indicate the extent of the diurnal
variation in dissolved oxygen due to photosynthetic activity. In August, mea-
surements were generally taken during the same period.
Figure W-5 presents the spatial distribution of total and inorganic nitro-
gen, total and inorganic phosphorus and algal biomass as measured by chloro-
phyll 'a1 during the July and August 1971 survey period. Peak chlorophyll 'a'
levels of greater than 250 yg/l occur near Salisbury and decline to about 25
yg/1 near the mouth. Inorganic nitrogen concentrations (summation of ammonia,

-------



S0.0. SATURATION
1	
	i : j
LEGEND:
 JULY	21, 1971
 JULY	22, 1971
A JULY	23, 1971
	I	I	I	
22 20 18 16 14 12 10 8
-0.0. SATURATION
i ft A
>1 1816 14
I	MILES AE
ft
LEGEND:
 AUGUST	10, 1971
 AUGUST	II, 1971
A AUGUST	12, 1971
I I	'
2
204 18 16 14 12 10 8	6	4
ABOVE MOUTH OF WICOMICO RIVER
DAM SALISBURY
STP
FIGURE W4-
DISSOLVED OXYGEN - WICOMICO RIVER
SUMMER 1971
3-?

-------
4.0
10
z
I
o
 2.0 h
2
UJ
o
o
a: i.O
A
 
O Q
A 
NITROGEN
LEGEND:	(,B j^y ^ ,97, g \
TOTAL J m JULy 22, 1971 O ) '^"nrcM
JULY 23, S7I a/NITR06EN
~
s
A

~
22
20
18
16
14
12
10
N .4
a.
I
o
 3
cn
3
cc
o
X
a.
to
O
X
a.
.2
A
Q
3

A
0
&
Q
S
a
~
LEGEND:
TOTAL
PHOSPHORUS
fl
a
a
JULY 21,1971 o
 JULY 22,(971 O
| A JULY 23,197! A
3
a
~,
*
a
INORGANIC
PHOSPHORUS
I
1

22
20
18
14
12
10
300






LEGEND: 
JULY 21, 1971







JULY 22, 1971






A
JULY 23, 1971








1







_ 

A





 A







1
A

A
1
A
1 1

A
1 1
ft
1 1
* 9
I I
250
O
Jt.
~<
_l
>
X
Q.
o
cc
o
_i
x
o
150
100
50
22 i
20-i
18 16	14 12	10 -8	6	4
MILES ABOVE MOUTH OF WICOMICO RIVER
DAM SALISBURY
STP
FIGURE WS
WATER QUALITY DATA - WICOMICO RIVER
JULY 21 TO 23, 1971
3-/o

-------
4.0
2 3.0
I
O
5
 2.0
Z
UJ
o
g 1.0
1

A
 o
a q
1
a
S g
LEGEND:
, 	AUGUST 10, 1971	a 1 __ ^
TOTAL ) 0	AUGUST II 197)	O 1'NORGANIC
NITROGEN i	" (NITROGEN
A	AUGUST 12,1971	A J
X
8
3
Al
_a_
22
20
18
16
14
12
10
a. .4
i
o
2
^ .3

-------
nitrite and nitrate nitrogen) of about .5 to 1.0 mg-N/1 occur near Salisbury
with a decline downstream to less than 0.1 mg-N/1. Inorganic phosphorus
concentrations of about 0.1 to 0.2 mg-P/1 occur near Salisbury with a decline
downstream to less than .05 mg-P/1. Comparison of these data to the Michaelis-
Menton half saturated growth constants of .005 mg-P/1 and .025 mg-N/1 for
inorganic phosphorus and inorganic nitrogen, respectively, indicates that
neither nitrogen nor phosphorus appeared to be significantly limiting phyto-
plankton growth in the upper Wicomico River. The lower 5-8 miles of the estu-
ary however appear to be limited by nitrogen. This limitation does not appear
to be influencing the upper phytoplankton flows since the growth of that bloom
has ceased about 10 miles further upstream. Total nitrogen and total phos-
phorus both peak in the vicinity of the Salisbury STP discharge. A rapid
decline in total nutrients is observed downstream and cannot be simply
accounted for by freshwater dilution. The principle water quality problem
therefore is relatively high chlorophyll levels, coupled with occasional low
D.O. values.
Waste Loads
The major waste source in the tidal portion of the Wicomico River is the
Salisbury Sewage Treatment Plant (.STP). Operational data for the plant indi-
cated an average BOD^ load of 3,000 lbs/day which was utilized in the calibra-
tion and verification analyses.
No nutrient data were available for the above periods.	Based on a single
sample taken by the Environmental Protection Agency (EPA) on	April 6, 1972 a
total phosphorus effluent load of 179 lbs-P/day (7.2 mg-P/1)	and a total kjel-
dahl nitrogen (.TKN) load of 593 lbs-N/day (23.6 mg-N/1) were calculated and
applied in the verification analysis.
During July, 1974, the WRA analyzed composite samples of the effluent
from the Salisbury STP. Th.e resulting loads are presented in the following
table:
3 -/A

-------
TABLE 1
SALISBURY SEWAGE TREATMENT PLANT EFFLUENT LOADS
-JULY, 1974
Flow = 6.7 cfs
Concentration
Load
UOD Load
bod5
TKN
Total Nitrogen as N
Total Phosphorus as P
Parameter
(mg/1)
31.8
16.3
(lbs/day)
1,157
600
628
123
(lbs/day)
1,701
2,743
16.8
3.8
The TKN and total phosphorus loads are consistent with the loads calcu-
lated from the EPA data. As will be discussed subsequently, the loads in
Table 1 were utilized in the projection analyses.
Mathematical Model Development
Based on time and budgetary constraints, a steady state finite segment
model (Thomann, 1972) was chosen for the analysis of water quality in the
Wicomico River. Primary emphasis was placed on the evaluation of dissolved
oxygen and total phosphorus and total nitrogen to estimate the eutrophication
potential of the estuary under different loading alternatives.
The segmentation used in the analysis of the Wicomico River is presented
in Figure W-6. Twenty-four segments, usually one mile in length, were utilized.
The data for determining the geometry of each section were obtained from the
U.S. Coast and Geodetic Survey. The mean low water depths from these charts
were increased to mean tide levels. Figure W-7 presents the spatial distribu-
tion of mean tide depths, cross-sectional areas and cumulative volume of the
system.
The USGS gaging station records at Beaverdam Creek (drainage area - 19.5
sq. mi.) were the only freshwater flow data available for the periods of ana-
lyses in the summer of 1971. Estimations of freshwater flow in the mainstream
of the Wicomico River were determined from correlations developed from limited
data taken by the USGS during other periods. These data were plotted on a log-
log scale and the line of best fit was utilized to estimate the freshwater flow
at Naylor Mill Road as a function of measured flow at Beaverdam Creek. The
3-f3

-------
DAM
24
SALISBURY
STP OUTFALL,
SALISBURY
CREEK
WHITEHAVEN
m ___

ELLIS
BAY
20
MONIE BAY
SCALE
0	12	3
MILES
FIGURE WC
MODEL SEGMENTATE - WICOMICO RIVER

-------
30,000
S 25,000
? 9bo' 
DM SALISBURY
STP
IS 16 14 12 10	8	6	4
MILES ABOVE MOUTH OF WICOMICO RIVER
FIGURE WT
GEOMETRY OF WICOMICO RIVER
3 -!

-------
drainage area of the Wicomico River at Naylor Mill Road is 24.8 sq. mi.
Two other correlations were developed from information presented in Boggess
and Heidel (1968). With these correlations, freshwater flow could be obtained
at key locations in the upper Wicomico River. The modeling analyses were per-
formed with flow assumed constant below Tonytank Creek. Subsequent sensitivity
runs, in which flow was incremented at a rate of 0.1 cfs/sq. mi., did not sig-
nificantly affect the water quality parameters evaluated in this study.
The time necessary for a system to attain equilibrium is critical in any
type of steady state evaluation. A generally constant flow was recorded at
Beaverdam Creek for the summer of 1971. For the analysis of salinity measured
during the two surveys in 1971, two month flow averages were applied and are
considered consistent with the time to equilibrium for a conservative substance
in the Wicomico River under the final advective-dispersive regime utilized.
Substances with kinetic interactions come to equilibrium more quickly than con-
servative substances. For these substances, two-week flow averages were deemed
appropriate. Table 2 summarizes the flow regime inputted to the model for the
two periods analyzed and the 7 day - 10 year low condition used in the projec-
tion analysis.
TABLE 2
FRESHWATER FLOW AT KEY LOCATIONS IN WICOMICO RIVER
7 day-10 yr. July 1971	August 1971
Low Flow 2 Months 2 Weeks	2 Months 2 Weeks
Beaverdam Creek 1.4 18.0 14.8	16.0 21.0
North Prong at 23.0 55.0 49.0	50.0 61.0
Isabella
Tonytank 2.4 6.5 6.0	6.0 7.5
Total Below 26.8 79.5 69.8	72.0 89.5
Tonytank Creek
3-/4

-------
Transport Verification
Salinity was utilized as a conservative tracer substance to determine the
dispersional characteristics of the system and comparisons were made between
computed and observed salinities for the July 1971 survey. Adjustments were
made to the dispersion coefficients until such time that acceptable correla-
tions between the observed data and model results were achieved. Observed sal-
inity concentrations at the boundaries of the model were the only salinity
inputs to the model. The adjusted dispersion coefficients were subsequently
checked by applying the same dispersive regime to the August 1971 survey. The
resulting model verifications are presented in Figure W-8, in which comparisons
between computed and observed data for the two periods of analysis are presented.
2
Longitudinal dispersion coefficients, as noted, ranged from 0.3 to 0.8 miles /
day. Vertical homogeneity is assumed in the model. This assumption is consis-
tent with observed conditions for most parameters in the Wicomico River espec-
ially in the critical upper reaches.
As can be seen in Figure W-8, salinity was generally at or near background
2
levels above MP 16. The dispersion coefficient of 0.3 miles /day used in this
region was merely an extrapolation of downstream dispersion coefficients which
served to set an upper limit. In order to evaluate the dispersional character-
istics of this upper reach, a dye tracer study was performed by the State of
Maryland. The proper determination of the dispersional characteristics in this
region is critical since the Salisbury STP discharges within this reach.
An instantaneous release of 40 lbs. of dye was dumped at high slack tide,
6:20 p.m. on July 22, 1974, in the vicinity of the Salisbury STP discharge.
Longitudinal spatial distributions of the dye were measured at subsequent high
and low water slack periods. The observed dye distributions are shown in Fig-
ure W-9. These dye data were used to obtain an estimate of dispersion coeffi-
cients using simplified analytical solutions for instantaneous discharges (see
Thomann, 1972).
The dispersion coefficients calculated from the dye data varied from 0.04
 2
to 0.26 miles /day and are of the same order as those used in the model (0.3
2
miles /day) for this portion of the river. Sensitivity analyses were performed
2
using a dispersion value of 0.1 miles /day for this region and indicated no
3-/7

-------
DISPERSION COEFFICIENT (MILE2 DAY)
0.6
Q8
7/21/71
7/22/71 DATA
7/23/71
MODEL VERIFICATION
JULY
20 18 16 14 12 10 8 ' 6	4	2	0
MILES ABOVE MOUTH OF WICOMICO RIVER
DISPERSION COEFFICIENT (MILE2 DAY)
0.3
0.6
0.8
8 /10/ 71
8/II/71 DATA
8 / 12 / 71
MODEL VERIFICATION
AUGUST
OAM
MILES ABOVE MOUTH OF WICOMICO RIVER
FIGURE W 8
SALINITY VERIFICATION - WICOMICO RIVER
SUMMER 1971
3-/2

-------
24.
CD
a.
a.
2a
16.
Z
O
< 12.
a:
h-
Z
U fl
-
a
.

HIGH SLACK TIDE
-
\ it =a552 OAYS

 1
\ ^	1 : I.596 DAYS



/ /
/<
Xcy
^ vC*V\_  =2.572 DAYS

*1


rirr'V'l
i ~t< i i
I I I
as
LO 
-------
significant effect on the calculated distributions. The higher dispersion coef-
2
ficient of 0.3 miles /day initially developed, was used in all model analyses.
Model Verification-Dissolved Oxygen
Upon completion of the verification of the transport regime, the analysis
proceeded to the evaluation of reactive substances.
The Salisbury carbonaceous BOD^ load used in the modeling analysis was
3,000 lb/day based on available operating records. This load was corrected to
ultimate carbonaceous oxygen demand utilizing a ratio of 1.43. A TKN nitrogen
discharge of 590 lb/day was estimated from limited data and was converted to
ultimate nitrogenous oxygen demand by multiplying by 4.57.
Dissolved oxygen deficit boundary conditions for the Wicomico River at
the dam at Salisbury, Beaverdam Creek, Tonytank. Creek and Ellis Bay were deter-
mined directly from observed data.
The reaeration coefficients, K , for each segment were computed using the
O'Connor-Dobbins formulation where average tidal velocities were taken from
the tidal current tables. Reaeration coefficients for the Wicomico River varied
from 0.1 to 1.2/day after temperature correction.
A deoxygenation rate of 0.3/day at 20C for both carbonaceous (K^) and
nitrogenous (K^) oxygen demanding materials was used in the modeling evalua-
tions. Coefficients were corrected for temperature by using a 0 = 1.047 for
carbonaceous and 1.08 for nitrogenous. No information on the dissolved oxygen
uptake of the bottom sediments in the Wicomico River was available. Based on
2
the literature a 1 to 2 gm-0_/m -day sediment oxygen demand (SOD) is typical of
2
estuarine muds. An SOD rate of 1 ^sa-O^/vx -day was used in all segments of the
Wicomico River except segments 2, 3, and 4 which are located in the vicinity of
2
the Salisbury STP outfall. A higher rate of 2 gm-O^/m -day was used in these
segments on the basis of a higher rate of deposition of solids and phytoplank-
ton at that location.
A review of the observed dissolved oxygen data indicates that algal photo-
synthesis and respiration appear to have a significant effect on dissolved oxy-
gen levels in the Wicomico River, especially in the vicinity of the Salisbury
STP. Chlorophyll 'a' levels in this vicinity frequently exceed 150 pg/1. The
3 -2.G

-------
photosynthetic production of oxygen was estimated using general procedures
as follows. Based on numerous analyses conducted in other areas the saturated
photosynthetic oxygen production rate CP ) under optimum conditions was esti-
s
mated by the following:
P (mg/l-day) = 0.25 Chlorophyll 'a' Cpg/1)	CD
s
This saturated rate was corrected for non-optimal light and depth and
time averaged in accordance with Equations 8-26. Average incident solar
radiation and photoperiod were obtained. The light extinction coefficient
(K ) was estimated from available secchi disk measurements in accordance with
e
the following:
K = 1.7/secchi disk	C2)
e
This relationship has been verified with extensive data. Algal respiration
was estimated to equal 10% of Pg and was applied over the depth of the water
column.
With the determination and assignment of the foregoing input parameters,
the model was applied to the July and August surveys of 1971.
Favorable comparisons between the calculated and observed dissolved
oxygen profiles in the region between the mouth of the Wicomico River and
approximately MP 12, were achieved with the direct application of the para-
meters described above. However in the regions where abundant algae were
present, some changes in the theoretically computed rates for photosynthesis
had to be made in the model. Figure W-10 shows a comparison of the theoret-
ical rates and the final values used in the verification. The differences
can be explained by the limited information on some of the parameters used
in the analytical method and by the complexity and uncertainties of the phe-
nomenon. Final verifications for the two survey periods are presented in
Figure W-ll. The agreement between the observed and computed values is rea-
sonably good. A maximum oxygen deficit of 3.5 mg/1 at MP 10.5 was computed
for the period of July 1971. A maximum oxygen deficit of 2.5 mg/1 at MP 8.5
was computed for the period of August 1971. Dissolved oxygen at or near sat-
. uration was calculated in the vicinity of the Salisbury STP discharge.
3 -<2. /

-------
>
0
o
1
a
z
<
o
H
UJ
X
I-
z
>
tn
O
h-
o
X
Q.
I
UJ
o>
e
tr
I
Q.
w
UJ
t-
<
cr
a.o
6.0
40
2.0
<
  2.0
Q.
in
UJ
cr
-4.0
	 THEORETICAL
	FINAL RATES
RATES
JULY 21 - 23, 1971
/ \ /\\


\>
1 I 1
1 1 1
1 l 1 1
22 20
18 16
10

	.
8.0

>


o


a

a
i

z

6.0
<
o>


e

o


h-
cr
4.0
UJ
i
X
Q.

1-


z
cn

y-
cn
O
UJ
>-
<
2.0
t-
tr

O


X
a.
z
o
0
t-
1

UJ
<

z
tr
- 2.0

a.


m


UJ


cr

-4.0


AUGUST 10- 12, 1971
M


\ \


\


! I 1
1 1 1
III.
22
OAm
20'
SAUSBURY
STP
18
MILES ABOVE MOUTH OF WICOMICO RIVER
FIGURE W 10
COMPARISON OF THEORETICAL AND
FINAL NET PHOTO SYNTHETIC RATES
3-2.2.

-------
,0,	Z&,
BENTHIE DEMAND (GR/M2-DAY)
1.0
JULY
	7/ 21 / 7l"*\
	7/22/71 > DATA
A	7/23/71 J
~	MODEL OUTPUT
WITH NITRIFICATION
NO NITRIFICATION
22 20 18 16 14 12 10- 8	6	4	2	0
MILES ABOVE MOUTH OF WICOMICO RIVER
8/10/71
8 / II / 7I \ DATA
8/12 /7I J
MODEL OUTPUT
AUGUST
 NJ
WITH
NITRIFICATION
NO NITRIFICATION
22
20
DAM SALISBURY
STP
MILES ABOVE MOUTH OF WICOMICO RIVER
FIGURE W.ll
DISSOLVED OXYGEN VERIFICATION - SUM MER 1971
WICOMICO RIVER
3 -23

-------
Phytoplankton can utilize both ammonia and nitrate-nitrate as nitrogen
sources. Whether the ammonia is first oxidized by the autotrophic bacteria
to nitrate and then utilized by the phytoplankton cannot be ascertained from
the observed data in this study. In Figure W-ll, the computed profiles are
presented with and without the inclusion of the nitrification phenomena. As
can be seen, the response of the system is such that the model may be con-
sidered verified with or without the inclusion of the nitrification phenomena.
The major components of the deficit profile for the July 1971 survey are
presented in Figure W-12. The impact on dissolved oxygen of the Salisbury
STP carbonaceous BOD load is limited to the upper six miles of the River with
a peak deficit of about 1.0 mg/1. The inclusion of the nitrification pheno-
mena adds an additional 0.8 mg/1 to the peak deficit response. This may be
contrasted to the more significant impact on dissolved oxygen levels due to
the benthal demand and algal photosynthesis less respiration. Phytosynthesis
less respiration is calculated to contribute as much as 4 mg/1 of dissolved
oxygen in the critical upper reaches of the River. Further downstream, where
the River is deeper, photosynthesis less respiration consumes as much as 2
mg/1. The relatively minor impact of the Salisbury STP input indicates that
the severe depressions in dissolved oxygen observed in 1967 were probably not
due solely to the direct discharge of carbonaceous and nitrogenous oxygen de-
manding substances from the Salisbury STP.
Nutrient Analyses
Total nitrogen and total phosphorus were modeled in the Wicomico River.
Budgetary and time constraints did not allow for the specific modeling of
phytoplankton biomass. The impact of nutrient removal policies on phyto-
plankton biomass can, therefore, only be implied from these analyses and the
application of the principles of nitrogen/phosphorus ratios.
Utilizing the observed nutrient loadings and boundary conditions, total
nitrogen and total phosphorus were initially analyzed as conservative mater-
ials, i.e., no decay. Comparisons between calculated and observed profiles
indicate a loss of nutrients from the water column is due to the settling of
detritus and phytoplankton cells. For total phosphorus, favorable compari-
sons between calculated results and observed data for both surveys were


-------
6
total deficit
4
2
0
2
20
22
r 2
o ^
a: ^
ui 5
Q - ^ 0
cl
7500
5000
2500
- 0

22
1)
NITROGENOUS
CARBONACEOUS
POINT SOURCES
20
18
16
14
12
10
oo
o 

/-DEFICIT boundry condition
BACKGROUND

^		
BENTHIC DEMAND

, , , , ,
1 1 1 1 l !
22
20
18
16
14
12
10
b-

-------
4.0
3.5
10
2.5
2.0
.02
D03AY COEFFICIENT (1/ DAY )
.01

LEGEND:

 JULY 2!, 1971

 JULY 22, 1971

~ JULY 23, 1971
 A





* l\ *

 / \ 

/ "

 N.

 A \

A\ 

 \
	MODEL RESULTS

^ 
~


^>>>>><^ 

-A-  

 * A
1 1 1 1 1
1 1 1 1 1 1
2
I
O
2
2
UJ
o
o
tr
2 1.5
<
I-
O
1.0
as
22 20 18 16
12 10
DECAY COEFFICIENT (l/DAY)
0.2
K =0

 MODEL RESULTS
0AU SAUS8URY
STP
16 14 12	10	8	6	4	2
MILES ABOVE MOUTH OF WICOMICO RIVER
FIGURE W 13
NUTRIENT VERIFICATION - WICOMICO RIVER
JULY 1971
3

-------
DECAY COEFFICIENT (l/DAY)
.02
3.0
z
8/10/71 ^
8/11/71 }DATA
0/12/71 J
MODEL RESULTS
Z
1x1
cs
o
or
(-
z
_i
<
i-
o
1
05
20
2Z
0.6fr
O
(O
3
QC
O
X
CL

o
X
a.
o
>-
DECAY COEFFICIENT (l/DAY)
,02
QAM SALISBURY
STP MILES ABOVE MOUTH OF WICOMICO RIVER
FIGURE W I*
NUTRIENT VERIFICATION - WICOMICO RIVER
AUGUST 197!	?.j7

-------

o
2
UJ
o
>-
X
o
Q
UJ
>
-I
o
in
S2
a
-Q.CL SATURATION
'L
WITH NITRIFICATION
J	L
 D.O. STANDARD
J	L
22 20 18 16 14 12 10 8 6 4 2 0
s.
JULY I9T1 ( P-R 5
2
UJ
o
>
X
o
a
uj
>
_i
o
to
cc
D. 0. SATURATION
0.0. STANDARD
E5TIMATED
DIURNAL VARIATION
J	I !	L
22 20 18 16 14 12 10 8 . 6 4 2 0
O
2
14.
12.
ia
- /
/
~

\
\
\
\ 0.0. SATURATION-
S'
AUGUST 1971 (P-R )
ESTIMATED
DIURNAL VARIATION
0.0. STANDAR0-
22,
L	L
DAM SALISBURY
STP
IB 16 14 12 !0 8 6 4 2
MILES ABOVE MOUTH OF WICOMICO RIVER
FIGURE W \S
DISSOLVED OXYGEN PROJECTIONS
nAY - 10 YEAR LOW FLOW
3 -zg

-------
achieved using decay rates of 0.04 and 0.02/day for different portions of
the river as shown in Figures W-13 and W-14. This is equivalent to a net
effective phosphorus settling rate of about 0.4 ft/day. The calculated
profile for total phosphorus, as a conservative substance, is also shown
in Figure W-13 for the July 1971 condition. For total nitrogen, as shown
in Figures W-13 and W-14, favorable comparisons were achieved for both
surveys using a similar distribution of decay rates but halved in magni-
tude. It can be noted that the ratio of N/p at the outfall is about 7
indicating that either nitrogen or phosphorus may be controlling growth
of the phytoplankton downstream.
Waste Discharge Analysis
The two factors chosen for establishing critical periods for the allo-
cation analysis in the Wicomico River were low advective flow and high tem-
perature. The 7 day-10 year low flow (.refer Table 2), was employed at a
critical water temperature of 30C. Dissolved oxygen saturation values
were computed based on the temperature and salinity distribution projected
under the low flow condition utilizing a salinity boundary of 10 ppt at
Ellis Bay. The loads used in the projection analysis, as shown in Table 1,
were based on data taken during July 1974. All kinetic constants developed
in the calibration and verification analyses were applied.
Projected dissolved oxygen profiles under three conditions are pre-
sented in Figure W-15. Dissolved oxygen deficit boundary conditions were
disregarded on the basis that they did not significantly affect dissolved
oxygen in the areas of critical deficit. In Figure W-15A, the combined
effect on dissolved oxygen in the Wicomico River due to the carbonaceous
BOD load from the Salisbury STP and due to the benthal demand distribution
is presented. As indicated, the dissolved oxygen standard is marginally
met under these conditions. The inclusion of the nitrification phenomena
results in violation of the standard by about 1 mg/1 as shown in Figure
W-15A. In Figure W-15B and W-15C, the combined effect on dissolved oxygen
due to the carbonaceous and nitrogenous oxygen demand from the Salisbury
STP, benthal demand and algal photosynthesis, and respiration are presented.
3 -a. ?

-------
The algal photosynthetic and respiratory rate distributions used to develop
these figures were the same as those used for the July and August 1971
model simulations (refer to Figure W-10), respectively. In the vicinity of
the Salisbury STP where minimum dissolved oxygen levels are predicted as
can be seen in Figure W-14A, average dissolved oxygen concentrations are at
and above saturation in Figures W-14B and C. However, violations of the
5 mg/1 average dissolved oxygen standard are projected to occur further
downstream.
Calculated diurnal fluctuations in dissolved oxygen are also presented
in Figure W-15B and C. Based on data from other areas, the diurnal ranges
were estimated from the following:
D.O. = 0.18 P
s
where Pg is calculated from Equation (1) A check of the above relation-
ship was made using dissolved oxygen data taken on July 22, 1974 when a
continuous recorder was installed at Harbor Point (MP 19.5). The maximum
observed dissolved oxygen was 12.0 mg/1 and the minimum was 6.0 mg/1 in a
24 hour period. The observed chlorophyll ' ar level was 158 pg/1. Using
the above relationship, the computed diurnal fluctuation in dissolved oxy-
gen is 7.1 mg/1 which is in approximate concurrence with the observed range
of 6.0 mg/1. Note in Figures W-14B and C that the calculated diurnal range
in dissolved oxygen decreases as one proceeds downstream. This is due to
decreased levels of chlorophyll 'a1. Violations of the 4 mg/1 instantane-
ous dissolved oxygen standard are projected at various locations, especially
in Figure W-14C.
In conclusion, the direct impact on dissolved oxygen of the oxidizable
loads emanating from the Salisbury STP are overshadowed by algal activity.
As such, effluent limitations for the Salisbury STP should be directed to
the control of phytoplankton through nutrient limitations.
Projections of total nitrogen and total phosphorus under the 7 day-10
year low flow conditions are presented in Figure W-16. Total nutrient loads
from the Salisbury STP used in the projections are presented in Table 1.
3 -3o

-------
4.0
3.5
	_T0TAL NITROGEN PROFILE
	80UNDARY CONDITIONS ONLY
(2-2 mg -N/L AT OAM)
< 3.0
Z
i
ID
5 2.5
Z
UJ
O 20
a:
1.5
1.0
\
\

\
0.5
22 20
18 16 14 12
10
	TOTAL PHOSPHORUS PROFILE
	BOUNDARY CONDITION ONLY
(.175 mg- P/L AT DAM)
	BOUNDARY CONDITION ONLY
(.065 mg-P/L AT DAM)
r'

18 16 14 12 10 8 6 4
MILES ABOVE MOUTH OF WICOMICO RIVER
OAM SALISBURY
STP
FIGURE WIS
NUTRIENT PROJECTIONS
7 DAY -10 YEAR LOW FLOW
3-3/

-------
The settling rates developed in the verification analysis were applied. The
profiles in Figure W-16 present the calculated distributions resulting from
1)	the combined input of the Salisbury STP and the boundary conditions, and
2)	the boundary conditions alone. The boundary conditions used were the
average values of the nutrients observed during the July and August 1971
surveys. Above the dam at Salisbury, total nitrogen and total phosphorus
boundary concentrations were 2.2 mg-N/1 and 0.175 mg-P/1, respectively for
this period. Average profiles developed from other intensive data showed
total nitrogen to be consistently about 2.0 mg-N/1, of which half was in the
nitrate form, above the dam at Salisbury. However, a similar review of phos-
phorus data indicated a wide variability in phosphorus concentrations. The
average from the other data indicated a total phosphorus boundary concentra-
tion of .065 mg-P/1 above the dam. Figure W-16 presents projections for
both total phosphorus boundary conditions.
As can be seen in this Figure, peak total nitrogen concentrations of
greater than 3 mg-N/1 are projected in the vicinity of the Salisbury STP
outfall. Approximately 2/3 of this peak is attributed to the Salisbury STP
load. With complete elimination of the Salisbury STP nitrogen load, residual
concentrations of greater than 1 mg-N/1 are projected due to the upstream
boundary condition alone. Assuming complete conversion of the total nitrogen
of 1 mg-N/1 to phytoplankton biomass with a stoichiometric conversion factor
of 10 mg-N/mg Chi 'a', there is a potential for chlorophyll 'a' levels of
greater than 100 yg/1. Complete conversion, of course, would never be real-
ized so the above chlorophyll 'a' level is meant only for comparative pur-
poses.
An examination of projected total phosphorus concentrations shows peak
concentrations in the vicinity of the Salisbury STP outfall of greater than
0.4 mg-P/1 of which more than 3/4 is attributed to the Salisbury STP load.
Total phosphorus concentrations due to the high and low boundary conditions
alone are about .070 and .030, mg-P/1 respectively, at the Salisbury STP
outfall. Using a stoichiometric conversion factor of 1 mg-P/mg Chi 'a',
potential chlorophyll 'a' levels are 70 and 30 yg/1 for the high and low
boundary conditions, respectively. Based on the above analyses, the removal
of phosphorus relative to nitrogen will have a potentially greater impact in
3-3*

-------
the reduction of chlorophyll 'a' level under the lower phosphorus upstream
boundary condition. With the higher phosphorus boundary condition the dif-
ference is marginal. Therefore, further evaluations to establish the total
phosphorus levels above the dam and to eliminate the apparent discrepancies
in the available data are imperative. In terms of total N/total P ratios,
the boundary condition at the dam varies from 12-33 indicating that the
potential exists for forcing the Wicomico to be phosphorus limited. Also,
treatment to remove phosphorus at Salisbury would further force the system
to phosphorus limitation and reduce existing phytoplankton biomass.
Conclusions
1.	Chlorophyll 'a' levels in the Wicomico River in the vicinity of Salis-
bury have been observed to exceed 200 yg/1 during the summer. Dissolved
oxygen levels in this area vary from supersaturation during the day
under dry weather conditions to less than 3 mg/1 under wet weather-
high runoff conditions.
2.	Model analyses indicate that the effect of carbonaceous and nitrogenous
oxygen demanding material discharged from the Salisbury Sewage Treatment
Plant is limited to the upper six miles of the Wicomico River and is
relatively small when compared to the net effect of algal activity on
dissolved oxygen.
3.	Neither nitrogen nor phosphorus appear to be significantly limiting
phytoplankton growth in the upper Wicomico River although nitrogen may
be limiting growth in the lower River.
4.	The most significant sources of nutrients in the tidal portion of the
Wicomico River are the Salisbury Metropolitan Area and the watershed
upstream of the dam at Salisbury. The former source accounts for a sig-
nificant proportion of total nutrients tinder low flow conditions. Up-
stream nutrient inputs, however, are still substantial under low flow
conditions.
5.	The modeling analysis of dissolved oxygen indicates that the reduction
of the discharge of nitrogenous oxygen demanding materials from the
Salisbury Sewage Treatment Plant will have a relatively insignificant
effect on overall dissolved oxygen levels in the Wicomico River when
compared to the fluctuations in dissolved oxygen due to algal activity.
3-3 3

-------
Therefore, good secondary treatment is considered adequate at present.
6.	The modeling analysis of total nitrogen and total phosphorus indicates
that the reduction in the discharge of phosphorus relative to nitrogen
from the Salisbury Sewage Treatment Plant will have a greater impact on
phytoplankton biomass in the tidal portion of the Wicomico River with
potential reductions in chlorophyll 'a' to less than 100 Vg/1. Further
reduction in chlorophyll 'a' will necessitate upstream controls of
phosphorus.
7.	Therefore, it is concluded that the first step in nutrient reductions
to decrease chlorophyll 'a' levels in the tidal portion of the Wicomico
River should be directed toward phosphorus.
Recommendations
1.	Additional evaluations should be performed to more adequately define
nutrient conditions, especially phosphorus, in the Wicomico River above
the dam at Salisbury. Analyses should also be initiated to determine
the impact of nutrient controls in the Wicomico watershed above the dam
at Salisbury.
2.	For the values of the parameters that were assumed in this study because
of lack of data, such as the dissolved oxygen benthal demand, field or
laboratory measurements should be -made. Should nutrient controls be
implemented, intensive monitoring before and after should be conducted
to evaluate the impact on water quality.
3.	The modeling framework should be expanded to include phytoplankton bio-
mass. The model should also be continually refined in light of new data
especially after the implementation of nutrient controls, if any.
4.	Because of the loss of nutrients to the sediments, an investigation
should be conducted on the sediment-water interactions towards deter-
mining the potential for the re-release of these nutrients under
future conditions.
5.	An evaluation of the effect of high runoff - low incident light con-
ditions on dissolved oxygen in the Wicomico River should be conducted
since such conditions appear to be critical.
3 - 3

-------
REFERENCES
Boggess, D.H., and Heidel, S.G., "Water Resources of the Salisbury
Area, Maryland", Report of Investigation No. 3, Maryland Geological
Survey, U.S.G.S., 1968.
Pheiffer, T.H., Donnelly, D.K., Posschl, D.A., "Water Quality Conditions
in the Chesapeake Bay System", Technical Report 55, Annapolis Field
Office, Region III, Environmental Protection Agency, August 1972.
Salas, H.S. and R.V. Thomann, 1975. The Chesapeake Bay Waste Load
Allocation Study. Prepared by Hydroscience, Inc. for the Maryland
Dept. of Nat. Res., Water Res. Admin., Annapolis, Md., 287 pp.
Thomann, R.V., 1972. Systems Analysis and Water Quality Management.
McGraw-Hill Book Co., New York, 287 pp.
Walker, P.N., "Flow Characteristics of Maryland Streams", Report
of Investigation No. 16, Maryland Geological Survey, U.S.G.S. 1971.
Webb, W.E., and Heidel, S.G., "Extent of Brachish Water in the Tidal
Rivers of Maryland", Report of Investigation No. 13, U.S. Geological
Survey, 1970.
3-3 S~

-------
Examples of Sensitivity Analyses*
Water Body	Sensitivity	Remarks
Black. R. , N. Y.	K,	CBOD problem; dam reaeration
d
New York Harbor, N. Y.	Q, K , K , K	Point and distributed
n a	sources of CBOD
North Canadian River, OK	K , K,, K	Treatment decision
a d n
*
John A. Mueller
3 - 34

-------
Sensitivity Analysis
BLACK RIVER
New York
Ref: "Water Pollution Investigation: Black River of New York",
Hydroscience, Inc. for USEPA, Region II and V; EPA-905/9-74-009
J - 37

-------
Oj
I
to
- PERCH HIVCH
/	ft Z>
OC * i f flrn*fv(LccOo
0.3
Ql I [Hi[ I
ST REGisJ -2 J.-t/fS". 0 (tmt UP6Rrf\H?)
:H t M-pt 2.^	*
1[crown zellerbach| 12.4-
fcl t N lWN
I CLIMAX
I.G
JP LEWIS |
ON'ARlO
0,^	 BC*VC 
-------
2400
2000
USA
1200
-130
70 60 50 40 30
MILES ABOVE MOUTH
1200
1000 -
300 -
600 -
400 -
200 -
100 90
70 50 50 40 30
MILE ABOVE MOUTH
FI6.2. ORAINAGE AREA AND RIVER BED ELEVATION FOR
BLACK RIVER(FORESTPORT TO MOUTH)
3-3J

-------
AUGUST 14, 1973
o>

i
z
Id
O
>-
X
O
Q
UJ
>
_l
O
c/7
cn
a
FU3W at WATERTQWM s 1700 tfs
TEMPERATURE = I8.3C - 26 5C
70 H	ISA I12
24 "23 a) iA IS n 16 15 H13 II 1 ^ S * 3 2 I STA
a 3 {
1
h
C 0. SATURATION
2 o a
WATES QUALITY
STANDARD
7
2 ,
100 90 80 70 50 50 40 30 20 10 0 -10
MILES ABOVE MOUTH
MOOSE RIVER
SEAVER RIVER
o>

UJ
o
>
X
o
a
'jj
>
_i
o
07
n
a0. SATURATION
0 O
- 'KATiS QUALITY
3TAN0A30
I'll!
10
5 4 2 0
MILES ABOVE MOUTH
Z
UJ
<3
>-
X
o
a
UJ
>
_i
o
en
cn
a
a -
oo. saturation
WATIS QUALITv
STAN0AS0 	;
!0 9 o 4 2 0
MILES ABOVE MOUTH
FIG. 3 RIVER DISSOLVED OXYGEN DATA (AUGUST 14,1973)
3 -V-o

-------
in
3
O
0.
lli
a
o
tfj
<
UJ

-------
Ccxlculxt icnS
A Mueller
y/f4/73 survey
12-
z
O 0
i.o background Bobj-
0-
o
co
o
4-0
ao
DATA *. O Bois
~ BODu
i/
cc
K
Z
0)
u
z
o
u
A
o
CO
Q.^r~
16-
S"
0 -
CALC, 0CDu- Wy* C.ic/H^G. tlo'C.
"/f/73 su.Rver

-------

8/IV73 5>iRvcy
Q= 1700 cfi

STA. N 0
f^V00
u/i/73 JuRygy
Q = 14-00 cPs
T- 7.'7 -|I.6"C
0.0 MP
\\j\y73 JUffVE/
q -5500 c-fs
I -
0 Hyc? 10 = C.IS/do/
@	= O.U
	= o. IS"
1 mm mum ii iiisti iri	
- ])usolve^ 0x/Jm 3 ^Ven^/cft'tiohj

-------
FLOW AT WATERTOWN -SOOcts
TEMP = 25 C
10 -
LU
O
>-
X
O
a
UJ
>
o
cn
C
a
8 ="
4(
x
o
a.
0 Im. \n
UJ
0 0. SATURATION
WATER QUALITY 3TANDAR0
>

Ui
en
8
z
X
X
CI
'J.
z
J 3-
o
90
80
70
SO
50
40
30
20
10
MILES A3CVE MOUTH
WASTEWATER LOADS
INDUSTRIAL- 5EST PRACTICABLE CONTROL
TECHNOLOGY CURRENTLY AVAILABLE
MUNICIPAL - 3ECONOARY TREATMENT
FIG. 7 (DISSOLVED OXYGEN PROJECTION
FOR LOW FLOW CONDITIONS
3-++-

-------
o>

Ixl
a
o
a
4.0
3.0 "
y 2.0
1.0
GEORGIA PACIFIC PAPER CO.
UOO = 14,200 L9/0AY
"100 90 30 | 70 SO 5Q 40 30
MILES ABOVE MOUTH
20
10
V.
o>
E
i.	2.0
o
u.
LU
a
o
Q
40
3.0
ST. REGIS PAPER CO.
UOO =7,700 L9/0AY
"100 90 80 70 so 50 40 20 J 20
MILES ABOVE MOUTH
10
a>

o
d
4.0
3.0
y 2.0
1.0
WATERTOWN STP
UOO s 5064 L3/0AY
J	L
100 90 90 70 60 50 40 30
MILES ABOVE MOUTH
20
10
FIG. fr DISSOLVED OXYGEN DEFICIT PRODUCED BY
INDIVIDUAL WASTEWATER DISCHARGES
3-+S~

-------
Sensitivity Analysis
HUDSON RIVER
&
NEW YORK HARBOR
New York
Ref: "Seasonal Steady State Modeling", Hydroscience, Inc.,
Task Report 314, NYC 208, prepared for Hagen & Sawyer,
Engr. & NYC Dept. of Water Resources, Mar. 19.78
3 -<+>

-------
NYC 208 STUDY
HYDROSCIENCE, INC,
WCSTCMCSTCft
NEW JERSEY
umta
tssr
*tve*
urn*
mcs
m*r
LP*** cast
aivtit
QUEENS
mvt*
FIGURE 1
SCHEMATIC OF NYC 208 MODEL SEGMENTATION
3-y. 7

-------
NYC 208 STUDY
HYDROSCIENCE. INC.
socv
fUQZ
*UQi
SOOi
SOOJ
FIGURE 2.
MAJOR FEATURES OF RAINFALL RUNOFF Simulator
3-v?

-------
TABLE 1
SUMMARY OF TOTAL BOD,. LOADS BY SOURCE AND YEAR
Period	Total BOD5 Loads (lbfj/day)
Verification New York	New Jersey	Bypass Raw	Leakage	Miac	Runoff	Total Load
Sept. 1975 448014	1030610	129343	440021	107135	262760	435800	2.85 x 106
Nov.-Dec. 1976 527065	1219130	274150	281227	107135	262760	177600	2.85 x 106
July 1977 490687	949789	137506	281227	107135	262760	192000	2.42 x 106
SUMMARY OF TOTAL COLIFORM*1* LOADS BY SOURCE AND YEAR
Period		Total Total Coliform Loads (MPN/100 ml x MGD x 8.34) 	
Verification New York New Jersey Bypass	Raw Leakage Misc Runoff Total Load
Sept. 1975
5340
23599
33313
47073
15604
219
19070
144219

Nov.-Dec. 1976
111435
402
40001
36529
15604
219
7775
211965
July 1977
13486
14554
25483
36529
15604
219
8374
114249
^^All numbers x 10^
{MGD x MPN/100 ml x 8.34) x (4.54 x 10^) = No/day of coliforms

-------
15
KOTf-Mvtso* om.r,	o 'ko>c*tzJ rj Oft' scf tm
FLO* *T BEAfl WOUNTklN k I 1100 C<1
TE uPERATjne * II-2**C
LE&CHO
O SURFACE MEAN*
Q BOTTOM mean
CONFIOENCE
LEVEL or mEJ>*
calculated PROFILE
I
10 -
ao. saturation
5 -
TOP LAYS ft
BOTTOM LAYER
30	40	30	20	10	0	-10	-20	-30
HUDSON RIVER TRANSECT - BEAR MOUNTAIN BRIDGE TO ATLANTIC OCEAN (MILES)
LESCHOx
DEFICIT PRODUCED BT
FLOW AT BEAR MOUNTAIN a 7600 etl
TEMPERATURE" 17  27*C
N.Y AND N.J. WPCP'S.
 RAW LOADS,
(s) senthal oxygen oemano
 BYPASS AND LEAKAGE LOADS
0 RUNOFF LOADS.
 MISCELLANEOUS OTHER LOADS. DEFICIT
LOAOS, NBOO OXIDATION,BOUNDARY
CONDITION
 calculated unit response over
DEPTH
(BOTTOM LAYER IN HUDSON ]
TOTAL 0.0. DEFICIT
50	40	30	20	/O	0	-!0	- 20 -30
HUDSON RIVER TRANSECT - BEAR MOUNTAIN BRIDGE TO ATLANTIC OCEAN (MILES)
Pis. 3 Dissolve QxvceN verification + umit ResPoN-sej
3-S~c,

-------
15
<3
2
z
UJ
o
>-
X
o
Q
UJ
>
_l
o
tO
V)
10
FLOW AT BEAR MOUNTAIN a 7600 els
TEMPERATURE ~ I7-27*C
LEGEND:
	CALCULATED BOTTOM LAYER PROFILt

JULY 1977
TRANSPORT
0 BEAR MOUNTAIN
NOV."UCC. 1976 TRANSPORT
0 BEAR MOUNTAIN 
18400 crs
7600 CFS
SUMMER 1965
TRANSPORT
OBEAR MOUNTAIN?*
3200 CFS
50	40	30	20	10	0	-10	-20 -30
HUDSON RIVER TRANSECT - BEAR MOUNTAIN BRIDGE TO ATLANTIC OCEAN (MILES)
o
2
e>
>
x
o
o
UJ
>
-I
o
(/)
CO
10
r- 0.0-
I SATURATION
r N0V-0EC.I976
TRANSPORT
JULY 1977
^TRANSPORT-
SUMMER
1965
TRANSPORT
O
2
2
UJ
to
V
X
o
o
UJ
>
-I
o
CO
CO
rao.
\SATURATION
JULY 1977
20
10
THE KILLS (MILES)
'SUMMER
1965
TRANSPORT
HARLEM RIVER
15
(9
2
UJ
C5
>-
X
o
a
UJ
3
o
n

-------
15
2 '0
UJ
o
>
X
o
a
UJ
5
O
V)
in
FuC'.V AT BEAR MOUNTAIN a 7600 cfi
TEUPERATURE a |T -27*C
LtSCNO:
	 calculated bottom
	LAYER PROFILES
Kj ~ de oxygenation ceff.
^0.0. SATURATION
0.15 /DAY AT JO* C
.Kj<0.2S/0r AT 20*C
KdOJS/OAY AT 20C
I
I
I
5 
2 
X
o
o
cn

-------
5.0
flow at bear mountain = 7600 ei
- TEMPERATURE3 1727*C
4.0
o
2
kl
to
o
0.0/DAT AT. aoC
50	40	30	20	10	o	-10	-20 -30
HUOSON RIVER TRANSECT - BEAR MOUNTAIN BRIDGE TO ATLANTIC OCEAN (MILES!
FIGURE 6
TKN SENSITIVITY TO NITRIFICATION RATE (Kn)
(JULY 5-29,1977)
3-?3

-------
6.4
6.0
5.6
5.2
4.6
4.4
4.0
3.6
3 2
ISC MONITOR 6
THE NARROWS
AT
FT. WADSWORTH -
4.
 6~. IS fog/2
J	' i
J	L
i
_L
NO. DATA
DA TA L EGEND : POIN TS *
A SUMMER 1976 64
 SUMMER 1975 23
 SUMMER 1974 21
0.1 mg/l CLASS INTERVAL


I

QOI
0.1 Q2 0.3
10 20 30 40 50 60 70 80 90
PERCENT CUMULATIVE FREQUENCY
95
98 99
99 8 99.9
99.99
FIGURE I
PROBABILITY PLOT OF SUMMER DAILY AVEP-^E DISSOLVED OXYGEN DEFICIT-ISC MP^.ITOR 6

-------
II
10
9
8
k
7
6
5
4
3
2
I
0
<
'Aft 4>
F|<
0.0. SATURATION-
MEAN N Y. STATE
STANDARD
\
\
\
\

\
/
/
/
/
/
LEGEND:
	ZERO DISCHARGE
	 SECONDARY TREATMENT
	 BASELINE
	 PRESENT
0
)UNTA!N
10
30
J-
20	10	0
DISTANCE - MILES FROM BATTERY
HUDSON RIVER TRANSECT
-10
-20
-31
OCt
PREDICTED DISSOLVED
OXYGEN CONCENTRATIONS foh

-------
15
FLOW AT BEAR MOUNTAIN a 7600 cf*
TEMPERATURE'S 17-27'C
LEGENO:
	 CALCULATED bottom
	LAYER PROFILES
o.o. saturation
K > 0.0/DAY AT 20*C
K, "0.03/0AY AT 20*C
K >0.10/0# AT 20e //
MILES
SO 40	30	20	10	0	-10	20
HUDSON RIVER TRANSECT - BEAR MOUNTAIN BRIDGE TO ATLANTIC OCEAN
15
o
2 10
0.a SATURATION
^o.asj
>0.0
>0.03
K >0.10
15
is
s
z
LU
CD
>
X
O
Q
UJ
3
O
tn
i/i
10
rO.Q
\SATURATION
 k ao
*n 0j05
Kn OJO
15
o
2 10:
Ui
o
>
X
o
Q
Ui
>
J
o
 0.10
20	10	0
THE KILLS (*MILES)
0	10
HARLEM RIVER
10 - 20
EAST RIVER ( MILES )
30
FIGURE 7
DISSOLVED OXYGEN SENSITIVITY TO NITRIFICATION RATE (K
(JULY 5-29,1977)
3-s~e>

-------
Sensitivity Analysis
NORTH CANADIAN RIVER
OKLAHOMA
Ref: "Review of North Canadian River Water Quality Analysis", Gallagher,
T.W. and Thomann, R.V., prepared by Hydro Qual, Inc., for USEPA
Washington, June, 1981
3-S- 7

-------

PRoPoicd
/sloSTVl CAJOt>i#-J UJIaJTP
la *e
ove iioL^e r
1.
Co
one Sou-nil Itg
Cnf
|o
fJoer/4
-X. ftPPe.xi/*me nn-fPoirJT
FIG. I MAP of STUby AREA of NORTH CANADIAN CREek, OKLAHOMA

-------
| un
Uj
k
auq mo
sepT mo
Zo
^Vl'
I

X
0
A
0
T  *P
_ f\A
i V-
J fll.}.
3oU
SITji&ivtipiJ
*  1 * 
IO	I
S
Za
 v |k
" IZ
a
/i
b<
; 4-
~fer*p - za "c_
1.J LiATiVI'eJ-
1 I lo 3o 4o i o
	fOlLtS fcf Lu.\ LUtf* OVftJlM.'.
c
* ' ' J
Z.C	)o	Ao	St>
ClilSi 6Ctm-) La'* Oifili:
0 OXYGEN 1>ATA

-------
U)
I
D
c^e x Ka^ir.y/Jgy r Ha - o.35/J*yt K- 0.5-o/rfay
"Wl

h"
(J
a
lii
z
lu
i3
*
X
o
A
UJ
>
_I
o
X
<
2
ult Cfco'b = ;.s  C6ot>-
xt 	"To <oti = 4.c * *1
?o	Zi.
^1*
Jt>	iz
CAiE HI	Kg* 5".0 fduy ) Wje I.o/ * Ct,oX
rleot> -- 4.s 
e.
EPFL^eNT 6 0 Q^S/i)
EPPCUet/t)
FIG. 3
5EWfiTiviTy o-F "D. o. >ep|ciT (max) to Hiwetic. coeppicieNTf

-------
STATE OF OHIO
ENVIRONMENTAL PROTECTION AGENCY
BOX 10U9
361 E. BROAD STREET
COLUMBUS, OHIO 1+3216
ROCKY FORK WASTELOAD ALLOCATION
Office of Wastewater Pollution Control
Division of Water Quality Planning and Assessment
Prepared by
June, 1981
Draft and Subject to Revision
3 -<* 1

-------
Sunsnary and Conclusions:
1.	Wasteload allocations were conducted for Mansfield WWTP and, due to
interaction, Heatherwood Subdivision, Lucas WWTP and eight (8) industries
on the Rocky Fork of the Mohican River were included in the allocation
process.
2.	Mansfield WWTP, at present, is not meeting the effluent limits specified
in its existing NPDES permit. Most of the industries are also discharging
concentrations ouch higher than specified in their existing permits.
3.	Wasteload allocations were conducted by employing the decay rates measured
during the field survey. The results were compared with those obtained by
employing text book decay rate values. In both cases, dissolved oxygen
sag was not located in the Rocky Fork of the Mohican River. Preliminary
studies indicate the D.O. sag to be located below the confluence with
Black Fork.
4.	High concentrations of heavy metals discharged by the industries, upstream
of Mansfield, have a significant adverse impact on the performance of
Mansfield WWTP.
5.	Model calibration and verification was not considered due to presence of
excessive amounts of conservative parameters and interaction between
conservative and non-conservative parameters.
6.	The field survey results and wa6teload allocations clearly show the need
to reduce the oxygen demanding pollutants -ftr-at least the recommended
levels, in order to improve the water quality in Rocky Fork of the Mohican
River.
7.	Once mansfield WWTP and the industries meet their recommended effluent
limits, another field survey should be conducted. The results will be
used to calibrate and verify the model, and the wasteload allocations will
be revised accordingly.
3-6 2.

-------
INTRODUCTION
A study was initially performed Co determine effluent limitations and to
complete AST Justification for the Mansfield WWTP on the Rocky Fork of the
Mohican River. Conventional pollutants and metals are addressed in this
report. Conventional pollutants are allocated to Mansfield WWTP and, due to
interaction, Richland County Heathervood Subdivision and Lucas WWTP's are
included in the allocation process. Metals are an acknowledged problem (see
"Biological Assessment") and have a major impact on the water quality of the
Rocky Fork. Therefore, metals are allocated to eight (8) industries and
Mansfield WWTP.
While water quality problems due to conventional pollutants can be attributed
predominantly to the Mansfield WWTP, the metals problem is due to dischargers
^ipstream of the Mansfield WWTP.
Design flow of 20.0 MGD exceeding the "Simplified Method" limit of 10.0 MGD
and interaction with other dischargers necessitates using QUAL-II model to
allocate loads to Mansfield WWTP. Biological and economic assessments are
presented (see "Biological Assessment" and "Economic Assessment").
3-4 3

-------
DISCHARGER
The Mansfield WWTP, located in Che southeast portion of the City of Mansfield
on Illinois Avenue, discharges to Rocky Fork at river mile 11.18 (see Figure
2). The planning area includes the entire incorporated area of the City of
Mansfield and adjacent areas to the northwest, east, southwest and south, that
are in the Rocky Fork drainage basin. In addition to domestic waste, the
plant accepts waste from a number of industries, including food processing,
inetal surface preparation and plating, and tire and automobile manufacturing.
The metals from these industries not only cause water quality standards
violations once the effluent enters the stream, but can also inhibit plant
performance.
Currently, the plant is an activated sludge type facility with separate sludge
digestion and sludge filtering, with a design capacity of fifteen mgd and a
maximum hydraulic capacity of twenty-five mgd. The treatment train consists
of bar screens and grinders, two aerated grit tanks, twin primary settling
tanks, six secondary aeration tanks, and two final clarifiers.
With industrial and population growth in the Mansfield area, the treatment
plant must expand to 20.0 mgd from the current 15.0. mgd. Effluent limits were
prepared for the Mansfield WWTP baaed on this design flow employing the
QUAL-II SEMCOG version.
3-C 

-------
Figure 3: Water Quality Sampling Sites on Rocky Fork
Unnamed Trib
i 17.65
Sites 1,A,B,C, are 24-hour composites
Sites 2 throunh 7 are 2 grabs-composite
Sites 8 through 13 are 1 grab/day
erman School
.58
Unnamed Trib
16.41
Luntz Corporation ^76^ 15.85
Chemtron Corp. E203
15.75
^Cyclops Corp. D203 (001)
, 14.77
14.70
14.48
14.95
P203 (003)
D203 (004)
D203 (002)
of flow
SITE
Unnamed Trib (SITE 13)
14.43
Ohio Brass N261 (003) ^13.85
	N261 (002) J 13.82
13.80
N261 (OOP
Touby Run (SITE 8)
SITE
13.73
13.08 ffhite Consolidated C203
12.95 globe Steel Abrasives S251
SITE;5
SITE
3-65-

-------
0.95
Figure 3: (Continued)
Culligan Water Conditioning N2Q8
12.30
Unnamed Trib
Unnamed Trib (SITE 6)
Stone Container Corp. A201
4.75
11.40,
12.40


Unnamed Trib (SITE 9)
>.2
Madison City MHP

1.5
Richland Co. Hillsdale
11.98

WWTP 6707
11.70
Unnamed Trib (SITE 10)

.Emerson Electric S228
SITE jA
Mansfield WWTP E701 J 11.18
Unnamed Trib (SITE 7)
3.9
tich. Co. Heatherwood Subd.
10.70
SITE B
Unnamed Trib (SITE 111
7.07		
Unnamed Trib (SITE 121
'3.67
3.65 L Lucas WWTP B738
<		
Ts'ite  c 1
Black fork


-------
RESULTS
t*;eload allocation:
he proposed Mansfield WWTP was nodeled under summer Qy jq conditions. The
dissolved oxygen sag was not located in the fiocky Fork (see Graphs I and
II). The treatment level of 10.0 mg/1 BOD5, 2.0 mg/1 NHj-N and 6.0 mg/1
D.O. resulted in a dissolved oxygen concentration of 5.31 mg/1 at the mouth
of Rocky Fork without reaching the sag point. However, this treatment level
can be considered as an interim sumer limitation. The dissolved oxygen sag
was determined, by preliminary analysis, to be located in the Black Fork,
approximately 2.0 miles below the confluence of Rocky Fork. This finding is
supported by the Biological Assessment of the Rocky Fork where, it was
documented that violation of HQS for non-conservative parameters resulted
from the effluent of Mansfield WWTP and the dissolved oxygen recovery was not
apparent in&ediately below the confluence of Rocky Fork with Black Fork (see
Biological Assessment).
Under winter design flow conditions, the background flow increases and
temperature decreases. This changes the streets geometry and reaction rates.
Winter temperature and pK also affect the NH3-N standard. These changes
result in winter allocations being less stringent than the summer
limitations. The results of winter wasteload allocation appear in Table 3.
Qua ts lnesraetien with Mansfield WWTP'a affluent, the Heatherwood
Subdivision and Lucas WWTP's were included in the wasteload allocation
process. Heatherwood Subdivision is located on an unnamed trib and the
)eatment level of 10.0 mg/1 BOD;r 2.0 mg/1 NH3-N and 6.0 mg/1 0.0. is
equate ta maintain susner water quality standards. The discharge flow of
bucas WWTP is negligible compared to the upstream flow. Therefore, wasteload
allocation for Lucas WWTP taa conducted by neglecting the effect of
Mansfield's discharge. Lucaa WWTP can discharge 30.0 mg/1 BOD5, 15.0 mg/1
NH3-N and 5.0 mg/1 D.O. and maintain Water Quality Standards in the
stream. The results of winter wasteload allocation appear in Tables 4a and
4b.
Since the measured decay rates were considerably lover than the text values,
a steady state simulation was conducted using 0.6 and 0.3 day"* for
KcBOQ KnB0D> respectively. Lower measured decay rates may be
attributed to high concentrations of conservative parameters discharged by
the industries. Results of the two simulations using the treatment level of
10.0 mg/1 BOD5, 2.0 mg/1 NH3-H and 6.0 mg/1 D.O. were compared. The
lowest D.O. concentration, under the measured decay rates, was 5.31 mg/1 at
the mouth of Rocky Fork. The simulation with the text values resulted in a
D.O. concentration of 2.7 mg/1 at the mouth (see Graphs III-V).
Alternative Treatment Levels:
Federal guidelines (5) require that alternative treatment levels be
evaluated. They vary from secondary treatment to advanced secondary
treatment with filtration and nitrification. The exact effluent BOD5 and
myti evaluated are listed in graphs I and II.
7

-------
Sensitivity Analysis
In order to assess the impact of errors in measurement of the input variables
utilized in the vasteload allocation process, the sensitivity of the
allocated BOD5 was calculated for Temp, pH, upstream BOD5, Kj, &2 and
k3.
BOD^ was most significantly influenced by the reaeration rate -
Using Owens option resulted in D.O. sag being located at RM 11.0, 0.4 miles
below Mansfield WHIP, with a treatment level of 20.0 mg/1 BOD5, 3.0 mg/1
KH3-N and 5.0 mg/1 D.O. However, the reaeration rate with Owens option
varied between 94.49 and 30.92 day"*.
Ohio EPA limits Kg values Co 20.0 day"* and anmonia toxicity in the
stream is 2.6 mg/I. Therefore, it is recommended that Tsivoglou option
rather than Owens option be used.
Pretreatment:
The industrial survey on the Rocky Fork has been completed.
Thm consultants are in the process of sampling the influent and effluent of
the Mansfield WWTP as well as the industries considered to be the major
contributors to the Mansfield WWTP.
The fiaal report can be expected At the end ort981.


-------
RECOMMENDATIONS
id on NLA results, ic is reconnended that the following be done Co insure
maintenance of stream use designations and RQS in the Rocky Fork of the
Mohican River:
1)	Once the Mansfield WWTP is upgraded to the recommended level,
Ohio EPAr during the low flow season, should locate the D.O. sag*
2)	Chemical data should be collected, on monthly basis, at the
mouth of Rocky Fork and on Black Fork below the confluence of
Rocky Fork.
3)	Once Mansfield WWTP is upgraded and all other discharges
contributing heavy metals comply with their permit limitations,
Mansfield should install continuous monitors at the mouth of
Rocky Fork and at the location of D.O. sag (composite and grab
samples) for the following parameters:
D.O.
BOD
nh3-n
TKN
3-C.?

-------
CONCLUSION
The proposed 20.0 mgd VWTP at Mansield can discharge an effluent of 10.0 mg/1
BOD, 2.0 rog/1 NH3-N aid 6.0 mg/1 D.O. in the summer, and 25.0 mg/1 BCDc,
15.0 mg/1 NH3-N and 5.0 mg/1 D.O. in the winter. These limits should Be
considered as interim limitations as the D.O. sag was not located under surmer
or winter conditions and the severely degraded biological condition of the
stream below the Mansfield VWTP persisted downstream to the confluence with
the Black Fork, with little improvement being shown (see Biological
Assessment).
The Heatherwood Subdivision can discharge an effluent of 10.0 mg/1 BOD5, 2.0
NH3-N, and 6.0 mg/1 D.O. under simmer and winter conditions. The summer and
winter limitations are adequate to maintain water quality standards in the
stream.
The Lucas VWTP can discharge an effluent of 30.0 mg/1 BOD5,
15.0 rog/1 NHj-N and 5.0 mg/1 D.O. under sunnier and winter conditions and
maintain water quality standards.
Ohio EPA requires extensive justificaton detailing the need and economic
benefit of waste treatment greater than 10.0 mg/1 BOD5 and
2.0 rog/1 NH3-N. This justification must include comprehensive physical,
chemical and biological studies. It is recommended that in the interim, the
Mansfield WWEP NIOES summer and winter limitations be set at the reccnmended
levels (as shown in Table 4).
Heavy metals affect the chemical and biochemical reaction of the
non-conservative parameters. However, the complete affect of metals, in seme
cases, is not fully understood. Therefore, reduction of conservative and
non-conservative parameters is essential to maintain stream use designations
and water quality standards in the Rocky Fork of the Mohican River.
Once the plants are upgraded to meet the proposed permit limitations (as
specified in Tables 4 through 5), it is recommended that Rocky Fork be
evaluated by using the results of continuous monitoring data and another
intensive survey from EM 11.2 of the Rocky Fork to the point of D.O. sag. The
results of these surveys would be used for:
1} Calibration and verification of the model and establishment of
constant rates.
2)	conducting an additional stream assimilation study.
3)	Evaluation of the stream use designaticn/attainahility.
3-1 o

-------
TABLE 3
Mansfield Wasteload Allocation Results
for Design Conditions

Sdsbbt
Winter
BOD g
R/A mg/1*
25.0 mg/1
TSS
B/A mg/1*
25.0 mg/1
BHj-N
H/A mg/1*
15.0 mg/1
D.O.
H/A mg/1*
5.0 mg/1
Ca
4.24 lb/day

Cd
2.14 lb/day

Cr
16.68 lb/day

Ca
10.01 lb/day

Pb
5.381 lb/day

"za
33.55 lb/day

Hg
0.033 lb/day

O&G
834.4 lb/day

~See results "Wasteload Allocation," page 18.


-------
TABLE t*
Reconnended Effluent Limits For Mansfield
Sumner	Winter
BODj
10.0 mg/1
25.0 mg/1
TSS
12.0 mg/1
25.0 mg/1
HHj-N
2.0 mg/1
15.0 mg/1
D.O.
6.0 mg/1
5.0 mg/1
Ca
4.24 lb/day
4.24 lb/day
Cd
2.14 lb/day
2.14 lb/day
Cr
16.68 lb/day
16.68 lb/day
Cu
10.01 lb/day
10.01 lb/day
Pb
5.381 lb/day
5.381 lb/day
Za
33.55 lb/day
33.55 lb/day
Bg
0.033 lb/day
0.033 lb/day
O&G
834.4 lb/day
834.4 lb/day


-------
Table 4a
Reccnmended Effluent Limits for
Beatherwood Subdivision

Summer
Winter
bgd5
10.0 rag/1
10.0 mg/1
TSS
12.0 mg/1
12.0 mg/1
13-N
2.0 mg/1
2.0 mg/1
D.O.
6.0 mg/1
6.0 mg/1
TBVBIE 4b
Reoarm ended Effluent Limits For Lucas WWTP

Sumner
Winter
bcd5
30.0 .mg/1
30.0 mg/1
TSS
30.0 mg/1
30.0 mg/1
IBj-N
15.0 mg/1
15.0 mg/1
D.O.
5.0 mg/1
5.0 mg/1
^-7-3

-------
Table 5
Heavy Metals Allocation Results for Industries
EHTITY	FLOW (MGD)	PARAMETER.	ALLOCATION (lb/gay)
Lantz Corp	0.045	O&G	32.11
Cyclops Corp.	2.75	Fe	23.72
O&G	84.46
Ohio Brass	0.359	Cu	1.51
Zn	5.06
O&G	7.41
White Consolidated	1.11	Cu	0.415
Cr	3.21
Cn	0.80
Hi	14.61
O&G	34.58
Globe Steel Abrasives 0.147	Fe	9.39
Zn	1.59
Emerson Electric	0.064	O&G	2.67
Borg Warner Corp.	0.137	O&G	11.43
Stone Container Corp. 0.078	Cd	0.398
Cr	0.906
Ctx	0.128
Fe	2.14
Pb	0.998
Hi	4.12
Zn	0.232
0&G	14.27
3-7/

-------
Figure 2: Rocky Fork Schematic
herman School
.05cfs)	*
1.58
^ Unnamed Trib
1.48
Unnamed Trib
^0.07cfsLuntz Corp. N276
Chemtron Corp. E203
IU.QU3 cfs)
14.95
0203 003
(O.y cfs J
(0.67 cfs )D203 004
(0.94 cfs) D203 002
14.43
(0.116 cfsEhio Brass N261 003
13.85
(0.015 cfs) N261 002jl3.82
13.80
13.73
(0.24 cfs) N261 001
Touby Run
13.08
12.95
(0.059 cfs) i(jea7 Electric
12.30
7.65
cfs
16.41
15.85
15.75
Cyclops Corp. 0203 001
U.U; ctsj
14.77
14.70
14.48
Unnamed Trib
Direction of flow
Jfhite Consolidated C203 (1.11 cfs)
JSlobe Steel Abrasives S251 (0.227 cfs)
12.40
Unnamed Trib
3-7 X-

-------
0.95
Unnamed Trib.
0.95 	
Unnamed Tributary
Figure 2 (Continued)
Culligan Hater Cond. N208 (DISCHARGES TO MANSFIELD SANITARY SEWER)
Stone Container Corp. A2Q1
Emerson Electric Co. S228
*	(0.09 cfs)
11.40
I.98
II.70
Unnamed Trib
2.20
1.50
,Hadison City MHP
Richland Co. Hillsdale WWTP
Mansfield WWTP E701
(30.94 cfs)
Unnamed Tributary
1.18
0.70
3.90 Rjchland Co. Heatherwood Sbc
(0.1 cfsJ
Unnamed Tributary
7.07 ^			-
Unnamed Trib.
3.65
Black Fork
3.57
Lucas WWTP B738
(0.\-Lcfs)
(14.02)

-------
Graph I: NH3-N vs River Mile
16.0 J_
14.0
12.0 J_
10.0	
# a"
6.0	
4.0-L
2.0-,
12.0	10.0
am A: 16.0 mg/1 BCDS, 24.0 mg/1 NH3-N, 5.81 mg/1 D.O.
Ria B: 10.0 mg/1 BCDg, 3.25 m^l NHj-ilr 6.0 mg/1 D.O.
Rm C: 10.0 mg/1 BQDS, 2.0 mg/1 HHj-N, 6.0 mg/1 0.0.
(B)
.(C)
H	1	1	1	~
'	I
8.0  6.0	4.0
River Mile
*I1(
2.0	0.0
*-??

-------
Graph H: D.O. vs River Mile
7.0
6.0-L
ff 4-0--
Bun A: 10 mg/1 BCDg, 2.G mg/1 NHj-N, 6.0 mg/1 D.O.
ftm B: 10.0 mg/1 BCDj, 3.25 mg/1 NH3-N, 6.0 mg/1 D.O.
3.0	
Run C: 16.0 mg/1 BCDg^ 24.0 mg/1 NH3-N, 5.81 D.O.
l.QJ_
(O
2.0
0.0
4.0
6.0
8.0
10.0
12.0
River Mile
n5-?<5>

-------
Graph 2XL: BODg vs River Mile
12.0
t
t
1
1
10.0 1
T
1

IP
4.0 -r-
Run
76.0 mg/1 B0D5, 24.0 mg/1 NHj-N, 5.81 mg/1 0.0. (Battle Decay Ratas
16.0 mg/1 B0D-, 24.0 mg/1 NH--N,..5.81 mg/1 D.O. (Book Values)
Run
Run C: 10.0 rag/1 BODg, 2.0 mg/1 NH3-N, 6.0 mg/1 D.O. (Bottle Decay Rates)-
Run
10.0 mg/1 B0DS, 2,0 rag/1 NH3-N, 6.0 mg/1 D.O. (Book Values)
1.0 
12.0	10.0	8.0	6.0	4.0	2.0	0.0
River Mile


-------
18.0
Graph IV: NH,-N vs River Mile
Run A: 16.0 mg/1 BODj, 24.0 rog/1 NH^-N, 5.81 mg/T 0.0. (Battle Decay Rate
12.0	
Run 8: 16.0 mg/1 BODg, 24.0 rag/1 NHj-N, 5.81 mg/1 0.0. (Book Values)
10.0	
OS
t
Run C: 10.0 mg/1 BOD,., 2.0 mg/1 NH^-N, 6.0 mg/1 B.0. (Battle Decay
6.0	
Run D: 10.0 mg/1 B0D5, 2.0 mg/1 NH3-N, 6.0 mg/1 D.0. (Book Values)
4.0	
2.0	
0.0
2.0
4.0
8.0
6.0
10.0
12.0
River Mile


-------
Graph V: D.O. vs River Mile
7.0 
6.0 
Standard
6.0	4i0
River Mile
Run A: 10.0 mg/1 BOD5, 2.00 mg/1 NH3-N, 6.00 mg/1	D.O.
Run B: 10.0 rag/1 BOD5, 2.00 rag/1 NH3-N, 6.00 mg/1	D.O.
Run C: 16.0 mg/1 BOD5, 24.0 mg/1 NH3-N, 5.81 mg/1	D.O.
Run D: 16.0 rag/1 BOD5, 24.0 mg/1 NH3-N, 5.81 mg/1	D.O.
(Bottle Decay Rates)
(Book Values)
(Bottle Decay Rates)
(Book Values)

-------
IBTRODUCTIOB ABD BASIC COBCEPTS*
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 n"* land. They are transferred between and among these media,
undergo transformation within each and accumulate in viable and nonviable
constituents. The magnitude and significance of the problem has became
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.
Th-ia 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 oust 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 3uch levels as to yield the benefits
without deleterious effects. This goal necessitates the development of
assessment methods which permit an evaluation ultimately a prediction
of environmental concentrations. The approaches developed herein are,
therefore, directed to two broad areas: an evaluation of the present extent
and distribution of these substances, 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

-------
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 controlled labora-
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 only 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 metals 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 vater 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
elements 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 well-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 reli*nie 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-

-------
mena 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 presents
various mathematical models of natural water systems, incorporating 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 of the overall approach, it is
first appropriate to indicate the basic concepts which axe 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 diagrammatically in Figure A-l, 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:
c^ = concentration of the chemical in compartment, i.
J = transport through the system
R = reactions within the system
T 3 transfer from one phase to another
W  inputs
T aT-" J! ~ t*i ~ Hi ~ w
(1)
in which

-------
Equation (l) 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 (T), distinct from the transport (j) and reaction (R), 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 physiocheai-
cal regime - the dissolved and particulate in the vater, atmosphere and bed
- as veil 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. 'Hie pathways are determined by the
hydrodynamic 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 biolbgical 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:
(2)

-------
p  particulate concentration in i compartment (M/L^)
= oass of chemical/unit of interacting mass (M/M)
m^ * concentration of the interacting species (M/L^)
The. mass balance equation for the particulate component, similar to equation
(1), is then:
dp	dm. dr.
i.  r, + m, - J + DR + ZT + EW
d u	1. dx	x dX
(3)
It is apparent from equation (3) that an equivalent expression must
be vritten for the concentration of the interacting compartment, su. In
principle, the analysis of the problem requires the simultaneous solution
of the three equations: the concentration of th$ chemical dissolved in
the vater, 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:
?1 - 	(4)
The specific conditions for vhich 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
biamass. Thus 3 ot from vhich an equilibrium concentration of solids
or biamass follows, resulting in tvo simultaneous equations to be solved,
instead of three.
B. 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,
vhich, in time, leads to a dynamic equilibrium between the tvo components.
Consider the most simplified conditions of a batch reactor in vhich the
1-s-

-------
mi ring is of sufficient magnitude to maintain a uniform concentration
throughout the volume of fluid. Assume the concentration of absorbing
solids, m (M/L^) is constant. Let c and p be the concentrations (M/L ) of
the dissolved and particulate components. If there is neither transfer
nor decay of the chemical, the total concentration, c^,, remains constant
in time and is equal to the sum of the dissolved and particulate:
cT  c + p	(5)
The latter is related to the concentration of suspended solids, m, as shown
by equation (2):
p  rm
The equilibrium betveen the dissolved concentration in the water and
the mass concentration of the solids is usually expressed in terms of a
partition coefficient:
t a  = E	.,.
c mc	(6 J
or	1Fm = ^
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 + Hmc = + p	(T)
The product, Hm, is a convenient dimensionless parameter, characteristic of
a particular system under equilibrium conditions. For a specified value of
Hm, 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 fashion. Accounting for the distribution for various types
H-6

-------
of adsorbing solids and various levels of the food chain, each with its
characteristic partition coefficient, equation (7) may be more generally-
expressed:
cT a c[l +	(8)
The distribution may thus be categorized in accordance with the adsorbing
solids (organics, clays, silts and sands) or the accumulating biomass
(phytoplankton, zooplankton, fish and maicrophytes). Since the total bio-
mass mass in most natural vater systems is usually an order of magnitude
less than that of the non-viable 3olids, 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. kuramc mTERA.cnon
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 *.ih ng place between the dissolved and particulate com-
ponents the former is being transferred by volatilization or transformed
by chemical or biological degradation:
h K3
P*TC
The reversible reaction (K^^Kg) 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^) describes the decay or volatilization. The kinetic
equations are:


-------
If.- (K2 ~ K3)= ~ KlP	(10)
tf'-w	(u)
By differentiating (10) and substituting (10) and (ll) into the second-order
differential equation, there results:
.2	.
=-| + + K2 + K3] It + K1K3C = 0	(12)
dt
An identical expression results for p. Assuming the initial concentration,
c , is totally in the dissolved form, the initial condition is
c a c at t  o
o
Applying the second condition:
dc  . ,
dt " " 2Co at * " 
the solution of the differential equation (8) subject to these initial condi-
tions is:
c  c^Be86 + (l-6)eht]	(13)
in which g,h are the positive and negative roots of the quadratic
6fc = -  [1 + m]
in which K a
K2
It may be readily shown that g and h are always real and negative.
In the case of adsorption-desorption, the assumption of instantaneous
equilibrium is frequently made - i.e. the coefficients and are of
sufficiently large magnitude so that the exchange between particulate and
^-8

-------
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
or
!~ v3=-
-
	L_			(HO
dt 1 + Kg/K^ C
in vhich
*2
  distribution or equilibrium coefficient
h
An additional insight is gained by developing equation (lU) in an alter-
nate manner by adding equations (10) and (ll) vhich yields
dc_
R5"-*	(15>
Assume 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, c^, by equation (7) substitution of which in (15) yields
dcT K3
itm:cT	(l6)
The total concentration decays in accordance with the dissolved coeffi-
cient modified by the parameter fm. As a physically realizable example,
consider the transfer represents a volatilization process, in which is
the gas transfer coefficient. The total concentration c^, decreases at a
slower irate than would be the case if there were no partitioning to the par-
ticulate form, with the total in dissolved form (Am  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
f-7

-------
with the particulate component, the coefficient would be reduced toy the
fraction 1fm/[l + ffm], in accordance with equation (7).
If both the particulate and dissolved components are subject to decay,
by more than one mechanism, equation (l6) becomes
dc_	DC . flmlK .
	2. 3 _ r. ci +	Ei.] c	(17)
dt	L1 + 1m 1 ~ UmJ T	v ;
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
(Ik) through (17) is a valid representation, or model, of kinetic reactions
provided the time to equilibrium, determined by and is rapid relative
to the other phenomena which affect the substance & K^. This condition
is generally applicable to the adsorption-desorption process, since its
equilibrium time is usually much shorter (min-hours) than that of other
kinetic effects, which may be in the order of days, months or years.
In summary, 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 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.
3y 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 realo,
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.
H-to

-------
TRANSPORT KINETIC ROUTES WITHIN THE WATER COLUMN

EVAPORATION
AIR
PHOTO-OXIDATION
INTERFACE
WATER
DIRECT INGESTION
IN VARIOUS LEVEli
OF FOOD CHAIN
AEROBIC
BIODEGRADATION
NtKTONIC

lar
ACCUMULATION
IN FOOD CHAIN
OESORPTION ABSORPTION
SUSPENDED
SOLIDS
SETTLING
SCOUR SETTLING
BENTHIC
WATER
SEDIMENT
ANAEROBIC BIODEGRADATION
FIGURE A1
TRANSPORT - KINETIC ROUTES WITHIN THE WATER COLUMN

-------
Note ' Fij*lr is for coruta.n'fc v*J*e of S
il4Ji.we5 FRACTION
x
Particulate FHAcriow
0.1
l.o
0.01
00.0
0.0
to
FIGURE A2 Equilibrium Concentrations of Dissolved, and
Particulate Toxicant as a Function of Hm


-------
ADSORPTION-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 conturast to the sand and
silt components.
The substance, in the complexed form may be then affected
by ad4itional 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 resuspension
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 physiochemical characteristics
of the estuary tend to promote desorption and the constituent
may be released to be recirculated with the estviarine system
or transported to the ocean. Therefore, in analyzing the
distribution of substances which are subject to adsorptions 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 following sections describe the various factors which
affect the adsorption-desorption processes and, based on these,
*Oonald J. O'Connor
Kevin Farley

-------
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 solidsJ The adsorptive capacity of a two-phase
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 less 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  given homologous series,
the solubility is inversely proportional to molecular weight
and it has been observed that the adsorption capacity increases
with increasing molecular weight.
The affinity of the solute for the solid may be due to an
attraction or interaction of an ionic, physical (van der Walls
forces) or chemical nature. Most adsorption phenomena consist
of combinations of the three forms and it is generally diffi-
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 equilibrium
relationship between the concentration of solute and the
amount adsorbed per unit mass of adsorbent is known as an
1-W

-------
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 proportional 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:
|| = Kxdc^-Cpl - K2cp	(14)
in which
c = dissolved concentration of solute (M/L)
Cp = particulate concentration (M/L)
CpC = capacity of the adsorbent solids (M/L)
K1 = adsorption coefficient (^7^)
K2 = 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
gf = KjC m[rc-r] - K2rm	(15)
At equilibrium, the rate of change of concentration is zero
and equation (15) becomes after rearranging:
V-/s-

-------
crc
r = y-Z-	(16)
E + c
K1
in which b = 
2
Equation (16) is known as the Langmuir isotherm in which the
parameter, b, is related to the energy of adsorption. At
r = rc//^'	concentratln equals 1/b. Lacking direct exper-
imental data on r , its value and that of 1/b may be evaluated
c	11
graphically by a linear plot of - versus -. The intercept
equals 1/rc and the slope l/brc-
The capacity rc 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-
brium condition, as depicted in Figure B-5, 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-


-------
CLAYS
 n
Dissolved Concentration - M/L
~
Figure B-5
Langmuir Adsorption Isotherms

-------
centrations of solute. At lower concentrations tne twu
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 Fruendlich
isotherm, which has been found to be more satisfactory in
certain cases, is as follows
r = KcI/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 = ttc	(18)
H-f?

-------
Klrc
in which it = -=
2
The parameter, ir, is a partition coefficient. At high concen-
trations of solute c >> 1/b, the adsorbent is saturated at its
capacity rc. These characteristics are more dramatically
borne out when logarithmeti^; 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
c	~
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,
H -If

-------
LEGEND:
 RANGE KMNT (26 % ORGANIC)
~ THALAS5IA (60 ft ORGANIC)
A JAMES SCDfHENr 1 (4.4 % ORGHf
O JAMES SEDIHEMT I (' 5% ORG.)
BENTON ITE
A KAOLINITE
O SAND
EPA GULF BREEZE LAJB DATA.
10"	10*
Dissolved Concentrations - \tq/l
Figure B-6
Equilibrium Concentrations of Kepone

-------
CT, is the sum of the dissolved and particulate:
CT 3 c + cp	(19)
The dissolved component may be expressed in terms of 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:
| + rm	(20)
The particulate fraction as a function of solids concentration
for various values o 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-8 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


-------
WOlJ *
WATER	 . gROPJMS , fWOOiNS | 3TABIE
^ rtOM& * HOV/MG ' RFD
, .	BED	ACD
to
 A*
4J
U
fl
M
Cm
mSSTIIT-
' / ' /
-	.// //&/ s,
/ /V3	ict	10s id
Solids Concentration - mg/2,
Figure B-7
Relationship - Particulate Fraction - Solids Concentration
Y*2A

-------
LEGEND'-
0 A MISSISSIPPI RIVER
O MOBILE RIVER
 OJO
aaa	300
Suspended Solids - mq/L
400
500
Figure B-8
Total Mercury - Suspended Solids Correlation


-------
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 em 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:
(21)

-------
in which DT  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
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.
y-xs~

-------
Legend
Symbol Compound Diffusivity Film
Consc
2 , . - 6
cm /secxlO
0 .40
1.9
50
cm/sec
0.0191
0.0037
0.0252
DnOCHP
DNOSBP
DNP
O	206	406	800	tOOO	\ZdO	MGQ	liAO
Time - .Minutes
DNOCNP 2,4 - DINITRO - o - CYCLOHEXYLPHENOL
DNOSP 2,4 - DINITRO - o - SEC - BUTYLPHENOL
DNP	2,4 - DINITROPHENOL
Figure B-9
Example - Adsorption Kinetics


-------
AOSORPTION-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. SA6, Proc. Paper
9430, pp. 1021-1036.
Keinath, T.M. et al. April, 1976. "Mathematical Modeling of
Heterogeneous Sorption in Continuous Contactors for Wastewater
Decontamination." Final Report, U.S. Army Medical Res. Command.
Keinath, T.M. 1975. "Modeling and Simulation of the Perfor-
mance of Adsorption Contactors," in Mathematical Modeling for
Water Pollution Control Processes, ed. Thomas M. Keinath and
Martin P. Wanielista, Ann Arbor, Mich. Ann Arbor Science Publ.
Matthews, A.P. and W.J. Weber, Jr. November 1975. "Effects of
External Mass Transfer and Intraparticle Diffusion on 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. Wiley-Interscience, 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. Rumer Jr. Third Quarter 1965.
"Intraparticle Transport of Sulfonated Alkylbenzenes 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-2.7

-------
SUMMARY OF REACTION RATE COEFFICIENTS
Chemical	Direct
pH, Temp Hydrolysis Photolysis Biolysis
	 day"1	day"^	day"1
Carbaryl	5	4.6 x 10 ^ 0.11	2.3 x 10 ^
6	5.3 x 10~3
7	0.046	0.11
8	0.53
9	4.6
Propham	7	6.9 x 10~^ 2.7 x 10 3 0.22
Chloropropham	7	6.9 x 10 ^ 5.7 x 10 ^ 0.24
Malathion	6	slow
8,0 C	0.058
8,27	0.46	slow	6.1
8,40	17.3
Parathion	7,20	2.8 x 10 3 0.017
Diazinon	7,20	0.023	0.022
2,4-D Butoxy	6,28	0.63	0.049
ethyl ester	9,28	27.7
Captan	8,28	1.39	slow
Methocycnlor	1,21	1.9 x 10 3 0.05 3
0.1-0.3*
Toxaphene	7	slow	slow
DDT	7,27	2.4 x 10~4 1.3 x 10~4
Atrazine	3	0.011	0.017
11	8.6 x 10~3
*
sensitized photolysis in natural waters
if

-------
MODELING FRAMEWORK:*
This section of the notes presents the development and application of
various mathematical models vhich define the spatial and temporal distribu-
tion of toxic substances in natural water systems. The previous sections
discussed the various transfer and Icinetic factors vhich affect the concen-
tration of such substances. These factors are nov combined vith the trans-
port regimes characteristic of the different types of natural vater systems,
both freshwater and marine. The former include reservoirs/lakes and
streams/tidal rivers* and the latter estuaries/embayments and the coastal
The purposes of the modeling framework are tvofold: the first relates
to the general hazard assessment of proposed or existing chemicals vhich,
in turn, may lead to v&ste-load allocation procedures. Such analyses may
usually be accomplished by means of the spatial 3teady-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 betveen the dis-
solved and particulate components. Thus equations are developed for each
of these components and in addition for those solids vhich 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 vater systems vhich interact vith the bed, additional sets of equa-
tions axe developed to account for distribution in the benthal layer and
its effect on vater column concentrations. Given these concentrations,
the dissolved and the particulate in the vater column in the bed, the
distribution through the food chain is then considered.
# Donald J. O'Connor
zone.

-------
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 axe 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 ^ = J. + ZR. + ZT. ZW	(1)
dt i i i
in which
c^ = concentration of the chemical, in compartment, i.
J = transport through the system
R = reactions within the system
T = transfer from one phase to another
W = inputs
Equation (l) 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 (T), distinct from the transport (J) and reactioj
v^o

-------
(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 phase of the physiochemi-
cal regime - the dissolved and partial late in the water, atmosphere and bed
_ as veil as to each element of the food chain - the phytoplanJcton, zooplank-
ton, fish and detrital material. The transport, reaction and transfer terms
may be positive or negative depending on the direction of kinetic routes
betveen the chemical in compartment i and its concentration in other compart-
ments with which it reacts or exchanges. The pathways are determined by the
hydrodynamic 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:
Pi,3	(2)
p  particulate concentration in i compartment M/L^
r  mass of chemical/unit of interacting mass M/M
m^  concentration of the interacting species M/L^
I

-------
The mass "balance equation for the particulate component, similar to equation
(l), is then:
dp.	dm.	dr.
-r^r- 3 r, i + m. = J + ZR + IT + ZW	(3)
at i at i ax
It is apparent from equation (3) that an equivalent expression must
be written for the concentration of the interacting compartment, nu. 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:
pi  ^ rini	
-------
the dissolved and particulate components. If there is neither transfer
nor decay- of the chemical, the total concentration, c^, remains constant
in time is equal to the sum of the dissolved and particulate:
cT  c + 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 p
c * mc	(6)
or
tm  >
c
Equation (6) is the linear portion of the Langnruir 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 a c + flmc  + p	(7)
The product, fm, is a convenient dimensionless parameter, characteristic of
a particular system under equilibrium conditions. For a specified value of
1m, the equilibrium distribution between the dissolved and particulate con-
centrations is established by equation (7), as shown In Figure A-2^ Chap. I.
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 a c[l +
(8)
The distribution may thus be categorized in accordance with the adsorbing
solids (organics, clays, silts and sands) or the accumulating biomass
(phytoplankton, 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 shown in the above equation.
U. 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:
Ki K3
p^c*	(9)
^7
The reversible reaction	Kg) may represent the adsorption-desorption
between the dissolved component and the particulate in inorganic phase (sus-
pended or bed solids) or the assimilt.ion-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^) describes the decay or volatilization. The kinetic
equations are:
- <, ~ fc3)c ~ KjP	(10)
H*z>i

-------

(11)
Addition of equations 10 and 11 yield
dC
3T--V	(12>
If equilibrium is rapidly achieved by contrast to the other time con-
stants, specifically identified as Kg in this example, the dissolved compo-
nent, c, may be expressed in terms of the total concentration, c^, by equa-
tion (7), substitution of which in (12) yields
c
0
[Be^ + (l-6)eht]	(13)
in vhich g,h sure the positive and negative roots of the quadratic
g,h - - \ [1 + m]
in which K 	+ ^3
m" f

K2
It may be readily shown that g and h are always real and negative.
In the case of adsorption-desorption, the assumption of instantaneous
equilibrium is frequently made - i.e. the coefficients and 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
or
<"= - " *3 ,	(,,,'
dt 1 + K2/I
-------
in which
K2
 = district ion or equilibrium coefficient
h
An additional insight is gained by developing equation (lU) in an alter-
nate manner by adding equations (10) and Cll) which yields
dcT
dT'-V	<15)
Assume 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, c^,, by equation (7) substitution of which in (15) yields
dc	K
dt~ = " 1 + 1m CT	(l6)
The total concentration decays in accordance with the dissolved coeffi-
cient modified by the'parameter Am. As a physically realizable example,
consider the transfer represents a volatilization process, in which is
the gas transfer coefficient. The total concentration 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 (1m = o). In defining the
rate of change of the total, the decay or transfer coefficient is simply
modified as shown by equation (l6). Conversely, if the decay is associated
with the particulate component, the coefficient would be reduced by the
fraction 1m/[l + 1m], in accordance with equation (7).
If both the particulate and dissolved components are subject to decay,
by more than one mechanism, equation (l6) becomes
dc	DC . ImlK .
T	r ci	Bli	/,_v
dt 3 " ^1 + 1m + 1 + 1m1 CT
in which the subscripts, c and p, refer respectively to the dissolved and
particulate decay coefficients.
V-3S

-------
The assumption of "Instantaneous" equilibrium as expressed by equation
(lU) through (17) is a valid, representation, or model, of kinetic reactions
provided the time to equilibrium, determined by and K2 is rapid relative
to the other phenomena which affect the substance, Kc &	This condition
is generally applicable to the adsorption-desorption process, since its
equilibrium time is usually much shorter (min-hours) than that of other
kinetic effects, which may be in the order of days, months or years.
In summary, 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 other 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 (Ustribution 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.


-------
it
s
I ?
u
a
f I
*1
t
VaUfc-milATOi
m
1	I
K
AOfefctTtotf
Ot'oftM**
l*
__	a i*'*HT*k
 |tTkf4CC
%9m
"sW
r
-far?
e* .$#$ e*

((o|ar_
w
"Ee?"
~7F-

Ki
KiwtTlC 4
Tl2.fr MSfEfc. fKCTOZS
FIGURE 1
S0UO& *
ffrfc.ric.iiLh.TC.
OMO- PUfe30
* 0ttOLNf t>
O iSTfcl ftUTJOKl OF
SOLIDS * TOXC

-------
B. CLASSIFICATION OP ANALYSIS AHD MODELS*
Equation (l) 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 water system and the nature of the substance, it takes
on a more definitive form. As described previously, the distribution between
the dissolved and particulate components of the toxic material and the kinetic
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 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
gnrt transfer routes are common to all types. Each of these factors are
discussed in this section, concluding with the proposed classification.
1.	Kinetic and Transfer Routes
The components and their interactions are shown diagrammatically in
Figure 1. The concentrations of the toxic substances axe 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, and K^, 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-
form 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 (U) and dispersive (E) 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
H-3J

-------
nating 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 tvo 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,tQ.
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 mixed. 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 the 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, measured in terms of months or years, by contrast to
the settling velocity of the various solids in suspension, measured in
terms of hours or days.
U.. 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.
+-*o

-------
TYPE I - STATIONARY BED
A stationary toed is basically characterized by zero to negligible
horizontal motion. This condition is most commonly encountered in lakes
and reservoirs of relatively great depth,' with minimal vinds. It also occurs
in freshwater streams under low flow conditions and in marine systems with
little tidal mixing. It may therefore be associated with any one of the three
transport systems shown in Figure A.
The essential characteristic of this type of system is relatively low
degree of vertical "'""'"e 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-
t
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	or zero nH-Hng in the layer in contact with the
water.
TYPE II - MIXED LAYER
This condition, which is probably more common, is characterized by some
degree of ^Hng in the contact layer of the bed. The mixing may be due to
either physical or biological factors - increased levels of shear, associated
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 **"g in lnterfacial 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 water depths are sufficiently shallow to permit wind effects to be
transmitted to the bed.


-------
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 ^B.
MO.

-------
A
Idiod'Aovxi
Current"
r.
unices &MO
CofihVrac vgA-rtm
FKKS- PlumiUC
Tei*is eiwu.2
t) - hfi^oVri tci oct^
y  TierVel
^ - uerhc4\ w*wg
Q - ^lw faTt
V - VUm
in
TxtoUM
Otvcrtxya-i
*7SCoolTti
pSTuA,e.l AfciCS
TC4(rm.i
Ql CompVcwH
FicueE 14- * T&M4ST*ofe7 serines
w^ree
BttO
X
* 1
vi *
s*racao^ kaH
ft BP
ccrteoy C*0.
- -We
e

>i^
i n H i
T
is-*
->* +
BKP -rUA*rfcPco.T
*><& w4.oa Of
)AMM tuTKnal *^
^ Vu - rSu^pe^*v\
4
ft*-

FlGufcEXfc- BED C0^Drr;i6iis
'V-Y-3

-------
TABLE 1




BED C
D N D I T I 0 N





I
STATIONARY
BED
II
MIXED
LAYER
WITH
BED
III
SEDIMENT
TRANSPORT
WITH LAYER
& BED



Ub
0
0
>0



s
>0
> 0
>0

A
LAKES
RESERVOIRS
COASTAL ZONE'
DEEP,"
MINIMAL
WINDS
MODERATE
DEPTH,
WINDS
LITTORAL
ZONES

B
STREAMS
& RIVERS
LOW
FLOW
MODERATE 
FLOW
HIGH
FLOW
M
C
ESTUARIES
EMBAYMENTS
ENCLOSED
BAYS
MINIMAL
TIDES
LITTORAL
ZONES
MAIN
CHANNEL
LOW FLOW
MAIN
CHANNEL
MODERATE
FLOWS
C3
w
as
E->
OS
O
cu
CO
05
E-t
a
h-t
3
-3
fr>
D
COMPLETELY
MIXED
APPLICABLE TO ALL TYPES,
PARTICULARLY TO LAKES
RESERVOIRS & EMBAYMENTS



4-44-

-------
LAKES AND RESERVOIRS
A. INTRODUCTION*
The analyses of water quality in lakes and reservoirs are considered
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 geomorphology and dimen-
sionality of the respective systems but*al30 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
defined boundary of channel cross section. Furthermore, this uni-dimen-
sionality , which applies both to flowtand 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 an important factor in this regard. Because of the
greater depths, thermal differences and density structures are seasonally
encountered. 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. O'Connor
445"

-------
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 tine 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 completely 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 analysis.
+-4-C

-------
B. ANALYSIS OF COMPLETELY MIXED SYSTEMS*
1. Type I Analysis - Stationary Bed - No Resuspension - Sedimentation
pends on the physical characteristics of the incoming sediment and the
hydraulic features of the system and inflov. The important characteristics
of the solids are the grain size and settling velocity distributions and the
behavior of the finer fractions'with respect to aggregation and coagulation.
The detention time and the depth of the water body are the significant hydrau-
lic and geomorphological 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 admit at least an order of magnitude analysis of the problem. They are
precisely 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 uniform 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 fluxes:
in which
m^ = concentration of solids in inflow
mi = concentration of solids in water body
vg = settling velocity of the solids
Aa = horizontal area thru which settling occurs
The .flux Qm^, equals the rate of mass input, W. Dividing through by the
volume, V, the above equation becomes
a) Suspended Solids
The concentration of suspended solids in a reservoir or lake de-
(1)
(2)

Donald J. O'Connor


-------
in which
i
t = detention time =  (T)
o	Q
L
K - settling coefficient -z {=)
S	1 X
H = mean depth = (L)
3
Under the steady state condition, equation (2) may be expressed.as,
W/Q	t-> \
*'  1 > K t	t3a)
s o
Division "by W/Q yields
w7q ~ 1 + K t	^3b ^
s o
which is the fraction of the incoming solids remaining in suspension and,
with the assumption of complete mixing, is also the concentration in the
outflow. The fraction removed is simply
f = 1 " 1 + K t	^
s o
The dimensionless parameter, Kgt represents the combined effects of the
settling characteristics of the solids and the average detention time of
the system. The coefficient, K , may be replaced by its equivalent, v /H,
^	HQ	S
and the dimensionless parameter is v /v . in which v = - = the overflow
^	s o'	o- t A'
rate of the system.
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 influx of the settling solids. The rate of
change of mass of solids in the bed is therefore
dM2
dt = * A'Vl
The mass, M2, equals the produce of the bed volume V2, and bed concentration,
m2. Thus
dM2 _ d(V2m2) _ 1112 dV2 .	V2 dm2 . , _ *
TT ~ ST= ~ +	 = + Asvsmi -5a)
4-4-?

-------
Dividing through the , and expressing the resulting as V^, the final
result is
(51,)
dt i 1 i
at steady-state - i.e. when the mass settling rate equals the accumulation
rate:
v
mj a m 	(5c)
u
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 maimer similar 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
interaction with the other. For the dissolved component, the mass balance
includes decay and transfer terms^^^ in addition to the inflov and outflow.
The basic differential equation
H' "r-fi-lcc'=' -ViC>	(6)
o
in which
V = reservoir volume (L3)
Wc = rate of mass input of the dissolved component (M/T)
ci = dissolved concentration in water body (M/L3)
Kc  overall first order rate coefficients (T_1) which may include biolog-
ical degradation, hydrolysis, direct photolysis & volatilization.
Kq  the adsorption coefficient (L3/M-T)
m  suspended solids concentration (M/L3)
K2  the desorption coefficient (T~x)
pi  particulate chemical concentration (M/L3)
For the particulate concentration:
W
It1" V2" " t1 " Ksip, " K2Pl + K0m Cl	(T)
o	1
4--+1

-------
in which
Wp = rate of mass input of the particulate adsorbed, chemical (M/T)
Kg  settling coefficient (T~l)
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:
dcm  c.
I
o
&  ? - -T- - K==' " V	<8'
The sorption coefficients, Kq and K2 are usually orders of magnitude
greater than the decay and transfer coefficients of the 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 c^ by equation U, substitution of which in equation (8) yields:
dcTi _ W _ cTt	Kci	Ksifmi
dt Vi~ t ~l+flmi Ti~ 1+Hmi Ti
o
Under steady-state conditions, the above may be expressed, after multi-
plying through by t :
CTi	1	~		(9)
1	* '""".J
For those substances, whose dissolved components are not susceptible to trans-
fer/decay, such as heavy metals, equation (9) reduces to
=T	2^-,		(10)
' 1 ~ Wiife-I
Note that equation (10) is identical to equation (3a) with the exception ty-a.t
the dimensionless settling parameter KstQ is multiplied by the fraction	"
y-so

-------
The latter term expresses the fraction of the total concentration which is in
the particulate form. For values of Hm  1, it is apparent that equation
(10) is identical to (3a). With reference to equations (9) and (10), the
fraction removed is
f * 1 - 375	(u>
Inspection of equation (U) indicates that the removal efficiency of
suspended solids is dependent on the detention time and settling coeffi-
cient , which is the ratio of the settling velocity of the solids and the
average depth of the reservoir or lake. For heavy metals and conservative
chemicals, the additional parameter required is the partition coefficient
(equation 10). In the case of organic chemicals, which are susceptible to
biodegradation, evaporative transfer, hydrolytic or photochemical reaction,
knowledge of the relevant reaction coefficients is necessary (equation 9).
The detention time and average depth, which are readily determined,
are based on the average seasonal or annual conditions, given the time and
space scales of the analysis. The settling velocity and settling coefficient
may be measured directly or implied from inflow-outflow concentrations in
accordance with equations (3) and (U). The partition coefficient may also be
evaluated directly, which, with the solids concentration, yields the dimen-
sionless parameter Hm. Alternately given measurements of the total and dis-
solved concentrations of the heavy metal/organic chemical, the term Hm may
be calculated. With such information, the removal efficiency is readily
computed for those metals and chemicals which are non-reactive.
As indicated above, certain chemicals may be subjected to additional
transfer or transformation. The fundamental properties of the constituent
are indicative of the potential magnitude of these routes - e.g. the vapor
pressure and solubility ire properties which permit assessment of the evap-
orative transfer (M(5). Laboratory experiments may be necessary to deter-
ment the chemical and biological routes - e.g. the biodegradability of the
substance (6)-(9). In any particular case, an assessment, either analyti-
cal or experimental, should be made to establish the degree to which trans-
formation or transfer may be significant. Solutions of the above are ohowi.
in Figure B-2.


-------
The bed. concentration may be described by constructing its mass balance.
Influx is- due to the toxic substance associated with the settling solids and
the volumetric accumulation is accounted for by the sedimentation velocity,
as in the bed solids analysis (equation 5)
dc_
-rjL = f K c_ - f K, c_	(12)
dt pi s2 Ti p2 d2 T2
at steady state
f v
c = P1 3 c	(13)
CT2 f v Ti
P2 d
in which
f = the fractions dissolved and particulate
pn
vg = settling velocity
v, = sedimentation velocity
a
Since the bed solids concentration m2 >>> mi and Hm2 is usually >>> 1,
as a reasonable approximation
f ** 1 and f, ^ 0
P2	d2
v	v
C_ = P2 = f  Cm =  T> 1	(1*0
Tz FZ PI vd Ti vd-J
substituting for p = rm
v
s
i"2m2 3  rimi
d
since v^m2 = ^mi under steady state, then
p2 = ri	(15)
The above analysis does not taJce into account the possibility of the
exchange of the dissolved component between the bed and the water. This is
discussed in the following section, which considers solids resuspensior. - t
condition more likely to enhance exchange of the dissolved component.
4-52

-------
2. Type II Analysis - Mixed .Bed - Resuspension
The type of analysis described in this section is identical to that of
the previous, with the addition of a resuspension term in both the solids
and toxic equations. The physical structure of the system is shown dia-
grammatically in Figure B-l, from which it is apparent that a mass balance
equation must be developed for both the water column and the bed, since
they are interactive.
a) Suspended Solids
The mass rate of change of solids in the water column is:
vi = Qui. - Qi - V A mi + v A m2	(l6)
1 dt	i	s s	us
in which
v^ a resuspension velocity - L/T
m2 3 concentration of solids in the bed - M/L3
and the remaining terms are as previously defined by equation (2) of the
previous section.
Expressing the input flux of solids Qmi as W and dividing through by
the volume V^, yields
V	V
dmi W mi s . u	,
dt V " to " Hi mi Hi mz	^
in which
Hi = average depth of the water column
A mass balance of the bed solids includes the influx of the settling
solids from the water and mass outflow from the bed due to the resuspension
and sedimentation:
. V mi V m2 V.fflz
*21 . -1-L . JLl _ _Li	rl8)
dt H2 Hz H2	uo;
in which-
H2 = average depth of the bed
At steady-state conditions, = 0, the concentration in the bed may be
expressed in terms of the concentration in the water from (18):
+-S3

-------
m2 = bi i	(19)
In which
v
s
V + V.
u d
Substitution of which in equation (17) under steady state yields
T7	V	V
 W	rl Si . u	d
0   -	mi L + tt-J + tt~  	mi
V	1 Lt Hi Hi v + v, 1
o	u d
v
Expressing == K and	solving for mi, after simplification, gives:
II s
mi 
in which
		(20)
1 + 8 K t
Si 0
V + V ,
u d
The value of  falls between zero and unity. The latter represents
the case of no resuspensioh v^ = 0 and 6=1, reducing (20) to (3) and the
former of no sedimentation v 3 0, reducing (20) to
mi = W/Q	(21)
In this case the settling flux is exactly balanced by the resuspension
flux, resulting in zero net change and the concentration of solids is simply
that of a conservative substance, as indicated by (21).
The bed concentration follows from substitution of (20) in (19):
* W/Q
" l.[K<	<22)
s 0
Algebraic simplification yields
> /
-------
(v < ICM/YR), the @ term is more than an order less than the sedimentation
term and (22) reduces to
-rr	<21"
di
in which
Vd
di ' Hi
b) Toxic Substances
The equations for the toxic substance are developed in an identical
fashion as in the Type I Analysis. Each phase in the water column, the dis-
solved, c, and the particulate, p, is analyzed separately with adsorption and
desorption Nineties in addition to the input, outflow and settling terms.
Furthermore, allowance is made for the exchange of the dissolved component
between the water and the bed, expressed in terms of the difference in the
dissolved concentrations. Addition of the two equations cancels the ad-
sorption-desorption terms and yields:
(25)
T?" * TT * * V1 * K.P! * S, * c"
in which
the subscript 1 refers to the water column and 2 to the bed
c,^ = total concentration of toxic in the water column
v
K = =  selling coefficient (l/T)
si Hi
v
a ~ a resuspension coefficient (l/T)
K
" dissolved exchange coefficient (l/T)
K  transfer coefficient of the dissolved between water and bed ()
m	T
Expressing p and c as fractions of the total concentration (equation U of
the previous chapter) and combining similar terms yields:
_IL . -f - [i ~ rpi KS1 ~ r4i cTi ~ tfp! Ku. ~ fd! ^1 =T; (26)
the bed equation is developed in a similar fashion
4-ST

-------
dc
~dt
in which
P-- [f K + f. K. ] c_ - [f (K + K. ) + f. K. ] c-	(27)
t	pi S2 d.1 02 Tl	P2 U2 <12	<12 c>2 2
f = particulate fraction in each segment, 1 and 2
f. = dissolved fraction in each segment, 1 and 2
di ,2
The working equations for the steady-state condition are developed in a
manner 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 > mi and flm2  1, f ^ 1 and
f, ^ 0. For this simplification, which is realistic for 1f>l000, the water
d2
and bed concentrations are respectively
	 W/Q	
:Ti 3 1 * fJfd [HaiKgi +	t
W/Q
c- 3 ' '  r"- "	(28)
o
f K + f X
. 3 -2-11	c	(29)
"t2 K K,	Tl
U2 0-2
in which
v
6" = u
v + v,
u d
"d 1+Umj
1Fmi
^p ~ 1+flmi
v
Ks = 1T
K.  Km
^ H~
K = Vo
U I"

For the condition of negligible exchange of the dissolved between va-ei
and bed (K^O), the above equations reduce to
4--5C.

-------
C  .y/Q		30
Ti 1+Bf K t
pi si o
cT2 " " cTi	(31>
in which, in accordance vith equation lU
v
 - 5-
~ +v,
u d
For toxics of high partition coefficient and systems of high solids (Ami
>5), the above respectively reduce to equations (21) and (19), the
equivalent solids equations.
+-57

-------
TYPt
CBsu6?ea^ovj
sobseeteTS
t VAJ&TfeC.
t t>
0?
SOI.10%
Uv<
4-
V O 
Vi \ \fVK
M reTT"
//-=T5R^"
toxic

X	Tk a
*31	"^.>0
Trfttv$^ft1 "^cro
LfcGEMb
UMItS
w
ttktfc luftUK
Vr

F\.ow

V
VOCOMl
I*
w

L
1*4
9uUS
M/c,
cT
TO*iC - ToTM
h/l
u
OttSoWKO ffiMTtOil
-
tp
PtoTvCOkktC ffcAe/pou

v
*emnje. vciaciTf
L/r

eesusfeu&tou veiacir*f
M
vi
OTCkTvc^i vtu.crri

K*.
COKfftCtB-*Jr
*
Ke

It
K
4Cttuu4 dotfFoitMT
a
w*
o^ft.'neuuiT&
*
FIG. B-l Schematic of Type I & Type II Solids Parameters

-------
TYPE I ANALYSIS
0.0
o.s -
%) 
0.03
0.3
0.1-
]>IMo|ve^ FrtkctiQK
CowwM^tiva
0.0
0.0
0.3
0.2 -
PartriciJcfce Prvt
	Comenra.foi/
0.0
FIG. B2 Fraction Remaining for Various Detention Times
and Kinetic Parameters
H-S1

-------
TYPE I ANALYSIS
o.a
0.4-
0.4-
0.+ -
0.1-
KiG. B-2 (cont'd) Fraction Remaining for Various Detention Times and Kinetic Parameters

-------
*
Saginaw Bay - Solids and PCB Model
Steady State Toxicant Model - Theory
In order to understand the interactions between sed-
iments, 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 sediments,
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
various 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. Thomann and John A. Mueller
f/-/

-------
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 #1, and Is, using backward finite
differences is
 * "l * 12M1 * *12 "VV " '.IM1 * VulAM1S	(
0 - V , AM, - V , AM, - v AM.	(11)
Si 1 Ul Is sdl Is
where M. and M - solids concentration in water column segment 1,2
3
[M /L , ; L  volume of water plus solids]
s w+s w+s
M, " solids concentration in sediment segment, Is
3
[M /L ]
s w+s
w *> input solids loading [M /T; M ^mass of solids]
X	S	S
0  flow from segment 1 to 2 [L^/T]; Asediment
12	2	w
area [L ]
" bulk dispersion between 1 and 2 [L^/T]
v ,  settling velocity [L/T]
si
v  resuspension velocity [L/T]
v  sedimentation velocity [L/T]
sal
A similar set of equations can be written for segments 2 and 2s.
Equation (11) can be solved for the sediment concentration
as:
Vsl
Mls  't ,+v  '"l " Vi	'12>
ul sdl
.	Vsl
where a
1


-------
Substituting eq. (12) into eq. (10) and simplifying
gives:
. 0  W1 - 2^ ~ S<12	- WslAMl	(13)
where w . is the net loss of solids from water column segment
s 1
#1 and is given by
V V
si sdl
wsl " V +v
ul sdl
(14)
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 . A mass balance around the sediment
S X
segment then yields
~	- v . AM	(15)
sdl Is si 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 M. , only the net flux to the sediment
sdl	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 wgi 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	may be obtained from
eq. (15) or from solving eq. (13) directly for w with given
8 X
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
3 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 - Mi - *12*1 '* < W ~ 'ua^isB
where v is scour velocity and M. is sediment solids concen-
uB	lsB
tration available for scour.
Let WL -	2	- m	(17)
where m[M/T] is the net production (loss) of solids.
A useful procedure for this case is then:
.1) Compute m, the net mass production or loss of solids
for each segment
2) If m positive, then
m = w , AM, and
si 1
m
w  
si AM^
4-6*

-------
3) If m negative/ then
m  v
uB^lsB
and if desired, v the net scour velocity can be
UB
calculated.
Toxicant Model
The basic objective of the steady state toxicant model
is to obtain a modeling framework that utilizes available
specifying 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:
field data for calibration, and eliminates the need for directly
+ v . Af c + E' F c  E' f c
ul pis Tls Is 01s Tls Is 01 T1
:i3)


-------
The equation for the sediment segment, #ls is
0 " v A f c  v A f c. + E' f c
si pi T1 ul pis Tls Is D1 Tl
~E' f, c_, - v ,, , A c , --K, , f_, V c	11 a \
Is Dls Tls sdl pis Tls 11,3 Dls Is Tls	(19)
where W . * input toxicant loading [M_/T]
Tl	Tv
c c c
Tl  12, Tls-total toxicant concentration in segments 1, 2
and Is respectively [M /L ]
T w+s
K "overall loss rate of dissolved form (e.g. vaporiza-
tion, decay) [1/T]
K "decay of dissolved toxicant in sediment [1/T]
11, s
-volumes of segments 1 and Is respectively
E' "interstitial water sediment - water column diffusion
13	3
coefficient [L /T]
w
The fraction of toxicant in the particulate form is given by
f _ *1 M1
pi 1 +	(20)
and the fraction dissolved is
fDl  1  vx	<">
where it, is the partition coefficient [M /M r M_/L3^ ]
1	^ T s T w+s
at ambient water column solids concentrations.
Similar expressioas are used for f , and f , the
pis	Dls
fraction particulate and dissolved respectively in the sedi-
ment segment, Is, that is,
it, M,
f . - r-r5hr	(22)
pis	Is Mis
and	_, - 1/1 + ir, M,	^23)
Dls	Is Is
where it. is the partition coefficient* at ambient sediment
Is
solids concentrations.
4-CC

-------
If now equations (9) and (10) are added, one obtains
an interesting result:
0 " "ll " 12 CT1 * E12 (CTrCTl'. " "h'diVtI
VadlfplsACTls " Klls fDls VlsCTls
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 toxicant concentration.
Therefore, let
c -	M,
a -	- ii __Is.	(25)
T1 CT1	fpls
r [M /M ] sed.
where II " 	3			(26)
CT1 [Mt + Lw+g] water
where r, is the toxicant concentration on a solids basis
is
in the sediment.
The variable II 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
Si - '^7"'	'^7'	<">
sdl pis 1
.where r^ is the water column toxicant concentration on a solids
basis tMT/Mg] . Substituting eq. (25) into (24) and simplify!-.:
gives:
 " WT1 " Sl2CTl + Ei2 |CT2-CT1 * "X1 ACT1	1281


-------
where w [L/T] is the net loss of toxicant and is given by
T1
"ti  Ku di hi + aTi 'Wpi. + kiisdisbis!	<29)
where H and H are the depths of the water column and sediment
1	13
respectively.
Equation (28) is a mass balance on the water column
toxicant only and all sediment interactions are embedded in
the net loss of toxicant w_,. The estimate of this net loss
Tl
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 c ., estimate w , for each segment using a
Tl	Tl
water column model
2)	From w , and laboratory data on decay rates in
Tl
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
w - K f H
- T1 i 11 01 1	(30)
Tl
where 6, " v .,f , + K, , f_, H,
1 sdl pis lis Dls Is
eq.
rls - "rl	*1	131)
pl~	sl
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 and diffusion processes are negligible. PCBs are an
example. If then it is assumed that K,, and E' are zero,
lis	Is
then it can be shown that
K, . fm H! + f , W ,	(32)
Tl 11 D1 1 pi sl


-------
and rls " rl	U3
This result indicates that for PCB, if the net solids
loss to the sediment, w , can be obtained and information is
s i
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  0 and
si
WT1 " *11 fDl "l
and rls -
These special case models for K^0 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-137, 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 S Transport Coefficients
The segmentation was obtained from the Grosse lie 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
lie 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 tc
represent a long-term steady-state condition. The temporally
averaged flows and exchange coefficients that were used in the


-------
steady-state computation for the five segments in the water
column are as shown in figure 11 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/1 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,
shoreline 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-
mately 60% and a specific gravity c'i'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 IJC report cited previously. Phytoplankton
biomass was obtained from a algal model simulation performed
~4^70

-------
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/1 solids at the open lake boundary were
too low since calculated solids concentrations in segments
4 and 5 were well below observed^values and nan balances of
these segments indicated that the boundary fluxes dominated
these segments. Final values of 4.3 mg/1 for segment 4 and
5.5 mg/1 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).
Met 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 significant.
Equally acceptable calibrations are obtained for values betw,	,
10 and 20 m/yr. for segments 2,% and 5.
+-7f

-------
With the estimated net removal rate o solids
from the water column, the flux .of solids into the bed is
calculated as w ,AM, [M /T] . This is	equal to the sedimentation
si 1 s
flux which is calculated as v ..AM, .	Since both v and
sdl Is	sdl
M vary with sediment depth, no single value can be specified.
However, from eq. (15) the relationship between v and M
SCX	X S
is unique. If v is selected, then M is a predetermined
sdl	Is
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/1
for nine cores with a range of approximately 230,000 to 900,000
mg/1. 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 do not 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 "fluff" layers may be available for
interaction with the surface water column at concentrations
less than sediment data from cores. Conversely, estimated net
+-n

-------
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/1 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&ntation 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 G r o  re
He 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
4-73

-------
sources contribute an additional 25%. Although open Lake con-
centrations are reported to be in the 1 ng/1 range, the
boundary condition was selected as 10 ng/1 - the value needed
to calibrate observed data in segments 4 and 5.
Partition coefficients were selected on the basis of
observed dissolved and particulate fractions and values of
10,000, 50,000 and 100,000 Ug/kg per Ug/1 were selected for
segments 1, 2 and 2, 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	Por segment 2, for example,
the net removal rate w,,. is:
T2
W  W X f
T2 s2 p2
2M2	( .05) (11.2)	.
where fpJ - 1+ ^ - 1+(.05)(11.7) " 0,37
and then w  (12 . 7) (.37)4 . 7 m/yr.
T2
Similarly, the net total PCB removal rates for segments 4 and
5 are 4.8 and 3.5 m/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 where
settling and resuspension were equal, the PCB per unit weight
of solids in the water column (r^). ~ a reproduction of the
4-7*

-------
bottom panel of figure 15. Directly below, is a plot of the
PCB in the sediment	 where the solid line is the calculated
value of r assuming r, -r, . The data are segment averaged
Is.	Is 1
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  r is not
is l
appropriate.
A mass balance of total PCB is snown 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/1.
Of the 24 ng/1, approximately 6 ng/1 is due to the boundary
condition (center panel) and the remaining 18 ng/1 is the
effect of the loads. Thus, complete removal of the Saginaw
River loads and maintenance of the boundary at 10 ng/1 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 alor.e
(figure 19) shows that approximately 10% of the load entering
the Bay is incorporated in the sediment and 90% enters Lake


-------
Huron - 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) .
Conclusion
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 wate-r 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 conditions. The PCB simulation will be redone using
1979 flow and dispersion coefficients in order that transport
and loading information would be synchronous.
+-7G

-------
TABLE 2
ESTIMATED LONG-TERM AVERAGE SUSPENDED SOLIDS INPUTS
Model
Segment
Tributary
Loads
(lb/day)
Bank
Erosion
(lb/day)
Atmospheric
Loads
(lb/day)
Phytopiankton
Mass
(lb/day)
Total
Loading
(lb/day)
1
1,232,000*
28,200
10,100
132,200
1,402,500
2
123,900
92,600
31,400
341,600
589,500
3
34,900
63,900
15,100
143,300
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
Station	5 cm	12.5cm	17.5 cm
1A
510,000
1,350,000
1,130,000
6A
250,000
700,000
730,000
11A
230,000
560,000
620,000
to
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
Mean
390,000
670,000
720,000
Std.Dev.
200,000
320,000
240,000
(1)Data
from Robbins
(1980)

(2}
Stations all in Saginaw Bay model segment 2.
4-77

-------
TABLE 4
ESTIMATED TOTAL PCB LOADING FOR 1979
Tributary Atmospheric Total
Loads	Loads	Loading
Segment	(lb/day)	(lb/day)	(lb/day)
1	1.61(2)	0.05	1.66
2	-	0.16	0.16
3	-	0.07	0.07
4	-	0.12	0.12
5	-	0.12	0.12
Totals
(1)
1.61	0.52
Source: USEPA ERL Crosse lie
2.13
(2)
Saginaw River
TABLE 5
Total PCB PARTITION COEFFICIENTS
(1)
Segment
Partition Coefficient ( ti) from Observed
Concentrations
ir Used in Model

Mean
Aoprox. Range

1
10,000
700- 30,000
10,000
2
80,000
7,000-190,000
50,000
3
60,000
20,000-160,000
50,000
4
90,000
10,000-250,000
100,000
5
280,000
10,000-920,000
100,000
All
values in lig/g
per Ug/1

Data
from Grosse lie
Laboratory (1979)

4-78

-------
W;
it.
AT,
F>g. 10 	i)*.Vt A	xA.^
V 0 d < ).
4.-7
-------
SEGMENTATION
4-000
FLOW
'713+4*
SULK
llJPERSION
(c*s)
r&isi
lovn^
A+WJ I A
:i4l
3.515'M*
	f
yoiy
FIGURE M JE<3MeNTATI0y  (SSTtMATS 6 CbnC-TERM
Aveg,AGe transport coeppfcfewrj in
JAGIVaW BAy
*- eo

-------
0	Yr.-IW
ULATE



i
L BL1
r6'3W
B.C~6

msesmiiSACLJC-
CHLfttfftfi:
r. : : 2. SEGMENT ?)' '[' 4.
L- HUROM J_
DISTANCE
 | G URET 12
THAN*PO|\T CAL IDHATIOIV UII/JG l,ONG- TGftM
AveRAGe6 chloride- (Mta

-------
I
oo
r . |. . . .i . . j 

ill
SEGMENT

iMsa
SEG:i4-
fS
; { ;
I tcoo
tnat/yi.
H
SEGlJt
obtviv.
:j j ! K*$e
i IGMRB 13
JCMMtur JOLlbS CONCBMTMTIOr^ ($*/*)
TOU&J CALI8IATI0W lUlrtG LONG-TEAM SOLllS &ATA
5 EG ilS!
!li;:V:.i4
w .l. I it. toco

-------
LOAfc-S
irio
35*0
jvflCc 4", 3
'rBCs 5.5
NET SETTLING
boundary transport
SUMMARY
2970
&A&IMAW BAy I

U.HURON
ino

Note: All values Ch 1000 lla/(Uy
FIGURE 14
MAS* BALANCE of TOTAL SUJfBNfteO ToubJ
under lontekm av&rags conditions

-------


::::
..


v:\W\W
iiitliil
iliiii!::
iiiil'iii
liii
lili
ij!!
IS!!
ii!i
rrr
iiij
liii
[liii!



Mi;i!



iiij


; ! '!
-



IJ!
rl
!!ii!
|iii
llr!""
|ii!!ii




\::i

'i



sirr^r?:
i
i


::: I:
TTT"
;

!!::
Till
1
I
t.T
ili
U1
Mi!
P
11"
If
jiii
;!h

' i: * 1 :: *
TTnr
~r.
w
iiii
: :f
>><


  1
' 
L : !:::'





f ::  :  
rTTTTTT: i: 


fh!:
!:::





  i







illilii!




ill!
!ii>
i ::r
1
::i:
.,. w
::if
iB



j -f t!
  
rriJ .

":i 
-IP-


....
~


liiilllli
iiii
P
jjil
tin?

:: "

11: l
:i:n
i
calculated!.
I : : . :	!



:"! Hi

: ::i i'J !
\mm\
SeGM.
FIGURE '5 COMPONENTS PCB IN WATER COLUMN - ' l'T?
4-84-

-------

LLULA
SOjOOO
10 000
5 ofooo
SE6 M. 4-
loo.ooo
ftfct HlhOVll / \ A. ft
h*t VyyO 
c*-t
 J V Jt
to	800
 S -o>
O a c
CL In ^
. *9

100,000
3.5"
*977 MEAN t RANGE
fIGURE 16 PARf. PCB CALIBRATION UliMQ |979 L0A>5 +fcAT*

-------
LOAM *
0.I&
O.ll
rvBCc |0
*i/t
10
0.11
* Estimated I1H valuer
NET SETTLING
/U.JI iU,II
TVTt
BOUKlMFiy TRANSPORT
-SUMMARy
1.13
4.0?

=,"v oAGINAW
U. HURON
Note: All valnei ilk
HGURE 17
MASS BALANCE of TOTAL PCB
UNlER LONG-TERM AVERAGE CONblTlONS

-------

^i: :!'':::::^TT": . :-BPMAliigZS^^	BI
cons efroren ^izju^iiw at gR~c goraw
+-87

-------
LOAfcS
I.a
		i-
O.IG
o.ia
BCa 0.0
BC=0.0
o.ia
BOUNDARY TRANSPORT
0.40
0.01
NET SETTLING
o.oi
.SUMMARy
\ 2.13
' 5TSSA6IMAW F)AV I
U.HURON
Note: All valuet Ch Jib/day
HGU.ftE |9 MASS BALANCE of TOTAL PCB -
external loads only

-------
L 0Al>3 | q o
off i8c-10
i v"i"1 ^
'UJ	ijp!^C=IO
net settling o.ii jfO\n
p 1 1 
	  	i
* "io.ia
BOUNDARY TRANSPORT
5 U.MM ARy
4/hn
l~" ^ xL^v^i
vX
'^V^SAGIMAW BAY 1 U.HURON
"^*-4-^"*!o 4-6
\
0 A
-------
STREAM 4 RIVER MODELS
A. IHTRODUCTIOH*
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. Type 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. Type 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 Types I &
II and Type III is dealt with in the estuary chapter.
*Donald 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 Ax. The basic differential equation for the dissolved
solids is
3Q	3Q
A 3T = "ST (Qs) + sg "df + Ss ~dl	(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:
**Si. a U
g
in which
* = + = a rs _S1	(?)
dx Q dx Q 3x	g
1 dQ
q. - ^ 3 exponential flow increment
The subscript is dropped from the flow since the only source of flow is
the ground water. The solution is
~Donald J. O'Connor

-------
s  s [1 - e~^X]+ s e~^X	(
S	
in which
W
s  :r
0 Qo
V o mass input of dissolved solids at x  o
flow at x  o
Depending on the relative magnitudes of the ground water concentration
and the concentration due to the waste input, the spatfial distribution of
dissolved solids increases or decreases to an equilibrium value, s .


-------
2. TYPE I ANALYSIS - STATIONARY NON-INTERACTIVE BED
The condition of a stationary, non-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 smaller 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,
in which
m 3 concentration of suspended solids
V
K  settling coefficient  _s
3	H
vg= settling velocity
H  average depth of the stream
Expanding the first term on the right hand side of the above equation and
simplifying, the steady state form is
+*)a	(5)
in which
Q
U  velocity > ^
1 dQ
q = exponential flow increment   ~
the solution is
K
-(j! + q,)x
m  m e U
o
+-93

-------
in which
mQ a 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 a3 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 si miliar
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:
0  - U ~ - K m c + K_p - K c	(7!
dx o	<2* a
in which
Ka = evaporation coefficient
The particulate form is described in a similiar fashion with a settling term
0 = - U + KQm c - I^p - Kgp	(8)
Addition of these equations yields
dcT
0 - - " 5- - K.c - V	<9)
Substitution of the dissolved and particulate fractions for c and p gives
'-u^-=T	ao)
in which
f a i
d l+*m
f .Js-
p 1+Um
Assuming the river stretch is segmented such that each element may be
approximated by a constant concentration of suspended solids; the solution


-------
af the above is straightforward.
c.cv-.-t'dVy.S	(id
T To	*
in which
W
T
C  
T Q
M
 mass discharge of total toxic ()
,lA
Q = river flow (^)
Knowing the toted, concentration, the dissolved and particulate may be readily
determined from the f^ and f equations.
If the effect of incremental flow is significant, the above equation
is written in the following form:
C . C a-t(fdK* * fr,K)irl +	(12)
T To	p


-------
3. Type II Analysis - Mixed-Interactive Bed.
This case describes a bed vhich 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 vater
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-
~eloped and in addition, includes a source term due to resuspension. The
steady-state equation is:
dm
0 " * U dT" ' Kslnil + Kul2	(13)
in which	
V
u
 resuspension coefficient  
&2  concentration of solids in the bed
~ * resuspension velocity
The solution of this equation is:
I 	^
Kul2 r, ' "Ksl u-, . -K ,u	(lU)
^ [1 - e	J + mQe si
si
If the ground water flow is significant, the above is expressed as
[l - .-'Hr + 5)x] ~ m ."Ht *
^ul"^ ri _-(rr* + l)*i ^	+ 
-------
in which '
K.  sedimentation coefficient =
Qji	n g
Hg  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
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:
4oi
0 * - -E - KoVl + - Vl	(1T>
jin which, as in the previous case, allowance is made for a decay or transfer.
& volatilization transfer is assumed in the above.
The particulate component has an additional term due to the resuspension
effect:
dp]
0 - - "ST
Addition of the dissolved and particulate components yields the equation for
the total concentration,
dc
"dx " "ar*T " "si*! ' "ul*^
Substitution of the dissolved and particulate fractions1 for c and p are re-
placing p2  r^.
'	rdCT
0	d_x " " CT  + Kulr2m2
in which  = f _K + f K
da p s
vov the condition of spatial equilibrium of solids for which m = m , and
~ el
1 + KalCl " Vl * Ksl*l + Kul*2	(l8)
- - Ka1CT " Ka1Pl + K,oP9	(19)


-------
= Kslmel' tlie solu-t^on *3:
Kslr2mel 	ci
cT = 	-	 [1 - e u] + c?oe u	(21)
Simplification of the first term yields
E,lr2*el r2el
f < t, KL
P i 
S
(22)
in vhich K_  evaporation transfer coefficient = K H. (**/_)
h	Q, 1 T
vg = settling velocity of solids =	(L/ip)
For the case of spatially varying solids, the above equation may be used as
an approximation by segmenting the systefti 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
I^slr2mel ,, -( + q) x-, . -(+ q)x
			 Ll - e u ^ 1 + c e u *
cT 	L1 - e * H# ] + cToe u	(23)
It is to be noted that a direct simple analytical solution results for
the condition of spatial equilibrium of the solids. For the case of
spatially varying'solids, however, the differential equation is
dCT Kal + K.l ~ U>
0 * " "jl " t 1 ~ (,) 1 CT *	<21*'
-KslX
in which  vx) = Urn .(l - e	)
el	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.


-------
^AglicationJto_PCBs_JLniJ^he_JIudson_J*ivr^
INTRODUCTION AND GENERAL PROBLEM FRAMEWORK
The focus of this review is the description of the distribution and
fate of polychlorinated 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 folfd 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-
tamination 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 (l). 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-
ment transport and exchange. The model is intended to provide some guidance
on the order of magnitude Response that may be anticipated under different
environmental controls. Considerable research in this area is continuing
and the results of that research may influence the conclusions drawn herein.
Figure 1 is a schematic of the Hudson River which indicates the mile
points (MP) of key locations and also shows the divisions 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
(MP 25) and Poughkeepsie (MP 75) and under severe drought conditions, it may
reach as far north as MP 8(X The long term monthly average discharge and
the 1976 monthly average discharge from the Upper Hudson to the Lower Hudson
are 13,270 cfs and 22,100 cfs respectively.
ANALYSIS OF WATER COLUMN AND SEDIMENT 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
4-1
-------
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^,(yg/l) in a dimen-
sional system can be written as:
udCT  d T . r Hm  .	_ _ r itT llT ,
dX " dX2 1+Um s THTS ^ CT " TB TA TE	^
where x is distance downstream, u is the river or estuary velocity (cni/sec),
E is the tidal dispersion (m /day), m is the mass of suspended solids (mg/l),
"a" is a partition coefficient between the particulate and dissolved phases
(ug/g * ug/1), K , K , K , K. are coefficients [day-^"] representing sedimen-
sana
tation, evaporation, photooxidation, and biodegradation, respectively; and
^TB' WTA and ^TE are totaL^ inPu,t loads (kg/l-day) of PCB from bottom sedi-
ment interactions, atmospheric sources and other external sources, respec-
tively. For the Upper Hudson area, W^A can be assumed close to zero and
can be given from the resuspended bed sediment load as # r^ Wgs
where r^ is the concentration of PCBs in the resuspended sediment (yg PCB/g
sediment, a measurable quantity) and Wgs is the sediment input	) 
A mass balance on the suspended solids is therefore also required and is
given by
udro  d m j. ..	i n \
 - E = + K m = W	(2)
dX^ S SS
With m from (2) and estimates of the coefficients for (l), c can be calcu-
lated. Since the total concentration is the sum of the particulate and
dissolved, the dissolved concentration, c^, can be calculated from:
c = cT/(l+Um)	(3)
4-100

-------
The concentration then provides an estimate of the dissolved form of PCB
which may be available for uptake and bioconcentration by the aquatic food
chain. The approach to analyzing the PCB column data was to first fit the
suspended solids data using Equation (2) which provides an estimate of Kg
and W (but not uniquely). Then using field data of r_ and the determined
3 S	
distribution of m and Kg, the PCB data are calibrated using Equation (l).
In.using this latter equation, a knowledge of the partition coefficient H
V
is needed. The limited available data for the Upper Hudson River show a
2
large variation from 20-500 ug/g per.yg/1. Dexter in his work examined
the partitioning of PCB in the two phases and reported values from 13-T5 Ug/g
per Ug/1. A value of 100 yg/g per ug/l 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 Dam), the model was applied to
PCB surveys of March 18 and March 29-31, 1976. The resulting profiles and
the survey data cure 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 MP 65 - MP 90. In the top graph of Fig-
ure 3 are shown two profiles resulting from different assumptions 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 Ug PCB/g sediment for the lower Hudson. It is estimated based
on Figure 3 that the total PCB concentration from MP 0" to MP 110 ranges
from 0.1 - 0.5 Ug/l. The average dissolved PCB concentration (not meas-
ured) is estimated at about 0.1 ug/l (100 ng/l).
AHALYSIS OF DREDGIUG OF UPSTREAM SEDIMENTS
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
4H0I

-------
Edward is dredged to a bottom sediment PCB concentration of 1 Ug/g. Under
the second dredging alternative all pools of the Upper Hudson are dredged
to a bottom sediment PCB concentration of 1 Ug/g.
Figure Ua shows the results of the calculation under the two dredging
alternatives and assuming 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 Ug/1 to 0.28 ug/1 and. O.lU yg/1 under the two alternatives. This repre-
sents an approximate 20? and TO% 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
contamination of estuarine sediments via the naturally occurring sediment
discharged 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
assumed that the bed sediment-bed load input may drop by 5075. The results
of the calculation under this assumption are shown in Figure UB. 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 Ug/1.
THE NO-ACTION ALTERNATIVE - 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 March 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 PC3/day from the bottom sediment. From a similar
4102.

-------
mass balance at 1*8,700 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
1*50,000 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 (l) the soluble com-
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 = KjAc
where
N = evaporative loss in (M/T)
K. = liquid film coefficient in (L/T)
3
c = The dissolved PCB concentration in (M/L )
2
A = The surface area through which the transfer occurs (L )
the liquid-film coefficient was taken as 0.07 m/h, and the dissolved compo-
nent for the March 18, 1976 survey is 0.2 Ug/1 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 = .25 (day)~\
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
4H03

-------
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.
53). 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 balance
approximately kO# 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 biodegrada-
tion losses are included. Sediment burial and subsequent interstitial dif-
fusion rates may alao markedly reduce the time to flush out the Upper Hudson,
Such a calculation would require a detailed model of the bed sediment PCB
and interactors with the overlying water.
ACKNOWLEDGEMENT
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.
i(o4~

-------
REFERENCES
HYDROSCIENCE, INC. . 1978. Estimation of PCB reduction by remedial
action on the Hudson River ecosystem. Prepared for New York State.
Department of Environ. Conservation by Hydroscience, Inc., Westvood,
N.J.: 107.
DEXTER, R.N. 1976. An application of equilibrium adsorption theory
to the chemical dynamics of organic compounds in marine ecosystems,
Ph.D. Diss. Univ. of Wash. Seattle, Washington: l8l.
4-106"

-------
U ' L
0/NT
210-
200
l 90-
l 80 
iro-
160-
130-
I 40-
I 30-
120-
I 10
100-
90-
80-
TO-
60
50-
40-
30-
20-
10 -
0
-10-
-20-
-30
TRIBUTARIES
corintm
SPIER FALLS
 plens falls
 f r. eowaro
NORTHUMBERLAND
" SCHUYLERVILLE
FISH
CREEK
 STILLWATER
MECHANICVILLE
.WATERFORD
 TROY
 GLENMONT
MOHAWK
RIVER
CATSKILL
ESOPUS
CREEK
. KINGSTON
P0,NT
f-POUGHKEEPSie
	CHELSEA
BEACON
	WEST POINT
-BEAR MOUNTAIN
. VERPLANK
MAVERSTRAW
MOOONA
CREEK
-TAPPANZEE BRIOGE
-PlERMONT
-YONKERS
-C, W BRIOGE
-BATTERY, N.Y.C.	'
OA MS
AND
LOCKS
REACHES
FOR
PHYSICAL
ANALYSIS
BATTEN
Kl LL
. FT. EOWARO OAM
L T
	T.I. OAM
	L6
' L5, OAM
HOOSIC
RIVER
L4,OAM
L3, OAM
LZ
' L I
 FEDERAL OAM
WAPPINGER
CREEK
FISHKILL





0



E

C
r

i
V
c




ooc



A




0
V
E
C
T
1
V
E
/
0
1
s
p
E
R
s
1
V
E
M
0
0
E
L

















3

0

M



N.

N

Y

H

A

R

9

0

P

M

0

0

E

L
REGIONS
POP
fflOt. OGIC.iL
ANAL rS'S





FIGURE I
SCHEMATIC OF THE HUDSON RIVER AND SEGMENTATION
USED IH PCB ANALYSIS (BIOLOGICAL AND PHYSICAL)
A-l

-------
MARCH 18,1976
08 x s 12.700 CPS





 
' '
1 
r H
200	190	160	170	160	13
MILEPOINT
60
MARCH 18, 1976
E
to
a
o
in
a
UJ
a
z
bJ 20
a.

-------
CO
Jl
ID
U
a.
E
o>
5-
m
u
a.
2
o
I-
*-
o
ffi
2.0
I 8
I .6
I 4
12
1.0
8
.6
.4
.2
0C j = 12,700 CFS
NO OATA
n
L-
1
I
l'--"I
NO OATA
200	I80	160
| UPPER HUDSON
140
120
100
BATTERY
40 r~
20
(ISO)
1
1
I
[./
- t.fjL9 /Q*

rn
X		Lu.jiu.iiu
200	180	160
| UPPER HUDSON
140	120	100	80
MILEPOINT
60
40
20
0
BATTERY
FIGURE 3
TOTAL PCB CALCULATED PROFILE AND BOTTOM PCB DISTRIBUTION

-------
LEGE NO.
Q-PRESENT CONDITIONS
-DREDGING THOMPSON ISLAND POOL TO I Mg/gm
^|)-DREDGING ALL POOLS TO I
Q0 j  12,700 CPS
z
o
tc
z
U1
08
O
0.6
0.4
0.2
20
200
40
180
160
140
120
80
60
100
ESTUARY PCB CONCENTRATION OF BOTTOM SEDIMENT* 1/2 PRE SENT VALUES
O
Qal * 12,700 CPS
legend:
(J) - DREDGING THOMPSON ISLAND POOL TO l^g/g
-DREDGING ALL POOLS TO I fig /gm
z
o
h
<
(E
08
Z
lil
06
0.4
0.2
200
180
20
160
120
40
100
MILEPOINT
80
60
FIGURE 4
EFFECT OF REMEDIAL ACTION
ON PRESENT AND POSSIBLE FUTURE ESTUARINE CONDITIONS

-------
(A)
tributary PC0
AT .2 M 0 / I
o
o

6.1. "" '2J00 CFS
0
UPSTREAM
BOUNDARY
AT .2 m9/I
LOAD TO
ESTUARY



NET BOTTOM PCB LOSS
(B)

UPSTREAM
BOUNDARY
AT .2
TRIBUTARY PCB
AT .2 Mg / I
- / 700 ^5
EVAPORATION AND
BIODEGRAOATION LOSSES

LOAO TO
ESTUARY
NET BOTTOM PCS LOSS
(C)
TRIBUTARY PCB
AT .2 fj.<3 / I


O
o
' EVAPORATION AND
SIODEGRADATION LOSSE^


6.Z. >2,700 CFS
@
UPSTREAM
BOUNOARY
AT .2 ufl/l
LOAO TO
ESTUARY

SEDIMENT PCB DIFFUSION PCB
LOSS	LOSS
legend:
Q) PCB LBS/DAY
FIGURE -5"
PCB MASS BALANCE
(UPPER HUDSON RIVER)
+-110

-------
10,000
>-
<
a
x
in
ao
to
in
O
i
a
o
a.
S
o
o
03
-
u
z
100 
1,000	10,000
FRESH WATER FLOW (CFS)
100,000
FIGURE 6
NET PCB LOSS FROM BOTTOM SEDIMENTS
(UPPER HUDSON RIVER)
411!

-------
APPLICATIONS* TVAIC SUBSTANCES IN STREAMS
The following applications relate to the distribution of Polychlorin-
ated Biphenyls in the Hudson and heavy metals in a fresh water stream -
zinc, nickel An^ copper. Type I and ^pe II analyses are employed as
discussed in the respective examples.
1. Heavy Metals in a River
A map of the study area is presented in Figure 1-1. The major waste
water discharges are from three municipal treatment plants, all of which
are of activated sludge type. Industrial waste-waters are pretreated
before entering the municipal plants. The major source of heavy metals
is from the most upstream plant located at milepoint U7.
The drainage area is 760 square miles. The average annual flow is about
0.6 CFS/sq. mi., with a typical high flow in spring and low flow in Late sun&er
- early fall. A large percent of the flow in the river at the upstream site
is due to the.waste treatment plant, which discharges about U0'CFS. Pertinent
hydrologic data are shown in Figure 1-2. As evident from the upper figure,
the river flows through two different topographic terrains - average slope
in the upstream reach is 13 feet per mile and in the downstream 3 feet per
mile. In spite of the differences however, the velocities in each stretch
are comparable, as shown in Figure 1-3, on which is also presented the depth-
flow correlation.
Two surveys were conducted in 1978"  during May and July. Fifteen (15)
stations were sampled as well as waste water inputs and tributaries. Water
column and bed measurements were made on solids - dissolved and suspended
and metals - soluble and- particulate. Figure 1-1* presents the suspended
solids and dissolved solids spatial distributions. The solid lines are
calculated assuming steady-state conditions. "Hie dissolved- solids sub-
stantiate the flow distribution and the suspended solids were fit by assuming
resuspension fluxes in accordance with equation (13) (Type II Analysis).
Laboratory experiments were conducted to determine the adsorption -
desorption rates and the equilibrium concentrations, from which the partition
coefficient-was determined.. "A representative~example~of these data is shown
in Figure 1-5. Die time to equilibrium is relatively rapid - i.e. in the
order of. 1 or 2 hours  indicating the validity of the instantaneous equi-
librium condition. It is more appropriate to employ the kinetic equations
in the mile or so immediately downstream from the treatment plant, since an
Donald J. O'Connor
4-IIZ

-------
hour is the order of the travel time in this stretch. However the instan-
taneous equilibrium condition is a reasonable first approximation.
The heavy metal distributions for zinc, nickel and copper are shown
in Figure 1-6. The solid lines are calculated in accordance with equation
20, using numerical procedures. The finite-difference form of this and
the related solids equations are straightforward. Since the constituents
of concern are heavy metals, evaporative transfer is inoperative (Ka=0).
The partition coefficients assigned for the three metals were 70,000,
20,000 and 50,000. Due to the increasing flow in river, due to ground
water inflow, allowance for this dilution effect is made in accordance
with equations (3) and (5).
Figures 1-7 and 1-8 present the observed values and the calculated
profiles for the subsequent survey in July. The identical computational
procedure was followed, with the important exception that a Type I analysis
applied in this case.. Equations (5) and (6) are used for the calculation of
the suspended solids and equations (10) and (ll) for the total concentration
of heavy metals. The particulate and soluble fractions are readily deter-
mined knowing the partition coefficient and the concentration of suspended
solids. Additional surveys were conducted in 1979. The July and August data
and calculated profiles are presented in Figs. .1-9 through 1-12. A Type II
analysis was the basis of calculation for both survey sets.
Additional insight is gained by an examination of Figs. 1-13 & 1-1^,
which display the bed concentrations of metals for the May and July survey of
1978. In the latter survey, a delineation between the fine and coarse -
bed material was made.~ A size of 75 lim was selected to distinguish the
two general classes - sands vs. salts and clays. The solid phase concen-
tration of finer solids is about an order of magnitude greater than that
of the coarse. It is also interesting to note that the solid phase con-
centration in suspension tracks and exceeds that of the fines in the bed -
probably due to the fact that the former contains smaller size particles,
which generally have a greater adsorption capacity, than the fines in the
bed. This information is presented to indicate the importance of the
water-bed interaction with respect to the various size classes and the
resulting effect in the water column. Subsequent modeling is being con-
ducted to address these distinctions and bed transport. -
A - /'3

-------
acknowledgement
The work reported above was performed by Hydroscience, Inc. The
contributions of Thomas W. Gallagher, Dominic Di Toro and Michael
Kontaxis are recognized.
4-1/4-

-------
2. Polychlorinated Biphenyls - Hudson River
The analysis reported in this section was part of a larger
study which was directed to an evaluation of the need of remedial action
with respect to PCBs in the Hudson River. Although the most contaminated
areas are in the vicinity of the upstream source, above the Troy dam, the
entire length of the river through the tidal regions has been affected to
some degree. The primary emphasis of the study was placed on the accumu-
lation of the chemical in the food chain - particularly the migratory fish.
In the course of the project, a preliminary analysis was made of the physio-
chemical factors which determine the distribution of PCBs in the water and
in the "bed. A review of that analysis is presented in this example. A more
detailed description of the project with emphasis on the food chain, is
presented in a subsequent section.
It is specifically the purpose of this section to demonstrate the
utility of the analytical solutions of the basic differential equations in
order to make a preliminary assessment of the problem. Appreciating that
such solutions usually represent idealized conditions - e.g. constant area,
steady-state - nevertheless, they may be accepted as a first step providing
a basis for a .more detailed analysis. The major advantage of using these
solutions lies in the fact that an evaluation of various factors is readily
available - e.g. the selective effects on volatilization versus degradation.
A secondary purpose of this example is to present the procedural approach
and method of analyzing data. The latter was regarded as inadequate or, at
least incomplete. This situation is not uncommon in water quality analysis -
making the most of meager and perhaps inadequate data.
This application presented here deals exclusively with the fresh water
portion of the River from the Federal Lock at Troy, milepoint 156 upstream
to Fort Edward, milepoint 19^. The upstream location is in the vicinity of
the General Electric Plant, which was the original source of the PCBs. Al-
though the discharge was discontinued, there are significant residual concen-
trations in the bed which affect the concentration in the water column in both
upstream and downstream stretches.
A map of the area is shown in Figure 2-1. The river segment of in-
terest in this example extends approximately from Troy to Glen Falls. The
drainage area and flow variation from. Glen Falls to the mouth are shown in
Figure 2-2, the latter is based on the average annual flow of 13,000' CFS at
4-"5

-------
Green Island. This figure also indicates the types of transport in each
segment - flowing stream, tidal river and saline estuary. The following
analysis is related to the. upper stream stretch.
Data was collected in 1976 and 1977 during high flow periods and the
1977 flows were extremely heavy floods, in the order of 1 in 50 - 100 years.
The analysis of the 1976 data is presented in Figure 2-3, which indicates
the concentration of suspended solids and PCB for the various flow periods.
The solids distributions are calculated in accordance with equation (ll)
and the PCB with equation (23). Type II Analysis (water-bed interaction)
is appropriate as is evident from the comparison of the observed data and
computed profiles. The model portrays the general trend of both solids
and PCB data, providing a reasonable fit for each set.
By contrast, the 1977 data were anomalous as shown in Figure 2-4.
The March 29, 1976 data set and model results are presented for comparison ,
The suspended solids distributions are fairly well reproduced. The except-
ionally high flow of 160,000 CFS resulted in large concentrations of solids
to values of greater than 1,000 mg/liter. The PCB data, however, are erratic
for this condition. High concentrations are expected, but the measurements
indicated less than 1 Ug per liter. Furthermore, these levels are completely
at variance with the high flow of the previous year when measured values
were in the order 10 yg/liter and greater.
There are many possible causes for the apparent inconsistency. The 1977
flood may have affected the tributaries to greater extent than the main branch
thus introducing large concentrations of uncontaminated solids. This in-
creased mass of solids^acts as a dilutant for the presently contaminated
solids, which desorb and re-absorb to the fresh solids. An alternate
hypothesis may be presented: the excessively high flood may have re-
suspended large segments of the bed material, particularly the greater
size and more dense solids, which have a slower solid phase concentration.
In any case, the importance of tributary drainage and bed characteristics
is further emphasized by this example, information on which was inadequate
to analyze these high flow conditions.
ACKNOWLEDGEMENT
The application reported in this section was supported by Hydro-
Science, Inc., Westwood, N. J.-
4-Hi

-------
/
u

1
s
/
lcgcno:
~ U.S.G.S. GAGING STA.
~ - -
TftEATMCMX-
m
^fcfcAN.T
~ _
BIVE" MIUC "
10
NORTH
10	2	4
I	1	I	1 I
MILES
FIGURE 1. MAP OF STUDY AREA
4-"7

-------
3
o
ro
FLOW (CFS)
DRAINAGE AREA
( SQ MILES'.
rn w
CI
ci
m,
CREEK
CREEK
CREEK
' north e.:iO Ml DOLE 9R5HCH
u>
O
A
O
REEK
O
o
9
CREFK
NOR TH
.MOOLE
ui
o
o
a>
O
o
vl
o
o
as
O
o
<
o
o
o
o
\piVER EED ELEVATION
( FCET A3CVE M S L}

-------

o-
*-
O
O
I.
PcoJ- c^s


fii.ep**sr 3*-4v*
) Sb	N	i"	'*
pUu) - 6fS
FIGURE 3. VELOCITY-DEPTH FLOW RELATIONS
4-119

-------
0, 979 Ttifv&Y
50
40
30
20
20
50
40
30
MILEPOINT
1000
to
MAY a-10, 1978
800
600
UJ
O o*
to E
to 
400
200
20
30
50
40
MILEPOINT
2 50
200
to
UJ _
O 
150
100
50
30
MILEPOINT
20
50
40
FIGURE It. SUSPENDED & DISSOLVED SOLIDS - MAY 78
4-120

-------
zmc

M
J
a
3
o
m

t.00
1
o
s
u
Tme. moum
r	--^=
-a-
o
2
o
u
loo
SOLI DS  26
Me/.
4.
X
6.
~
O
J
O
M/j
I'&o _ 36 	i
m
(P. 36,oq<
TihI *Mogfts
FIGURE 5. LABORATORY DATA ON ADSORPTION-DESORPTION
4-/2/

-------
100
c

80
Nl


UJ
	
60
_l


CD
cr

U
_l
4.
40
o


10

20
0
60
_l
CD
3
-J
O
m
100
80
- 60
N
CP
4. 40
20
0
60
25
20
3
O
Ul 
_J- 15
m
J 4. 10
o 
CO
60
MAY 8-10, 1978
50

40	30	20
MILEPOINT
 
10
ZINC 50
40
30
c
N
Ui
 OI
u 4.
h
cr
<
a
0
60
COPPER
3
u
UJ
< -
_J v.
3 O"
O 4.
f-
cc
<
CL
0L_
60
50 |
 
I
I
40	30	20
MILEPOINT
  
10
FIGURE 6. HEAVY METAL CONCENTRATIONS - MAY 78

-------
n
Q
_)
O _
in C
O "-
uj o>
O E
uj
a.
in
m
tn
a
O
to
o _
liJ _
CT>
 E
in c
CO
<1
 400 
200 
JULY 17-19, 1978 SURVEY
1000
800 
600 
30 f	40
250
200 
150 
tn
ui	
O	
	\
or	cr
	E
1 100 
X
30	20
MILEP0INT
FIGURE 7. SUSPENDED & DISSOLVED SOLIDS - JULY 78
4-123

-------
IOC
1
80

vTmly n-MjISTfi
 l>>
~ _ to
_


-J



33 40



2

 1 _
 . "v r

20
_
		V
'r	


 
/ "
0

.t*
1
o *V -* .w
1	
JO
20
FIGURE 8. HEAVY M1 CONCENTRATIONS - JULY 78

-------
V/*
a
j
o

0 ^
Ui 

-------
t
NJ
03
3
O
on
IOO
_ co
v.
0
1	40
TO
O
to
03 .
o
_J
o
CO
loo
so
" Co
"N*
G*
^ 40
lO
Co
J
50
40
July 5"- fc,
X
30 lo
h\ 1 lE poimt
o
10
Zinc
r
rvi
>Jj
\oO
SO
01 10
r-
0
cC
L
ZO
o
GC
NICKEL ioo
*0
2
Ui
< - to
3 c-
J X 40
0^
<
(L
ZO
O
60
So
40
SO ^ 40
-ft^T
SO
Zo
30	2o
K\uE POi^ T
IO
IO
FIGURE 10. HEAVY METAL CONCENTRATIONS - JULY 79

-------
a
o
1/1 
o ^
Lu g-
a I
2	*
iu
a
/>
3
M
c
<
10
o
5
r-
3
to
z
a
Ui
W
(0
tf
N _
si
a
Ui
(O
I t6
I 00
So
4o
4
2o
-75 J** FRACTION
^VTctovl 5aSP. ohd&
A-
Au6 16.WM
P.M. Samples
so
o.zs
OlZO
>. OJ5

Q
M '
h- O.IO
IL
0.05
SO
4000
sooo
zooo
100 0
so
AO
I
40
40
X
3o	20
MILEPOINT
10

o.lT
J
JL
3O	ID
MlLtPOliJT
IO
a.
50	ZO
MILE POINT
IO
FIGURE II. SUSPENDED SOLIDS - AUGUST 79
4-/27

-------


Aoo
X*

80
N


u1

CO
1
"s.

AO
(7*
4o
2
2
-1


O


to

Zo
CO

Aug, Je.tqiq
AM
ZD
100

2 80
-
r: CO
_i ^
-
l
loo
80
Co
J ^ ,

-------
10,000
c
N
2 1,000
UJ
 * '00
to 4.
2
O
o
CD
10
MAY a-10, 1978
 
r-J	1	1	L
50 4 40 30 20 10
MILEPOINT
ZINC
10,000
c
isl
1,000
UJ
5 
 o>
O \
U CP
-
o
CD
100
JULY 17-19, 197B
_ A *
*
(. _
 
A-PARTICLES < 75/Um
I
50
y 40 30 20 10
MILEPOINT
10X100
z
UJ
2_
Q ^
UJ o>
cn ^
2~~
o
o
en
1,000
100
10
I
 
50 ~ 40 30 20 10
MILEPOINT
NICKEL
10,000
Z 1.000
UJ
2~-
~ o>
Q
UJ o>
WJ
O
O
as
100
10
 
k
 
A
  
50
| 403020
MILEPOINT
J0;000
z
UJ
2 
 o>
a \
ui a>
w
2 "~*
O
O
m
1,000
100
10
J	I
50
"40
30 20
MILEPOINT
10
COPPER
10,000
l_> -
1,000
 o>
a \
UI cn
V) i.
O
0Q
100
10
~A
I 
 *
50 -1 40 30 20 10
1	MILEPOINT
FIGURE 13. HEAVY METALS BED SEDIMENT
4-/2
-------
ZINC
MILEPOINT
10,000
f\i
1.000
~ o
5 "o 100
30 20
MILEPOINT
50
40
10,000
s 00
C/> X
50



A - PARTICLES < 75fj.
JULY IT-19, 1978
M 10,000
UJ
t-
<
-l
<_)
I o>
a: ^
I o
Q. 4.
a
UJ
o
Z
UJ
a.
V)
3
in
IjOOO
100
10
JULY 17-19, 1978
  ,

_L
_L
50
40
30 20
MILEPOINT
10
NICKEL
2 10.000
UJ
-
<
-J
Z3
O
1,000
t a>
a: \

a. 4.
Q
UJ
Q
Z
UJ
Q.
UJ

100
10
 
<
 
I
50
40
30 20
MILEPOINT
10
o
10X100
1,000
Ul
2 
 a
Q ^
i. i o>
u> i.
5 ~~
O
t-
o
CD
too
I 0
a*
1 

50 * 40 30 20 10
MILEPOINT
COPPER
o
UJ
10,000
3
( o
a: ^
<
0- 4.
Q
UJ
o
2
UJ
a.
VJ
3
cn
1,000
100
<
50
<
<
I
40
30 20
MlLEP0INT
10
FIGURE 14. HEAVY METALS BED SEDIMENT & SUSPENDED SOLIDS
4-130

-------
N
GLENS FA1.LS,


TROy
ALBANY i
KINGSTON

POUGH K EE PS IE
jSL^nD
scale:
io s o 10 ?o 10
MILES
ATLANTIC OCEAN
FIGURE 2-1
HUDSON RIVER BASIN
4-/3/

-------
is.
o
 V)
to
o
<
UJ
cc
<
UJ
o
<
2
<
EE
O
CO
Lu
U
10
O

o
6.
12.
10.
8.
6.
4.
2.
240 220 200 180 160
I 8
16
140 120 100
RIVER MILE
80 60 40 20
12
10
8
CZIVKK.
TlOJkl- BwCCE
CrSTu
note:
FOR AN ANNUAL AVERAGE DISCHARGE
AT GREEN ISLAN0 OF 13,000 CFS
Li.
240 220 200 180 160 140 120 100 80 60 40 20
RIVER MILE
FIGURE 2-2
DRAINAGE AREA AND FLOW DISTRIBUTION
(GLENS FALLS TO STONY POINT)
4-/32

-------
HUDSON ai VER
si
to
o
o

a
Ui
a
3t
Ul
0.
W>
D

1 CO
\CO -
120 -
eau^Tiou n
LEGgUQ
FLOW SVHBOi
tTfC, . Cfs
Ife - 13,000
|*\*e 29- 4-9.000
JkPfc 1 - lOd.OOd
\	no
M l^tpoinT-
I9>
E.CU A.TIOU 23
o:
\TO
H l L.C POtMT
FIGURE 2-3. SOLIDS & PCB DISTRIBUTIONS - 1976
4-133

-------
M u D Sow riveR.

a
-j
o
w>
o
ui
a
2
ei
a.

_i i
a
A
A
zoo
)3o
IftO	170
KlLfcPCMWT
160
ISO
FIGURE 2-k. COMPARISON OF 1976-1977 DATA AND ANALYSIS
4--/-M

-------
ANALYSIS OF COMPLETELY MIXED SYSTEMS* _ TOXIC SUSSTAUCES
1. Type I Analysis - Stationary Bed - No Resuspension - Sedimentation
a) Suspended Solids
The concentration of suspended solids in a reservoir or lake de-
pends on the physical characteristics of the incoming sediment and the
hydraulic features of the system and inflow. The important characteristics
of the solids are the grain size and settling velocity distributions and the
behavior of the finer fractions with respect to aggregation and coagulation.
Bie detention time and the depth of the water body are the significant hydrau-
lie "pd geomorphological 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 admit at least an order of magnitude analysis of the problem. They are
precisely 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 uniform 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
V-vlance of the solids takes into account the mass inputted by the inflow,
thst discharged in the outflow and that removed by settling. The mass rate
of change of solids in the reservoirs is the net of these fluxes:
mi = concentration of solids in water body
vg = settling velocity of the solids
Ag = horizontal area thru which settling occurs
The flux Qa^, equals the rate of mass input, W. Dividing through by the
volume, V, the above equation becomes
(1)
in which
m^ = concentration of solids in inflow
(2)
Donald J. O'Connor
4--I3?

-------
in which
t = detention time = x (T)
o	Q
s L
K = settling coefficient  ()
s	n i
y
H = mean depth =  (L)
s
Under the steady state condition, equation (2) may be expressed as,
mi
^3	(3a)
1 + K t
s o
Division by W/Q yields
57q = rrirr	<>
so
which is the fraction of the incoming solids remaining in suspension and,
with the assumption of complete mixing, is also the concentration in the
outflow. The fraction removed is simply
'L-rrrr
s o
The disensionless parameter, K "t represents the combined effects of the
settH- o characteristics of the solids and the average detention time of
the system. The coefficient, K , may be replaced by its equivalent, v /H,
S	H Q	S
and +he dimensionless parameter is v /v , in which v =  = tbe overflow
SO	O v	A
O
rate of the system.
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 bentha] concentration, on the other
hand, is due directly to the influx of the settling solids. The rate of'
change of mass of solids in the bed is therefore
dM2 . .
dt = * A'Vl
The mass, M2, equals the product of the bed volume V2 , and bed concentration,
m2. Thus
dM2 _ d(V2m2) _ m2 d.V2 . V2 dm2 _ .  
dt "  ~ dt + dt " + Vsmi	(5a)


-------
d z 9
Dividing through the Ag, and expressing the resulting as V^, the final
result is
dm2 Vs
dt
(5b)
at steady-state - i.e. when the mass settling rate equals the accumulation
rate:
(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 similar 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
interaction with the other. For the dissolved component, the mass balance
(2)(3)
includes decay and transfer terms	in addition to the inflow and outflow.
The basic differential equation
Kc = overall first order rate coefficients (T-1) which may include biolog-
ical degradation, hydrolysis, direct photolysis & volatilization.
Kq = the adsorption coefficient (L3/M-T)
(6)
o
in which
7 -3 reservoir volume (L3)
W- - rate of mass input of the dissolved component (M/T)
ci = dissolved concentration in water body (M/L3)
m = suspended solids concentration (M/L3)
K2 = the desorption coefficient (T_1)
pi = particulate chemical concentration (M/L3)
For the particulate concentration:
w
dt " V " t
 K p  K2P1 + K m Cj
s 1 1	o
_ (7)
o
4-'37

-------
in which
= rate of mass input of the particulate adsorbed chemical (M/T)
Kg = settling coefficient (T"1)
Adding equations (6) and (7) cancels the adsorption and desorption terms
and yields the rate' of change of the total concentration c^ in terms of the
dissolved and particulate:
dCTi W CTi		m
 * V-  "KCC1 -KS,P1	<3)
0
The sorption coefficients, Kq and K2 are usually orders of magnitude
greater than the decay and transfer coefficients of the dissolved and par-
ticulate. The rate at which equilibrium is achieved between the two phases
as 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 c,p by equation 1+, substitution of which in equation (8) yields:
fflL.iL fli. Kc V-
dt Vi t 1 + Umi Ti " 1+Umi Ti
o
Under steady-state conditions, the above may be expressed, after multi-
plying through by t :
c 	m		(9)
Ti	t
1 +	+ ,nlK ]
1+ilmi c 1	si
For those substances, whose dissolved components are not susceptible to trans-
fer/decay, such as heavy metals, equation (9) reduces to
c =			(10)
1 * K % UJ?' 1
si 0 1+Umi
Hote that equation (10) is identical to equation (3a) with the exception that
the dimensionless settling parameter K^t^ is- multiplied by the fraction
4-/38"

-------
The latter term expresses the fraction of the	total concentration which is in
the particulate form. For values of Hm  1,	it is apparent that equation
(10) is identical to (3a). With reference to	equations (9) and (10), the
fraction removed is
' -1 - m	(11)
Inspection of equation (U) indicates that the removal efficiency of
suspended solids is dependent on the detention time and settling coeffi-
cient, which is the ratio of the settling velocity of the solids and the
average depth of the reservoir or lake. For heavy metals and conservative
chemicals, the additional parameter required is the partition coefficient
(equation 10). In the case of organic chemicals, which are susceptible to
biodegradation, evaporative transfer, hydrolytic or photochemical reaction,
knowledge of the relevant reaction coefficients is necessary (equation 9).
The detention time and average depth, which are readily determined,
are based on the average seasonal or annual conditions, given the time and
space scales of the analysis. The settling velocity send settling coefficient
may be measured directly or implied from inflow-outflow concentrations in
accordance with equations (3) and (U). The partition coefficient may also be
evaluated directly, which, with the solids concentration, yields the dimen-
sionless parameter flm. Alternately given measurements of the total and dis-
solved concentrations of the heavy metal/organic chemical, the term 1fm may
be calculated. With such information, the removal efficiency is readily
computed for those metals and chemicals which are non-reactive.
As indicated above, certain chemicals may be subjected to additional
transfer or transformation. The fundamental properties of the constituent
are indicative of the potential magnitude of these routes - e.g. the vapor
pressure and solubility are properties which permit assessment of the evap-
orative transfer (U)(5). Laboratory experiments may be necessary to deter-
ment the chemical and biological routes - e.g. the biodegradability of the
substance (6)(9). In any particular case, an assessment, either analyti-
cal or experimental, should be made to establish the degree to which trans-
formation or transfer may be significant. Solutions of the above are shown
in Figure B-2.
4-/3?

-------
The bed concentration may be described by constructing its mass balance.
Influx is due to the toxic substance associated with the settling solids and
the volumetric accumulation is accounted for by the sedimentation velocity,
as in the bed solids analysis (equation 5)
dcT
-r=^ = f K c_ - f K c	(12)
dt	pi 32 Ti P2 d2 T2
at steady state
CT2"tK7CT,	(13)
P2 d
in which
f = the fractions dissolved and particulate
pn	^
vs = settling velocity
v, = sedimentation velocity
d
Since the bed solids concentration m2 > mi and flm2 is usually >>> 1,
as a reasonable approximation
f % 1 and f. 0
p2	d2
CT2 = P2 = fpi ^ CT. = ^ pi	(lM
substituting for p = rm
v
s
r2m2 =  rimi
d
since vdm2 = vsnii under steady state, then
p2 = ri	(15)
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 following section, which considers solids resuspension - a
condition more likely to enhance exchange of the dissolved component.
f -'40

-------
2. Type II Analysis - Mixed Bed - Resuspension
The type of analysis described in this section is identical to that of
the previous, with the addition of a resuspension term in both the solids
and toxic equations. The physical structure of the system is shown dia-
grammatic ally in Figure B-l, from which it is apparent that a mass balance
equation must be developed for both the water column and the bed, since
they axe interactive.
a) Suspended Solids
The mass rate of change of solids in the water column is:
Vi = Qm - Qmi - V^mi + vuAsm2	U6)
in which
v  resuspension velocity - L/T
m2 = concentration of solids in the bed - M/L3
and the remaining terms are as previously defined by equation (2) of the
previous section.
Expressing the input flux of solids Qmi as W and dividing through by
the volume V^, yields
V	V
dmi_W mi su	, ,
dt ~ V " to " Hi 1 Hi z	( 7'
in which
Hi = average deptluof the water column
A mass balance of the bed solids includes the influx of the settling
solids from the water and mass outflow from the bed due to the resuspension
and sedimentation:
V1 Vm2 Vrfm2
dm2 _ s	u	d	/ q 
dt ~ H2 " H2 " H2	( '
in which
H2 = average depth of the bed
At steady-state conditions, = 0, the concentration in the bed may be
expressed in terms of the concentration in the water from (18):
4-/4/

-------
ni2 = ^ni	(19)
in vhich
v
s
s =
V + V,
u d
Substitution of which in equation (IT) under steady state yields
V	V	V
 w r 1 . s, . u	d _
0 =  - nil (  +  ] + - 	 nil
V 1 lt Hi Hi v + v. 1
o	u d
v
Expressing  = K and solving for mi, after simplification, gives:
H s
mi =, , yg ,	(20)
i+Tk t
SI o
in vhich
B- ^
V + v,
u d
The value of  falls "between zero and unity. The latter represents
the case of no resuspension v^ = 0 and 8=1, reducing (20) to (3) and the
former of no sedimentation v^ = 0, reducing (20) to
mi = W/Q	(21)
In this case the settling flux is exactly balanced by the resuspension
flux, resulting in zero net change and the concentration of solids is simply
that of a conservative substance, as indicated by (21).
The bed concentration follows from substitution of (20) in (19):
m2 = i +Yk\	(22)
s o
Algebraic simplification yields
m2 = */Q -	(23)
8 Hi o
For lakes or reservoirs of shallow or moderate depth (H ^ 10M), moder-
ate high settling velocities (v ^ 3M/DAY) and low resuspension velocities
4-142

-------
(v < 1CM/YR), the B term is more than an order less than the sedimentation
term and (22) reduces to
02 ~ ~	(2U)
Kh V
di
in which
Kd, "ir
b) Toxic Substances
The equations for the toxic substance are developed in an identical
fashion as in the Type I Analysis. Each phase in the water column, the dis-
solved, c, and the particulate, p, is analyzed separately with adsorption and
desorption kinetics in addition to the input, outflow and settling terms.
Furthermore, allowance is made for the exchange of the dissolved component
between the water and the bed, expressed in terms of the difference in the
dissolved concentrations. Addition of the two equations cancels the ad-
sorption-desorption terms and yields:
= I|S. - I|i - Ksip, ~Kii,I + Kbl (C2 -=,)	(25)
in which
the subscript 1 refers to the water column and 2 to the bed
c^ = total concentration of toxic in the water column
v
K = -2- = selling coefficient (l/T)
si ai	~
v
K =  = resuspension coefficient (l/T)
K
K. = = = dissolved exchange coefficient (l/T)
Di tti
= transfer coefficient of the dissolved .between water and bed (^)
Expressing p and c as fractions of the total concentration (equation U of
the previous chapter) and combining similar terms yields:
-  ~ fpi KSl * 'dl V <=!, * tfp! Kui ~ fl2	cT; (26)
the bed equation is developed in a similar fashion
4-/+3

-------
do
[f K + f. K. ] c_ - [f (K + K ) +"f K_ ] c	(27)
dt	pi &2 di D2 Ti	P2 U2 d2	d2 U2 T2
dt	pi
in which
f = particulate fraction in each segment, 1 and 2
Pi ,2
f, = dissolved fraction in each segment, 1 and 2
dl .2
The working equations for the steady-state condition are developed in a
manner 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 >>>mi and Va2  1, f ^ 1 and
f. ^ 0. For this simplification, which is realistic for 1F>1000, the water
a.2
and bed concentrations are respectively
W/Q
CTi * 1 + Bf, [flmiK + K. ] t	(28)
a	Si bi o
f K + t.YL
Cm = -LS2_JJb2. Cm	(29)
in which
*T2 K K,	Tj
U2 d2
V
B
V + V,
u d
f, = 1
d 1+flmi
f s ,mr
p ~ l+Umi 
v
K.-r
K = Km
^ H"
K- = Vo
U 1-
K. = Vd
4 H"
For the condition of negligible exchange of the dissolved between water
and bed (Kb'v0), the above equations reduce to
4 -14.4

-------
in which, in accordance with equation lU
v
a c 	L_
V +V ,
u d
For toxics of high partition coefficient and systems of high solids (fmi
>5), the abore respectively reduce to equations (2l) and (19), the
equivalent solids equations.
4 -us

-------
I
Vv \ if*,*

TWt
cBsu%^eus\ovj
^0t>5cg\rTS
l \aj&tt.e.
t 6 SO
<3?
\
SOUOS
4ii'V^c
kv
4.
v, O
V^ft t Vi
^\xvw
^	~ _ ga
X	it'O
TL	^>o
Tr*^orl "^ero
l_iCE Mb
OMITS
N
luFLUX
*
Cfc
fvow

V
VoLUHl
t*
K
rstPtrt
L
/M
9 olIOS
M/ul
cT
TOMIC - ToTtil.
h/l%
U
blSSelvKb f CNt-noO
- -
*P
pKo.Tv.coi.kre
""
V,
^tmiue. vtiociri
Wr

eesu$Peistou vEioctrf
II
vi
SEOVUP^TiWkoU ^CVotprS
n
k*u
coifftc.wr
*
we
t>lSoWfft> DtCM A
n

cotfficn.uT
u
*>
4ft.-ncuL 4kT& OtCiS
%
TOXIC.
FIG. B-l Schematic of Ttype	II Solids Parameters

-------
T1YPE I - ANALYSIS
0.0
0.03
-
0.+ -
0.3
0.2-
1.0
FCKctlOh
Cofrrefrvq.'fcivq
0.0
0.03
0.3
	pKctu*
	Coniebactiy
FIG. B-2 Fraction Remaining for Various Detention Times
and Kinetic Parameters
4 -'47

-------
TYPE I ANALYSIS
fP * o.oa
I.o -

-------
3. Applications
The following analysis relates to the distributions of both
organic chemicals and heavy metals in reservoirs. It is based primarily
on the Type I Analysis, with reference to the lype II as appropriate.
a)	Suspended Solids
A plot of equation (4)}is.presented.in.-Figure B-3 for a range
of settling coefficients, K . Common values of the settling velocity of
8
solids in reservoirs are in the range of a few feet per day and average
depths are 10-100 feet, yielding values of K< in the order of 0.1 per day
with approximate limits of 0.025 to 05 shown. The majority of the
data is abstracted from reference (l) and supplemented by more recent
measurements (10-13) from reservoirs for which concentrations of heavy
metals organic chemicals axe also available. Data from the earlier
reference are characterized by K >0.1 per day. The latter data with
8 *
K <0.1 per day are representative of settling velocities between 0.25
8 
and 2.5 feet per day, as shown in Figure 2. This figure presents the
correlation in a more fundamental manner. It is evident from equation
(k) that replacement of K with V / yields the correlating term, t / ,
s	8 n	on
with V as a parameter as shown in Figure B-4. Settling velocities, in
s
the order of 0.5 to 5.0 feet per day, which .is representative of clays
and fine silts, encompass the majority of the data. These types of solids
are most relevant to the problem, since they have a greater capacity to
absorb organic chemicals and heavy metals than sands.
b)	Heavy Metals and Organic Chemicals
A water quality survey of heavy metals and organic chemicals was
conducted during the latter part of 1976 and the first few months of 1977
on the Trinity River through Lake Livingstone.(10). At a number of stations,
measurements of the total and dissolved concentrations in the water columns
and in the bed were made. Pesticides were measured in grab samples for
Coralville Reservoir at inflow, outflow and in-lake stations during 1969
and 1976, while bi-weekly suspended solids measurements have been made since
1965 (11,12). Data for I^ke Rathburn were collected bi-weekly from May
through August, 1978.(13).
From these data, a value of the removal efficiency of each reservoir
was determined and presented in Figure B-5. The"range of suspended solids


-------
removal (Kg = 0.02s, 11m > 10) in accordance with equation (U) is shown for
comparison. The purpose of this figure is simply to demonstrate the relative
removal of the various constituents. For many of the heavy metals, it is to
be noted that tbe removal is equivalent to that of the suspended solids,
implying that the particulate fraction is predominant. For some of the
organic chemicals the removal fraction is much less, indicative of a larger
fraction in the dissolved state or a source from the bed. Constituents which
have removal fractions greater than that of the suspended solids may be sub-
ject to additional mechanisms, such as biodegradation, evaporation, chemical
hydrolysis and oxidation, and direct or sensitized photolysis.
Since both the dissolved and total concentrations were measured in the
Livingston survey, it is possible to calculate the flm values for each sub-
stance.. Using these data a more fundamental relationship is presented in
Figure B-6 for Lake Livingston in which the particulate fraction, as deter-
mined by the observations, is correlated to the fraction removed. The
removal fraction is calculated in accordance with equation (11) for a range
of values, representative of conditions in this reservoir. The sequence
for pesticides shown in Figures B-5 and B-6 - Lindane, dieldrin, heptachlor
and endrin - is in accord with increasing tendency to the particulate state.
The data on metals indicate greater variation and are not as consistent,
particularly with respect to copper.
Removal fractions for non-conservative substances (i.e. those which are
removed by mechanisms in addition to settling) should exceed the expected
removals caused by sedimentation of sorbed material. Heptachlor may be
susceptible to evaporation and endrin to biological decay. Evaporation and
biodegration may also "affect dieldrin but to a lesser extent. Such factors
may account for the fact that these substances indicate higher removals.
Mean removal fractions for Lasso, atrazine, and dieldrin in Rathbun
Reservoir, are presented in Figure B-7. The representation in Figure B-7
is similar to that of Figure B-6.except that I^t^ is equal to U.O and
isopleths of KctQ are indicated for these reactive substances. It is
estimated t.hnt the. highly soluble herbicicides Lasso and atrazine undergo
rather rapid biodegradation in natural waters with KctQ = 10 and ^ respect- .
ively, and overall first order rate constants (Kc) of 0.06 and 0.02 per day.
Grab samples and partition coefficients from other rivers and reservoirs in
4-150

-------
Iowa indicate that a small fraction of Lasso and atrazine are in the particu-
late phase. Dieldrin removal rates were quite variable, but it appears that
the removal is due primarily to sedimentation of sorted material, and the
estimated first order reaction rate constant (K ) was nearly zero.
c
Equation (9) represents the most generalized correlation and is shown in
Figure B-8. The dimensionless parameter is the product of the particulate
fraction (1m/l + Urn) the reaction factor (l + K /K Hm) and the settling term
c s
(K t ). The vertical lines in the figure indicate the values of the latter
s o
term for the three reservoirs and are representative of purely particulate
Um
substances (:== 1) and conservative substances (K = 0). Data falling to
l+Um	c
the right of the respective verticals suggest that in addition to settling,
transfer and/or decay may be operative. The most marked deviations are for
copper and zinc with lower removals than calculated, which may be due to re-
lease from the bed (/fyPe II Analysis). On the other hand, the fact that
dieldrin is in reasonable agreement for the three reservoirs is encouraging.
The remaining values are in general accord assuming Endrin and Lasso are non-
conservative (Kc = 0.05/day). Atrazine and heptachlor are being removed by
sedimentation of adsorbed chemical as well as by gas transfer and/or decay
reactions.
Recognizing the simplicity of the analysis and appreciating the limited
number of observations, it is apparent that comparisons such as presented in
these figures are not necessarily validations of the model. It is encouraging
to .note that the observations are not inconsistent with the theoretical analy-
sis and in order of magnitude indicate reasonable agreement.
Given the nature o$ the assumptions on which the model was formulated,
it may be used to estimate long-term concentrations for average values of flow
and loadings. Furthermore, the time to reach equilibrium or steady-state con-
ditions may also be approximated. Additional field data are required to test
and validate the model. Such field programs should be conducted in conjunc-
tion with laboratory measurements of sediment-water partitioning, volatiliza-
tion and degradation reactions, the results of which may be incorporated
directly in the model.
4-l5f

-------
ACKNOWLEDGEMENTS
The support by EPA research funds in developing the above is gratefully
acknowledged: Grant No. R80U563-O3, EPA Gulf Breeze Laboratory, Gulf
Breeze, Florida, 1976-1979. Application of the Type I- Analysis was used in
an environmental assessment study by the U.S. Corps of Engineers of a pro-
posed reservoir on the Trinity River, in which the data on the Livingstone
Reservoir was collected. A report was submitted in 1978 to the Corps, whose
support is acknowledged. Jerald Schnoor, University of Iowa, kindly pro-
vided the data on the Iowa reservoirs. This research is supported by Grant
Ho. R806059-01, EPA Athens Laboratory, Georgia, 1979. Both are collabora-
ting in reporting this work in a paper which has been submitted to "Environ-
mental Science & Technology."

-------
REFERENCES
1.	Brune, G.M. Trans. Am. Geophys. Union. 1953, 3^_, 1+07-18.
2.	Smith, J.H.; Mabey, W.R.; Bohonos, N; Holt, B.R. ; Lee, S.S.; Chow, T.W. ;
Bomberger, D. C. ; and Mill, T. "Environmental Pathways of Selected Chemi-
cals in Freshwater Systems, Part I: Background and Experimental Proced-
ures." 1977, U.S. Environmental Protection Agency; EPA-600/7-77-113.
3.	Smith, J.H.; Mabey, W.R.; Bohonos, N.; Holt, B.R.; Lee, S.S.; Chow, T.W.;
Bamberger, D.C.; and Mill, T. "Environmental Pathways of Selected Chemi-
cals in Freshwater Systems, Part II: Laboratory Studies." 1978, U.S.
Environmental Protection Agency; EPA-600/7-78-071*.
i;. Mackay, D.; Leinonen, P.J. Environ. Sci. Technol. 1975, , 1178-80.
5.	Mackay, D.; Wolkoff, A.W. Environ. Sci. Technol. 1973, 7_, 6ll-k.
6.	Hushon, J.M.; Clerman, R.J.; Wagner, B.O. Environ. Sci. Technol. 1979,
13, 1202-7.
7.	Karickhoff, S.W.; Brown, D.A.; Scott, T.A. Water Res. 1979, 13, U21-8.
8.	Zepp, R.G.; Cline, D.M. Environ. Sci. Technol. 1977, 359-66.
9.	Paris, D.F.; Steen, W.C.; Baughman, G.L. Chemosphere. 1978, 319.
10.	"Trinity River Bottom Sediment Reconnaissance Study", Fort Worth Dis-
trict Corps of Engineers, Texas. June 1977.
11.	Mehta, S.C. M.S. Thesis, The University of Iowa, Iowa City, Iowa. 1969.
12.	McDonald, D.B. "Coralville Reservoir Water Quality,Study, Water Years
1965-1978", Reports to U.S. Army Corps of Engineers, Rock Island,
Illinois. 1979.
13.	Kennedy, J.O. "Lake Rathbun Pesticide Study", University of Iowa
Hygienic Laboratory, Iowa City, Iowa. 1978.
lU. Sanders, W.M. III. "Exposure Assessment, A Key Issue in Aquatic Toxicol-
ogy", in Aquatic Toxicology. ASTM, STP 667. 1979, pp. 271-283.
4 -

-------
1.0
Q
LU
>
O
S
UJ
cr
0.8
H
O 0.6
<
, u-
Vl
t/)
0.4
O
CO
0.2
0.0
SB yUD /fe5l /0251
J	I	L
J	I	I	I	L
RSI- Ks DAY-1
A BRUNE'S (1953) RESERVOIRS
 C0RALVILLE RESERVOIR, 1972-77
~ LIVINGSTON RESERVOIR, 1973-76
O RATHBUN RESERVOIR, 1978
	I	I	ll I	I	
5 7 10 20 30 50 70 100 200 300
t0 DETENTION TIME, days
700
2000 5000
Figure B-3. Suspended Solids Re ! Detention Time Relationship

-------
1.0
ffeol>(231 yffjolT/tQ3!l y|5^5l
l
1Tq~I
SETTLING VELOCITY,
FT/DAY
 CORALVILLE RESERVOIR
~ LIVINGSTON RESERVOIR
O RATHBUN RESERVOIR
	I	,	
.1
1.0	10
t0/H DETENTION TIME/MEAN DEPTH, days/ft
100
Figure B-^. _ Solids Removal versus Detention Time/Depth

-------
I
LA-LASSO
E-ENDRIN
Ni- NICKEL
A-ATRAZINE
Cd-CADMIUM
Cr- CHROMIUM
H-HEPTACHLOR
D-DIELDRIN
Zn-ZINC
L-LINDANE
> 0.8

CORALVILLE SOLIDS,
1976
O 0.6
~ LIVINGSTON SOLIDS,
1973, 74, 76
O RATHBUN 1978
Ks= .025
TIM>
I	1
5 7 10 20 30 50 100 2 00 300
t0 DETENTION TIME, days
700
2000 5000
Figure B-5. Removal Fraction vs. Detention Time

-------
<0
Nj
LIVINGSTON RESERVOIR
~ SUSPENDED SOLIDS DATA
I,
J CHEMICAL FIELD
i~ data
1 ENDRIN
igg
I HEPTACHLOR
I DIELDRIN I
I ZINC
^ 0.3
 = Kcto
DANE 1
I	A
0.0
0.1 0.2
11M
l-HIM
0.3 0.4 0.5 0.6 0.7 0.8 0.9
PARTICULATE FRACTION OF TOTAL
l.O
Figure B-6. Removal Fraction vs. Particulate Fraction

-------
t
w
1.0
0.9
.LASSO
-6ATRAZINE
O
UJ
>
O
5
UJ
tr
o
H
O
<
QC
^0 ( ) = ^
SOLIDS
DIELDRIN

RATHBUN RESERVOIR, 1978
Kst()'= 4
FIELD DATA MEAN
AND RANGE
L
J	L
1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
PARTICULATE FRACTION OF TOTAL
1.0
1 + HM
Figure B-7. Remo--J- Fraction vs. Particulate Fraction with Reaction

-------
1.0
Q
LU
> 0.8
O
>u
r
0.6
0
h-
1
0.4
0.2
METAL/
NO. RESERVOIR S.S. CHEMICAL
1 LIVINGSTONE  ~
-2 RATHBUN ~ O
3 CORALViLLE ~ , a
EQUATION (17)
Cu
Zn
1.0
TIM
1+TIM
2.0
Ksto
1 +
'3.0	4.0
Kr
KSTIM_
5.0
Figure B-8. Generalized Removal Function
4 -/r
-------
AMMONIA TOXICITY-^
Background
The discharge of ammonia to streams, influences water quality in several
ways: 1) ammonia may be oxidized by nitrifying bacteria resulting in a loss
of dissolved oxygen, 2) ammonia may be utilized as a nutrient by floating
and/or rooted aquatic plants and 3) high levels of ammonia may be directly
toxic to fish. It is this latter effect that has been a matter of increasing
concern in recent years although ammonia toxicity has been investigated for
almost 50 years. (See McKee and Wolf, 1963).
Ammonia gas is very soluble in water (.to about 100,000 mg/& @ 20C) and
dissociates in water into ammonium and hydroxyl ions. The reaction is:
NH, + H.O ^ NH, + OH ^ NH* + 0H~	CD
3 2	4	4
The ratio of the free unionized ammonia to the ammonium ion is a function
of pH and temperature. The test for ammonia nitrogen in "Standard Methods"
measures all forms of ammonia. Ruffier et al (.1981} used the following re-
lationship to calculate the % of NH^:
NH,	 
% = 100/CI + 10P a " pH)	C2)
NH,
4
where the pK^ values are temperature dependent and are given by Emerson (1975).
pK varies from 9.4 @ 20C to 9.2 @ 25C. CRecall that pCx) = -log x = log 1/x
Si
or pK = log 1/K where K is the ionization constant.) Figure 1 shows the
relationship of the % NH^ of total ammonia (NH^ + NH^ ) for various pH and
temperature levels. The effect of pH may be especially significant in water
quality studies since the range in pH may vary from 7-9 under conditions of
high photosynthesis.
Fish Toxicity Levels
High levels of unionized ammonia interfere with the ability of the
hemoglobin to combine with oxygen and the fish suffocates. Other effects
include kidney failure and neurological and cytological failure. There is
a strong interaction between low levels of oxygen and ammonia toxicity.
^Robert V. Thomann
A- 16 0

-------
The criterion most often cited is the US EPA level of 0.02 mg/i. of NH.^. This level
was based on a lethal concentration of 0.165 mg/Z to rainbow trout fry. As
pointed out by Ruffier et al (1981) this latter concentration has been more
accurately computed at 0.27 mg/Jl. The EPA criterion therefore incorporates
a factor of safety of 13.5. This factor of safety 9hould be recognized in
water quality analyses and waste load allocation studies. Indeed as summarized
by McKee and Wolf (1963), NAS/NAE (1972), EPA (1976) and Ruffier et al (1981),
the actual range of 96 hr-LC^g and threshold (infinite exposure)	concen-
trations is very large. For example, 96 hr. and threshold levels which
are appropriate for steady state water quality modeling ranges by about
one order of magnitude from 0.32 mg/Jt to 3.10 mg/Z. for 96 hr. tests and from
0.16 to 1.5 mg/i. for the threshold levels. The median threshold	level
is about 0.33 mg/&.
Water Quality Modeling Considerations
Since the percent unionized NH^ is a function of pH and temperature, an
assessment of the significance of these parameters must be made. Thus let
NH., N = NH,+ and Nm  N + N. Also let
3'	4	T
u
6 = NU/NT	Ik nB	<-3>-
u T 2 + 10 a
or "t  5 "u - Wu	<3a>
For steady state stream modeling the relevant equation .for the total NH^, N^,
is
dN
u ST - "Vt - + Vt	<>
where is the loss rate of total ammonia. Note that this	rate is a function
of nitrifying bacteria present to oxidize the ammonia (i.e.	1^) and/or uptake
of ammonia by plants (i.e. Kp). For some problems, one can obtain an estimate
of the former oxidation rate from nitrification studies and	an analysis of the
formation of nitrate nitrogen. Substituting Eq. C3a) into Eq. (4), expanding
and simplifying gives for Nu, the unionized form,


-------
Nit =, _rl _ ,N
dx lB dx V i
(5)
where the term involving 6 is the influence of longitudinally varying pH
and temperature on the percent of N^. Note that it affects the reaction
rate of the unionized form. This simply means that critical conditions
*
(i.e., maximum N^) may not necessarily be at the outfall but may be down-
stream depending on the change in pH and temperature. (In addition to the
effect of pH and temperature, the loss of NH^, a dissolved gas, due to
evaporative exchange with the atmosphere should be considered if the fraction
of NH^ becomes large.) A very simple illustration is shown in Figure 2 where
the pH is assumed to jump in discrete steps from 7-9. Maximum concentration
*
of NH^ occurs at t =10 where pH = 9. Care should therefore be taken in
properly accounting for spatial (and temporal) variations in pH Cor temper-
ature) in the computation of the unionized form of NH^.
A -\l>t

-------
REFERENCES
Emerson, et al., 1975. Aqueous ammonia equilibrium calculations: effects of
pH and temperature. Jour. Fish. Res. Bd. Can. 32:2379.
McKee, J.E. and H.W. Wolf. 1963. Water quality criteria. California State
Water Quality Control Board, Pub. No. 3-A, 548 pp.
NAS/NAE. 1972. Water quality criteria, 1972. Comm. on Water Quality Criteria,
Env. Studies Board Nat. Acad, of Sci., Nat. Acad, of Eng. Wash., D.C., 594 pp.
Ruffier, P.J., W.C. Boyle and J. Kleinschmidt. 1981. Short-term acute
bioassays to evaluate ammonia toxicity and effluent standards. Jour. WPCF,
53(3):367-377.
US Env. Prot. Agency. 1976. Quality criteria for water. Wash., D.C.
4 - '43

-------
100.0
80.0
60.0
40.0
20.0
10.0
B.O
6.0
<
z
o
4.0
<
2.0
o
UJ
M
2
O
1.0
0.8
2
3
0.6
2
lJ
o
cr
0.4
UJ
CL
0.2
0.08
0.06
0.04
0.02
0.01
0
5
10
15
20
25
30
35
TEMPERATURE (C)
Willingham, William T., 1976, Ammonia Toxcity, U.S.
Environmental Protection Agency, EPA-908/3-76-001,
iom February, 1976.
FIG. 1 PERCENTAGE OF UN-IONIZED AMMONIA IN AMMONIA-
WATER SOLUTION AT VARIOUS PH AND TEMPERATURE VALUES
4-/64

-------
(WH
u (J + m)
rJT
or
 oof
A/m-
uh-
(vjt
.!
/
10
@ rz ai-'c
r.
10 /
(o.if)
X
,s
to

*
* (J*ys)
FIG. 2 VARIATION IN UNlONIitb NH3 -Poh VARIATION th pH
4- IbST

-------
~
Toxics Concentrations in Streams
For the case of an interactive bed, where the stream bed and water column
have reached equilibrium concentrations of a chemical discharged by a point
source/tributary, and where the suspended solids concentrations in the reach
of interest are spatially constant in the water column and active bed, the
following relation applies:
CT1 . %
T1 Q
where
C_, = concentration of total toxicant in water column
T1
= original mass rate of chemical discharged into the water column
Q = longer-term average stream flow immediately downstream of the
discharge/tributary input
u = stream velocity
x 3 distance downstream of the discharge.
The term is the apparent removal rate of the total toxicant in the
stream, where:
*1 = *1 + 8 ^CK2 + fP2d'V
 m2H2fPl
and 6 =  f	(3)
r2 Cwu + Wd)fP2 + KL(VVf
d2
rl (wu + Wd?fP2 + KLfd2 + K2H2
Definitions of all symbols used are contained in Table 1.
Under the further assumptions that the stream reach is not sedimenting
(w, = 0), diffusion of the dissolved fraction of the chemical between the
d
water and bed is negligible = 01 and there are no degradation mechanisms
of the chemical in the active bed = 0), Equations 2 and 3 simplify to:
^ ^	(4)
r2 = r1	(5)
*
John A. Mueller
4-IU

-------
Thus, the distribution of the total toxicant in the water column (C^) decays
exponentially at a rate equal to the sum of the removal rates of the dissolved
It may be noted that settling and resuspension of the particulate fraction
do not contribute to the decay of the total toxicant. Since there is no sedi-
mentation and no degradation in the stream bed, net settling of the particulate
toxicant in the water column is equal to the resuspension of the particulate
fraction in the bed. Thus, there is no net flux of toxicant into, or out of,
the bed and the distribution of the chemical in the water column is not affected
by the particulate fraction with the associated suspended solids characteristics.
Wasteload Allocation Considerations
In the event of a reduction in an external load-together with a reduction
in the streamflow-the water column and bed will eventually reach new equilibrium
concentrations which are lower than those previously established. In the
interim, the bed concentrations will be more reflective of the previous loading
and long term average streamflow. Thus, an Interim analysis would consist of
calculating the water column concentrations as if the stream were subjected to
the new external loading and a flux of chemical from the bed. The latter value
is calculated as the product of the resuspension velocity and the previous
steady state bed concentration. For the previous condition of no sedimentation,
no degradation in the bed and no dissolved chemical diffusion between water col-
umn and bed, the interim value of the water column concentration is:
fraction (K^ = K^).
) (6)
where
 new loading
Q ., U = critical flow and velocity
vi -X+ nVHi
4-Ik 7

-------
'2 * P2wu/H1
u = original longer term stream velocity
Ct2() = original bed toxicant concentration at x = o
The original bed concentration at the discharge location is:
m2 ^P1 ^T1
>
where W,^ = original toxicant discharge rate
Q = longer term average streamflow
An example of the application of the preceding equations follows.
Reference
Di Toro, D.M., O'Connor, D.J., Thomann, R.V. and St. John, J.P., "Analysis
of Fate of Chemicals in Receiving Waters", HydroQual, Inc., May 1981.
4 -/6 b

-------
TABLE 1. Symbols Used in Stream Equations for Toxics

Symbol
Description
Unit
<1
apparent removal rate of total toxicant in water
column
1/T
*1
decay rate of chemical in water column, including
hydrolysis, photolysis, oxidation, biodegradation,
volatilization
1/T
K2
decay rate of total toxicant in the bed
1/T
L
diffusion rate of dissolved chemical between
water and bed
L/T
CTi CT2 .
V m2
total toxicant concentration
solids concentrations
M/L3
M/L3
rl' r2
particulate toxicant concentration, r  fpC^,/m
MCtox)/MCsol)
Hr H2
depth of water, thickness of active bed
L
Ws' V Wd
settling, resuspension, sedimentation velocities
L/T
V 112
partition coefficients
l3/m
fdl' fd2
dissolved fraction, f, = (1 + irm) ^
a
-
fPl* fP2
particulate fraction, fp  inn/(l + inn)
-
Note: Subscripts 1  water column, 2 - active bed
4-H-1

-------
STREAM TOXICANT DUTRlQ O.TION S IN WATER t BEb
0 ^	
%
>ATA
stream - depth
bed tnicrrntaj
	-plow - a. ve iS
-	des'i^h
-	velocity- - o^ver^ge
	desijh
suspended Sol ids
co n ce ntrec"t ion  wafcet* column
 bed
settling ve-focity
se velocity
chetaicQL 1
.tino.3S discharge rate - present
-	d es h
decay iroCte  wojt&r* column
- bed
pant it" i on coeff.  wa>t %tr
-	\>el
Hi
H,
9-
Qc
U
Uc
toi
bi^
Ms
Wti
V/ra
k.
Vr^
1T,
Hi.
l.o m
0.01	m
I o o of s
I o cfs
1.G4	the/day
0.1 C4 tm./tfUy
I 0 fi-
10 000 Chj /I
0.2?3 m/day
0.0 him/yh
I 00 0 M-/d"t efihin bed >.) = (| oooo x iooookk-1 )/(l + ld0#x'xirt) |oo/io| =t o.9<0
Kt = h\
*  I jday
a/7
^ = fpa	= O.HOx y.3xio~yi.o=
A/J = +fp, Ay-yH| =: 0.1+ 0. oiol x 0.^3/1.0= 0.175"*/Jay
4 -/7d

-------
A. PRESENT LOAblNG
Yr
For Average Flc^ of loo ells
CTI = CtiCO P-"tVu= I 000 U/U,	|,tS
100 cfi a 5^4-
f \ -^tVu
= Cra(o) 0
Cra(o)= bu _pi_ cr/(
-------
cT; u.s e^""* +~0.s4.+T (e-'0"4'"<-
A.S	i. 	a-pte-*- irhilepomt" S f "the be<
Is the 5o le joiuce of the waXef c- Ium ccnctf-ntr*,tion,f. At
Vhilepoint Z. "the bedl. effe. Li &." a.	j otnt^i tM/tin^
O.Q70	t"0 "kho w<^t ei coIkij,
B. RE^tLCet loa&inc- IM1TIAL Bg> conc.
QowghJ
U.hti I cu *he*X bed e-^uil i b h w,h c.onChcs\t no.tr ionJ wi 1/ be c/echeasi'nj -prom the/*	,
For trhe "ttrio* period j cl conjej-KR-trive estlih^te o"P w^te-r*
c^|w.*nh c0nc^jft>>t}
CT1 = Wjx e'^^t V
= *ioo e"'""v'''VL2MJ^_(i9o)fe"''Vu*. e-WOT*"')
I00X5-.1-	o.75>-O.lxCl) 'V	J
_	^ , _ -O./Olcx ,  / -O.OtCJTx o. IOTO X \
cT| =o.ifsTe + i.ssle	-e	)
^   	1	-y- -  1 1   - ^
Cti (w.c.)	C-ri(Beb)
As seen in Fij 2 the conceh"ti>.tioh ih "He- w*.ter co/a** \t
"the on.t"foJI is ho** Q.\tSi*y/L } ft* orde-t-  P ihajhit*J? lower /*
fp',5 ' c)* H^v^eref-j "the concent melons beyond toilejemt 12. a.re
greater "tnah	7c o " "c^e ot-ijin*// va/uas due- to "tAc be< .
FLow o"F |0 cP-S
CTI = Wri. e"^Vc + 	,i5_ c(0) /s-^/u.
9c	wr-hr(Vtl) v	'
lO*S>	0.11510.1(^41)^	;
-I.OTox	/ O.OC091X -1.070 *\
=s I.jje + 0. ?4-5(e	- e	)
Ft*is kF^ 1c j mtt/h wo/tei* coltmn conceitr*tTion Cjiftt TC-sOj a
-------
C.REEmcgfr 10AD-PINAL BSE CQdC.	%
A-Pteh C3L 5	tim- Itoi eUfscvf "te af/o* tfrj c.oncen6xtio*j
"tc come- "to tfce lov^er e-jujlifcn** v^fuej "tlie ollo*inj o.fphe-r.
A-Vef^fr Elcw of loo cfi
CT|(o)= IOo/(loo*J,+) = O.HS *.)/!
Ct,  o.us e-0-lx/,'"=	(.Se. F,j3k.)
(o)|=	rT1(ft)  >0000 x o.ow w q.ijs' = I
Inev n, ; fpi.	10 o.Sio
^	 0.06011X	1
Cto. H e	; as shown i h Ftj 3 R Qc = I a cfj
CONlHTtoH
PRSSeMT
! INTERIM
FINA L
LOADING
I 000
I 00
loo
1 MAXIM
UM Concentration (*ti/i)
A-CTIVC
Rel*
1 water! columa/
LOAb-tN bucaD
Bei~(Ai)u.ceD
1 "70
no
11
lfr.5"
I.S"^
1.55-
0 .Q>1
O.GT
0.0C7
4 -/73

-------
X
0
h
A
ui
C9
1
c<
h
o>
e
h
u
I
z
5
*
j
o
O
c
03
h
<

"J
u
z
O
U

x
o
H

150
100
50



is)


W= 1000 Ibt /day



Q: 100 cfs


1 1 1 1 1 1
: 1 1 1 1 1
I
W= 1000 lbs /day
Q= 100 cfs
BOTTOM SEDIMENT EFFECT
ia.n
W= 1000 Ibs/day
0=10 cf*
80TT0M SEDIMENT EFFECT

6 8  10 12 14 16 18 20 22 24
RIVER MILE BELOW DISCHARGE
FIGURE 1
EXAMPLE RIVER SEDIMENT AND WATER COLUMN CONCENTRATION PROFILES FOR
ORIGINAL LOAD
4-/74

-------
WT
*
U
I
X
o
Hi
ID
o>

200
150
100


to

INITIAL SEDIMENT

w= 1000 lbs/day


0= 100 cf


1 1 I 1 1 1 1 1 1 1 1
1
10 12 14 16 18 20 22 24 26
h
u
{
5
ec
at
h
<
.
Z
o
0
X
o
2.0
1.5
1.0
0.5
0
BOTTOM SEDIMENT EFFECT
lL
INITIAL SEOIMENT
W = 100 lbs/day
0= 100 Cfs
10
12 14
!
12.21
16
INITIAL SEOIMENT
W= 100 lbs/day
0= lOcfs
to
18 20 22 24 26
BOTTOM SEDIMENT EFFECT
4 6 8 10 12 14 16 18 20 22 24 26
RIVER MILE BELOW DISCHARGE
G..M*
FIGURE 2
INTERIM RIVER SEDIMENT AND WATER COLUMN CONCENTRATION PROFILES FOR
REDUCED LOAD
4-/75*

-------
%
Wt
t*

h

u

1!

N
X
CP
o
E


a
111

A

200
ISO
100
50
0


(*)

REDUCED SEDIMENT

w- 100 lbs/day


0 - 100 cfs

1'
	1	:	1	1	1					

10
12
14 16 18 20 22 24 26
h
0
1
z
5
3
j
hi
I-
<
u.
z
o
0
x
o
h
er>
.
2.0
1.3
1.0
0.5
0
2.0
1.5
1.0
0.5
0
REDUCED SEDIMENT
W= 100 lbs/day
Q - 100 cfs
REDUCED SEDIMENT
W- 100 lbs /day
Q i 10 cfs
BOTTOM SEDIMENT EFFECT
W
10 12 14 16 18 20 22 24 2b
(?)
2 4 6 8 10 12 14 16 18 20 22 24 26
RIVER MILE BELOW DISCHARGE
FIGURE 3
FINAL RIVER SEDIMENT AND WATER COLUMN CONCENTRATION PROFILES FOR REDUCED
LOAD
4-176

-------
TOXICS CONCENTRAT/ONJ IN LAfreS
T>ATA
Va
^10 OOO *Chj
V1> T - ll-y^/JL
Pftsticittc
A"t htt.2 i oe-
DDT
Mvdrolvsu
0.1 /eky
2.5"* lO'Ytly
PKcfo lytic
O.Ol/eU^
Vo I tt 11 j a- a."toh^
Biocf^KJa'tion
AsSkhx*
ft
.filAl
M.l/1
5"0
3"0 OOO
AS5k>n\a <*. jt:e5"33 cFj  J" 3 cfj
C+o acro/^-x ' ^ -
. R^off- foe* HT o^muje  q)6 = (.SOOOo/feto) X 0. 533 = 4-1.7 cfj
La H& O iv/fc -plow (^) = r  8.3^4-1. *"? 51 5~D- 0 cFj-
8 fw. 3
IfydratJic Decent i0^ Ti >,<. to =	4-. 3lx to8 ft
9 >50 x ^c+oo yicy
*J-04N A MUELLER
-f- /77

-------
 s t~lmcL.tr e Jvct	Solids Ne Se-'ttlnTy Rote	r^j
to = w/q
i + Ks t.
loo hvj/JJ. = ( I. 3fx lo' JUr/ji*y) / f J-D.O cfe X5.+)
I +" Ks (| 00 days)
K5 = */?/h = 0.5"OI /doy
= hj H = O.^l/^v x fft  l.o PtAUy
^t 11< (*/fcc Attoting Cone- i h Ukg
WATR = Uj = o. i +.o.oz= o. iz/<*y
CT =: n^t.X / f SD.O *-5:4-)
1 .SP.O	_ 0.007S >W ^.SW,
j +LL2( o. 11+- O.oas-x 0.5^	=====
1+-0.0O5 V	/
Note : C)K, CT/(I~ 7.^/(11-o.0os) = 7.5"/|. 00.5" ~ 0.0 4-j*j/L
91.57, Oi3i.
0.5"?. MRT
Estirvnct: DOT Leu.Ite C.onc?ht^"t5" Mrj^y
*  sToooo x loo / 1 o fe = 3" J Ks = o.s^/JLay
Kc. - 1.5x o~* + i.j"x io~* = 4-.o*io~f^ o.ooo^/ot^
cT '	r =o.ooo^ Ye= a/9i
I-*- |	fo. ooo^- -h.s-x o^st> J	==
Note-, C>tu = o.in/(\+s) ==	o.o\s/^/JL
Cp^t." O'T-1 X <5"/(l+5) 
I Q.H 70 Dusot^eb
"3.3 ?, PART/CKu^re
- - 	 	1
4-17?

-------
EXAMPLE WASTE LOAD ALLOCATION ANALYSIS*
The following waste load allocation analysis Is designed to provide an
example which is reasonably realistic but not so complex that it detracts
from the example's principal intent, which is to:
	demonstrate the major steps in a waste load allocation
analysis,
	show how the mathematical equations
a?e applied, and
	present the relationship between water quality impacts and
the overall task of performing a waste load allocation.
Because the purpose of this example is to present an overview of the steps
required for a waste load allocation, emphasis is not placed on providing
details on data requirements and calibration-validation procedures. These
technical aspects are discussed more thoroughly in other sections of the
manual.
Problem Setting. In this example, a city of approximately 60,000 people
discharges its wastewater into a relatively small river with an average an-
nual flow of about 250 cfs. The city's wastewater is presently treated by a
trickling filter plant which provides about 851 BOD removal and has reached
its design capacity of 7.5 MGD. The population is projected to increase by
more than 50Z to 92,000 people (with a range of 75,000 to 120,000 people) by
the year 2000. Expansion of the treatment plant to a capacity of 11.5 MGD and
provision of an activated sludge system for more efficient secondary treatment
are proposed.
The river, for thirty miles downstream of the treatment plant discharge,
.is classified as B1 which has a designated water use for fish and wildlife
Extracted from (with modification):
"Technical Guidance Manual for Performing Waste Load Allocations"; E.D. Driscoll,
J.L. Mancini and P.A. Mangarella; for US EPA, Office of Water Regulations &
Standards, Monitoring Branch, J.R. Pawlow, Proj. Off., Jan. 1981.
* 5-1

-------
propagation. The pertinent water quality standards for this example are a
minimum dissolved oxygen level of 5.0 mg/1 and a maximum un-ionized ammonia
concentration of 0.02 mg/1. The river is used locally for fishing and is
bordered by several campgrounds and a state park. No water quality problems
are documented, and the limited water quality data do not show any standards
violations. A summary of the problem setting and treatment plant data is
presented in Figures 2-11 and 2-12.
River Characteristics. The river flow is gauged by the USGS immediately
upstream of the treatment plant discharge. The average monthly flows for a
thirty-year period are summarized in Figure 2-13. The average annual flow
is about 250 cfs with a minimum monthly average low flow of 100 cfs which
occurs in the summer. However, minimum dissolved oxygen standards must be
met for a minimum seven-consecutive-day flow with a return period of once
every 10 years (7Q10)* From a statistical analysis of the flow records, the
7Q1Q is determined to be 30 cfs.
Critical conditions of dissolved oxygen and un-ionized ammonia concen-
tration in the river occur during the summer when the flow is low and the
river temperature is high. From eleven years of river temperature data collec-
ted as part of a limited river monitoring program by treatment plant person-
nel, the maximum average monthly river temperature is 27C and occurs in August.
Therefore, design critical river conditions for water quality impact analyses
are a river flow of 30 cfs and a river temperature of 27C.
For this example, assume that three surveys have been conducted which
measured stream cross-sectional area under different flow regimes. Cross-
sections were measured at 20 locations within the 30-mile study area.
5-2

-------
From cross-sectional area measurements, it is concluded that the river is
relatively uniform in the study area and, therefore, one average cross-
sectional area and length can characterize the study area for each flow
condition. If the river cross-sectional area varied significantly with dis-
tance, the river would have been divided into smaller reaches, each of which
would have approximately uniform geometry for each prevailing flow condition.
Dye study techniques provide an alternative means of accurately determining
average velocity for a given river section.
The average river velocity during each of the cross-sectional area
survey periods was computed by. applicaton of the continuity equation
VELOCITY  FLOW/AREA. The average flow for each survey period was obtained
from USGS records.
River cross-sectional area, depth and velocity generally form linear
correlations with flow when the data are plotted on log-log scales. Figure
2-13 presents these log-log plots for the example problem. Interpolations and
extrapolations of river geometry and velocity at specific flows can be made
directly from the log-log plots or computed from the equation of the line
of best fit. The equation for the line of best fit has the form: Y  IQS,
where I is the intercept at Q - 1 cfs and s is the slope scaled directly
from the plot-(inches/inch). As shown in Figure 2-13, these log-log rela-
tionships are summarized as follows:
AREA (ft2) - 19.5 Q (cfs)0,6	(2-21)
DEPTH (ft) - 0.312 Q (cfs)0,5	(2-22)
VELOCITY (fps) - 0.0513 Q (cfs)0,4	(2-23)
Using the above equations, river area, depth and velocity can be computed
for any river flow. If river geometry data are available at only one flow
5-3

-------
regime, the relationship presented in the ADDENDUM (equations 2-3, 2-4, and
2-5) would be used to calculate river depth, area, and velocity at other flows.
Review of River Water Quality Data. Historical river water quality data
within, the study area are limited. As part of the state environmental
department's overall monitoring program for this river basin, water samples
are periodically collected at stations located at river milepoints 11 and
25. These data represent approximately one grab sample per month during the
summer over a five-year period. A review of these data does not reveal any
water quality problems with regard to dissolved oxygen and un-ionized ammonia.
Because there is no evidence of a water quality problem, only secondary
treatment at the expanded plant has been proposed. No additional funds for
Advanced Secondary Treatment (AST) or Advanced Wastewater Treatment (AWT)
have been proposed.
Considering the relatively good water quality, an appropriate level of
effort for a waste load allocation (WLA) study initially can be limited to
the analysis of a single river water quality data set collected during stun-
ner low flow conditions. Accordingly, a survey was conducted during two
days in August when the river flow averaged 100 cfs and the river water tem-
perature was 25C. The results of this survey are presented in Figures 2-14
and 2-15.
The dissolved oxygen data in Figure 2-14, both August 1979 data and
historical data, show river dissolved oxygen levels above the standard of
5.0 mg/1. The increase in river BOD^ and ammonia concentrations at milepoint
1.0 show the impact of the treatment plant discharge. The gradually decreasing
ammonia profile and increasing nitrite .plus nitrate profile suggest that nitri-
fication is occurring in the river.
5-4

-------
Un-ionized ammonia, which is toxic to biological life, is dependent on
the total river ammonia concentration, river pH, and river temperature. The
higher the river pH and temperature, the higher the percentage of total
ammonia that is in the un-ionized form. Figure 2-15 presents the measured
total river ammonia concentration. The un-ionized ammonia concentration is
determined from the relationship summarized in Figure 2-16, which relates
un-ionized ammonia to pH and temperature. For a river temperature of 25C
and a pH of 7.2 (point A), un-ionized ammonia is 0.9 percent of the total
ammonia concentration. During the August 1979 survey, the river un-ionized
ammonia concentration was less than the standard of 0.02 mg/1.
Model Calibration Analysis. For this analysis, model calibration is the de-
s
termination of the coefficients (reaction rates) of the equations
chat describe the
spatial distribution of BOD, ammonia, nitrite plus nitrate, and dissolved
oxygen. The equations for each of these constituents are summarized as fol-
lows:
bod5
L5 " ^o  ~"r *	(2-24)
Ammonia (as N)
-K
NH3 ~ (NH3)Q  U	(2-25)
Nitrite plus Nitrate (as N)	(2-26)
,-K
(N02 + N03) - (NO2 + N03)o + [(NH3)o (l -	X)J
5-5

-------
Dissolved Oxygen Deficit
-K
Kd Lo
Ka "Kr
-K.
U
K_N
n o
Ka _Kn
a n
-K.
-e
-K..
-e
-K.
+ D0 e
(2-27)
In all these equations, the variables with the zero subscript are the con-
centrations at x = 0 (after integrating the upstream concentration and the
treatment plant load). U is river velocity and Ky, K^, Kn, and Ka are the BOD
removal rate coefficient, BOD oxidation rate, nitrification rate, and
atmospheric reaeration rate coefficients, respectively. LQ and NQ represent
(respectively) the ultimate carbonaceous BOD and nitrogenous BOD at x  0, and
Dq is the initial oxygen deficit at x  0.
Note that the oxidation of ammonia (as expressed by equation 2-25) is
analogous to the oxidation of BOD. Whereas, the oxidation of carbonaceous BOD
produces carbon dioxide as the end product, the end product of ammonia oxidation
is nitrite plus nitrate. Thus, the equation for nitrite plus nitrate states
that the nitrite plus nitrate in the river is equal to the concentration at
x = 0 plus the amount gained from ammonia oxidation. When all forms of nitrogen
are expressed as N, the terms in equation 2-26 are directly additive.
The coefficients in equations 2-24 through 2-27 are determined by the
following steps. The river velocity is calculated for the August 23-24,
1979 river flow using equation 2-23. The initial conditions (x - 0) are
determined from a mass balance with the upstream concentration and the plant
load. The BOD removal coefficient (Kf) is the value of Kr that provides the
5-6

-------
best fit of the August 1979 BOD data with equation 2-24; for secondary
effluents Kd - Kr (no settling). The nitrification rate (Kn) is the value
of that simultaneously yields the best fit of both the ammonia and
nitrite plus nitrate data with equations 2-25 and 2-26 respectively. The
atmospheric reaeration rate is determined in accordance with Figure 2-6
In addition, long-term BOD tests have been performed and indi-
cate the ratio of ultimate to 5-day BOD to be 2:0. A summary of these
calculations is shown in Table 2-2, and the calibration results are presented
in Figure 2-17.
In this example, the calculation of the dissolved oxygen profile agrees
with the measured data quite favorably and without any adjustments. Often
the calculated dissolved oxygen profile does not initially agree with the
data due to other sources and sinks of oxygen, such as nonpoint source loads,
algal photosynthesis and respiration, and benthal oxygen demands. For the
sake of simplicity, these complications have been omitted.
Model Projections. Having calibrated a model for BOD, DO, and nitrogen,
i.e., defining site-specific coefficients and accepting that some reserva-
tions on reliability exist because the model was not tested against an inde-
pendent data set, the model may be used to project water quality impacts
that might be expected under conditions of interest. Two specific cases
of interest are the water quality Impacts of existing wastewater loads and
for future design wastewater loads for the minimum river flow (7Q10) of 30
cfs. Dissolved oxygen, ammonia, and un-ionized ammonia profiles are presen-
ted for both cases in Figures 2-18 and 2-19. The model calculations for the
design load condition are shown in Table 2-3.
5-7

-------
The calculated profiles in Figure 2-18 show that present wastewater
loads would result in dissolved oxygen and un-ionized ammonia water quality
standards violations over approximately ten miles of river, if design drought
flow conditions were to occur (7Q 20	anc* a river temperature of 27C).
The lowest daily average dissolved oxygen concentration is about 3.0 mg/1,
and the highest daily average un-ionized ammonia is twice the standard of 0.02
mg/1. At 27"C and with a pH of 7.2, un-ionized ammonia is 1 percent of the
total ammonia concentration (point B - Figure 2-16).
Note that for the example, both the critical low flow (7Q10) an^ the
maximum average monthly temperature have been used in the projection, even
though historical records (summarized in Figure 2-13) show minimum average
monthly flow and temperature to occur in different months. This tacitly
assumes that although the minimum average monthly flow occurs in September,
the critical 7Q10 could occur in August, the month of maximum average temp-
eratures. In areas where it can be shown that the 7Q10	occur in a
month with lower temperature, then- the appropriate combination should be
used rather than each of the extreme values. For example, critical low
flows frequently occur during October in the northeast. An appropriate
approach in such cases would be to define the 7Q1Q and temperature condition
for each of the critical months (say June-October), determine which month is
most critical, and use that month in WLA calculations.
Calculated dissolved oxygen and un-ionized ammonia profiles for 7Q jo
flow conditions and the design wastewater load are presented in Figure 2-19.
For the design load, the carbonaceous BOD is only slightly greater than the
present load, but the ammonia and nitrogenous BOD loads are about 50% greater
than present loads (see Figure 2-12). The minimum dissolved oxygen is about
2.6 mg/1, and the maximum un-ionized ammonia about 0.06 mg/1.
5-8

-------
The projected dissolved oxygen and un-ionized ammonia profiles in Fig-
ures 2-18 and 2-19 indicate that whether or not the treatment plant expands
from 7.5 MGD to 11.5 MGD, some reduction of wastewater BOD (carbonaceous
and/or nitrogenous) and ammonia is required to meet water quality standards
during critical low flow conditions. One method of computing the required
reduction in wastewater BOD and ammonia is to calculate a series of dissolved
oxygen and un-ionized ammonia profiles and, through trial and error, arrive
at the proper combination of wastewater load reductions that meets water
quality standards. An alternative to the trial and error method for dis-
solved oxygen is to separately calculate the dissolved oxygen deficit due
to each BOD source (upstream BOD, plant carbonaceous BOD, plant nitrogenous
BOD). This has been done for the design wastewater load case and is shown
in Figure 2-20.
The top profile is the calculated dissolved oxygen distribution in
which the lowest daily average dissolved oxygen concentration of 2.9 mg/1.
(maximum deficit of 5.1 mg/1) occurs at milepoint 4. The next three profiles
are the components of the total .dissolved oxygen deficit produced individually
by the oxidation of ujpstrean BOD, treatment plant carbonaceous BOD, and treat-
ment plant nitrogenous BOD, respectively. On each deficit profile, the deficit
produced at the critical point in the river, milepoint A, is indicated. Note
that the deficits of the component parts at milepoint 4 add up to the total
deficit of 5.1 mg/1. Inspection of equation 227 shows that the carbonaceous
and nitrogenous deficits are additive. The upstream BOD may be considered
as a fraction of the total carbonaceous BOD in the river and thus separable
from the plant carbonaceous BOD.
Knowing the relative contribution of each BOD source to the total def-
icit, it is an easy task to select combinations of wastewater BOD reductions
j-y

-------
that will achieve water quality standards. At 27C, dissolved oxygen satura-
tion is 8.0 mg/1; therefore, for a dissolved oxygen standard of 5.0 mg/1,
the allowable maximum deficit is 3.0 mg/1. Assuming that the upstream BOD
deficit of 0.2 mg/1 is uncontrollable, 2.8 mg/1 of deficit would be available
for the total of carbonaceous and nitrogenous plant BOD oxidation. Consid-
ering the un-ionized ammonia standard and the economics of nitrification
versus advanced carbonaceous BOD removal suggests that providing nitrifica-
tion facilities for the expanded treatment plant is a cost-effective step
towards achieving water quality standards. Assuming that nitrifictation
remuves 90% of the ammonia (i.e., nitrogenous BOD) the un-ionized ammonia
standard would be met and the nitrogenous BOD deficit would be reduced to
0.2 mg/1, yielding a total deficit of 3.1 mg/1 (DO of 4.9 mg/1) at milepoint 4.
Although calculations show that nitrification and standard secondary
treatment for the design plant flow of 11.5 MGD will not meet dissolved
oxygen standards, the waste load allocation analysis should not be carried
any further with currently available information. Before the model is used
to calculate the additional carbonaceous BOD removal beyond secondary treat-
ment that may be required, some additional steps should be taken. First,
the model should be calibrated and validated against one or' two more data
sets to check the model coefficients under different flow regimes, especially
lower flows than the first survey, if possible. A sensitivity analysis
should be performed to relate the cost of required wastewater treatment to
cianges in population estimates. For example, if the population in the
year 2000 is 75,000 people (projected minimum), will additional carbonaceous
BOD treatment be required? A sensitivity analysis of the effect of different
reserve policies on required treatment should also be performed. For example,
what is the increase in wastewater treatment costs if the dissolved, oxygen
5-10

-------
reserved for future development is set at 0.5 mg/1 versus 0.25 mg/1?
It is clear from these questions that a final waste load allocation
should be the result of more than a model projection. Such a decision
takes many factors into consideration, one of which is the impact of
a design wastewater load on water quality.

-------
TABLE 2-2. CALIBRATION ANALYSIS
STP


9
River Temperature  25#C
100 CFS	- // A	 ~ Q * 111.6 CFS
~~/f GAGE
UPSTREAM CONDITIONS	PLANT EFFLUENT
 BOOg  1.0 mg/S	Q - 7.5 MGD (11.6 CFS)
NH3 (N)  0.2 mg/B	BOOg - 40 mg/2 (2502 lb/day)
DO - 8.2 mg/2 (SAT.)	NHj(N) - 15 mg/{ (938 lb/day)
DO - 8.2 mg/8 (SAT.)
A.	DETERMINATION OF RIVER DEPTH AND VELOCITY
(from equations in Figure 2-13)
Depth  0.312 Qos - 0.312 (111.6)0'5 - 3.3 ft.
Velocity - 0.0513 Q0'4 - 0.0513 (111.6jP'4 - 0.34 ft/sec. (5.6 mi./day)
B.	DETERMINATION OF REACTION RATES
1.	Reaeration (from Figure 2-6 or Ka" 13 U^/H3^ I
Ka - 13 (0.34)V4/(3.3)lA - 1.26/day at 20 C
Ka at 25aC -U6x 1.024s - 1,42/day
2.	BOD Removal and Oxidation Rates (from fit of river BOD data)*
Kr - K5-.4- i- 2.0*01]/^ M.t ao.4)s S\ OS'
Ultimate C800 (Lo) - 2 x BODj - 2 x 5.
-------
TABLE 2-3 PROJECTION ANALYSIS (design load)
STP
Q -30 CFS
 // *
// GAGE

 Q - 47.8 CPS
River Temperature  27#C
UPSTREAM CONDITIONS
BODj-I.Omg/8
NH3(N)-0J mg/C
DO - 8.0 mg/S (SAT.)
PLANT EFFLUENT
Q- 11.5 MGO (17.8 CFS)
BOD5 - 30 mg/8 (2877 lb/day)
NH3(N) - 15 mg/8 (1439 lb/day)
DO - 8.0 mg/8 (SAT.)
A.	DETERMINATION OF RIVER DEPTH AND VELOCITY
(from equations in Figure 2-13)
Depth - 0.312 Q0 5 - 0.312 (47.8)05 - 2.2 ft.
Velocity - 0.0513 Q0 4 - 0.0513 (47.8)0'4 - 0.24 ft7iee. (3.9 mi./day)
B.	DETERMINATION OF REACTION RATES
1.	R(aeration (from Figure 2-6 or Ka  13 u'^/H^ )
Ka  13 (0.24)%/(2.2),A - 1.95/day at 20'C
KB at 27"C - 1.95 x 1.0247  2.30/day
2.	BOD Removal and Oxidation Rates (from Calibration Analysis)
Kr and 5-.4.)= II. S tha/l
Ultimate C8O0 (Lo) - 2 x BOD5 2 x LL&_aL.a3.C,"myfi
NHj-N (x - 0) - [o.ax30*Jr."4 i-I43
-------
'	U-67
100.0
^Ln 8 t
"	C/7> ^
* ***. c^
''9Urz
<*-e
4t?"oo

"*.	'>l

'"'l
r#
0eoO>*,
^cr^r
**3^
^i4

-------
A. STUDY AREA
STP
CITY:
River Flow
25
Highway 64 ".
USGS
Gage
RIVER MILEPOINT
B. POPULATION PROJECTIONS
150-
Maximum (120)
100-
Design (92)
Minimum (75)
Present (60) ^
50-
T
T
1900 1920 1940 1960 1980 2000 2020
YEAR
C. RIVER CLASSIFICATION AND USE
1.	State ClassificationB1
2.	Designated- UseFish and Wildlife Propogation
3.	Water Quality Standards (partial)
a.	DO ConcentrationGreater than 5.0 mg/S
b.	Un-ionized Ammonia-Less than 0.02 mg/
4.	Activities and Use
a.	Active and Locally Popular Fishery
b.	Several Campgrounds and State Park Have River
as an Attraction
5.	Problems
No Documented Problems; Limited Water &jality
Data Do Not Show Violations
Figure 2-11. Problem setting.
5-15

-------
A.	TREATMENT FACILITIES
Present: Trickling Filter Plant Constructed in 1958
Plant Now at Design Capacity of 7.5 MGD
Effluent Does Not Meet NPDES Permit for
Secondary Treatment
Proposed: Activated Sludge System to Provide Efficient
Secondary Treatment
B.	EFFLUENT CHARACTERISTICS

Present
Design
Flow
MGD
7.5
11.5
BODs
mg/S
lb/day
40
2502
30
2877
CBODu
mg/8
lb/day
80
5004
60
5754
NH3-N
mg/8
lb/day
15
938
15
1439
NBOD **
mg/8
lb/day
68
4221
68
6475
 Preliminary Basis-Standard Secondary Treatment
 Long-term BOD Tests Indicate Ratio of CBODu/BODs" 2.0
(D NBOD" Stoichiometric Oxygen Requirements for Oxidation
of Reduced Nitrogen Forms-4.57 x NH3-N
(effluent oxidizable organic nitrogen is negligible)
Figure 2-12. Treatment facilities and effluent characteristics.
5-16

-------
A. RIVER FLOW
500
400
300
200
100-
0
Plow at Rt.64 Gaga
(1949-1979)
B. RIVER TEMPERATURE
50
J FMAMJ J ASONO
40-
K 30-
| 20-
UJ
a.
2 10 H
Temperature
(1968-1979)
Ldl
th
J FMAMJ J ASOND
C. RIVER GEOMETRY
Area9 19.5Q
1000-

mmii
50 100 200
FLOW (CFS)
500
Depth- 0.31200-5
20.0 -
10.0-
i i i i i iii	1 i i
50 100 200 500
FLOW (CFS)
D. RIVER VELOCITY
2.0 -
>
h-
CJ
o
Velocity "0.0513 Q
I l
50 100 200 500
FLOW (CFS)
Figure 2-13. River flow, temperature, geometry, and velocity.
5-17

-------
- 10-
Augutt 23-24. 1979
Saturation
turation	t
  I
	t		Standard	_	
I
State Environmental
Deosrtment Data (19491979)
Flow at Rt.64 Bridge* 100 CFS
T emperatu n " 25 C
-r-
0
10
-1
15
i
20
-1
25
30
STP Discharge at x  0
MILEPOINT
10	15
MILEPOINT
MILEPOINT
10	15
MILEPOINT
Figure 2-14. Dissolved oxygen, BOD, and nitrogen data
(August 23-24, 1979).
5-18

-------
o
e
z
<
z
o
5
5
<
5
4
3
2H
1
0
August 23-24, 1979
i
10
15
MILEPOINT
	T
20
	T	
25
30
Z
a
c*
"3b
E
Q o
H |
3
< *
u z
o
z
3
0.05
0.04
0.03
0.02
0.01
0
MILEPOINT
p
Average Temperature  25 C
Average pH  7.8
Standard


 ' .





10	15
MILEPOINT
20
25
30
Figure 2-15. Ammonia, pH, and un-ionized ammonia data.
5-19

-------
100.0
0	5	tO	15	20	25	30	35
TEMPERATURE (C)
Not*: Redrawn from
William T. Willlngham
Ammonia Toxicity
USEPA 908/3-76-001
Feb. 1976 (4)
Figure 2-16. Percentage of unionized ammonia in
ammonia-water solution at various pH
and temperature values.
5-20

-------
Saturation  8.2
Standard
Flov  Rt.64 Bridge '
Tamperature  25C
100 CFS
-r
10
15
MILEPOINT
20
25
30
6-
r
o
o
o
5
10
15
20
25
0
30
MILEPOINT
2-
r>
Z
5
0
10
15
20
25
30
MILEPOINT
3-
MILEPOINT
Figure 2-17. Model calibration analysis.
5-21

-------
2-
Flow at Rt.64 Bridge-30 CFS
T omperture 27C
	1	
15
MILEPOINT
~~i
25
10
20
30
MILEPOINT
Temperature  27*C
pH  7.2
Un-ionized Ammonia
1% Ammonia Concsntretion
Z
3
Standard
MILEPOINT
Figure 2-18. Projected dissolved oxygen, ammonia, and
un-ionized ammonia (present wastewater load).
5-22

-------
10-
Saturation
Standard
4-
Flow at Rt. 64 Bridge"30 CF.S
Tempe ratu r  2 7 C
MHLEPOINT
MILEPOINT


b.
0.10
<
z
0.08-
o

2
0.06-
2

<
0.04-
o

N
0.02-
Z

o
0
z

'3

Temperature - 27*C
pH - 7.2
Un-ionized Ammonia  1* Ammonia Concentration
Standard
MILEPOINT
Figure 2-19. Projected dissolved oxygen, ammonia, and
un-ionized ammonia (design wastewater load).
5-23

-------
Saturation

O

a*



Q
V *
E



\J


Flow at Rt.64 Bridge*30 CFS
Temperature  27C
10	15
MILEPOINT
i
20
25
30
Upstream BOD
0.2
i
10
i
15
MILEPOINT
BOOg - 1.0 mg/2
~T
20
I
25
30
Treatment Plant Carbonaceous BOD


Plant Q- 11.5 MGD
2-.T
EFP. BOD5 - 30 mg/e
10	15
MILEPOINT
20
25
30
Treatment Plant Nitrogenous BOD


Plant O - 11.5 MGD

NHj- N - 15 mq/8
2.2

10	15
MILEPOINT
25
Figure 2-20. Dissolved oxygen component unit responses.
5-24

-------
ADDENDUM
Variations in River Velocity, Depth, Area with Flow
Projections of water quality impacts for some future critical low-flow
condition are normally required in waste load allocation studies. The
predominant impact of reduced stream flow is usually to reduce dilution
provided, for the waste load. Thus initial concentrations of BOD (LQ) become
significantly higher. However, reduced stream flows also result in changes in
stream velocity and depthfactors which both strongly affect the reaeration
rate coefficient. Therefore, the effect of stream flow changes on depth and
velocity must be determined.
In some cases stream cross-sectional measurements and time of passage
(travel time) information will be available from studies performed by USGS
or state environmental agencies. In addition, data may be available from
the Corps of Engineers in locations where projects have been designed.
Time of passage data can be used to compute averages of velocity (U) and
depth (H). Each set of data will be related to a specific stream flow regime,
and different values can be expected for other flow regimes. In seeking infor-
mation on depth/velocity relationships in a stream reach, it is important to
distinguish between time of travel study data and information which might be
derived from USGS flow gaging stations. Gaging stations are usually located
5-25

-------
at places where Che geometry favors the accurate determination of flow rate,
and as a result, depth and velocity at such locations are not typical of
general stream conditions.
Leopold and Maddox have suggested the following empirical relationship
bgtveen the pertinent physical stream factors and stream flow.
U - aQn	(2-3)
H - bQm	(2-4)
W - cQ*	(2-5)
where:
a, b, c are constants for the stream in question
m, n, f are exponents defining the basic relationships
Recognizing that stream flow is the product of cross-sectional area and
velocity (Q  A f U), and that cross-sectional area is the product of width and
depth (A  W f H), it can be shown that the sum of the exponents (m+n+f) is
1. Using this and experience from a variety of streams, the value of the
exponents can be approximated as follows:
n  range (0.4 - 0.6); typical 0.5
'm = range (0.3 - 0.5); typical 0.4
f  range (0 - 0.2); typical 0.1
Where the analyst has more than one set of data, a log-log plot of area (A),
depth (H) and velocity (U) against stream flow (Q) will permit extrapolation
to other flows of interest. The slope of such plots provides the local value
of the exponents. When data at only a single flow regime_ is available,
5-26

-------
estimates for other flows of interest can be developed by the following ratios,
derived from the foregoing relationships:
velocity : U2/U j - (Q2/Ql)"5	<2_6)
depth	: H2/H1 - (Q^Qp0,4	<2"7)
cross-sect.: A2/Aj  (Q i^	(2-8)
area
travel : Tj/Tj - (Q^QP"0,5	(2-9)
time
It should be recognized that these relationships exist only in free-flowing
streams, and that the exponents may vary by 503! for any river. Impounded
reaches in rivers have exponents m and f~0t and n"l. Thus, acquiring
data to develop site-specific relationships of this type is normally ap-
propriate.
Because of the nature of the relationships, reduced stream flows tend
to result in increased reaeration rates, principally due to the beneficial
effect of shallower depths. For example, a 50% reduction in stream flow may
increase Kfl by about 30Z. However, the net effect on stream DO impacts is
negative because the improved reaeration is outweighted by Increases in ini-
tial BOD concentations (L0), which would double for a 50Z reduction in stream
flow.
5-27

-------
Wasteload Allocation Analysis - Initial Deficit, Benthal Demand, P-R
In the preceding example, the effects of point source and upstream sources
of carbonaceous and nitrogenous BOD on the dissolved oxygen resources of a
stream were examined. Three other sources which may significantly affect the
dissolved oxygen in.a stream include an initial deficit, benthal demand and
algae - as expressed in photosynthesis and respiration (P-R). These three
sources will be added to the CBOD and NBOD loads in the preceding example and
their impacts examined under the design low flow condition.
Carbonaceous and Nitrogenous STP Loads
Under the STP design conditions, 11.5 MGD (17.8 cfs) will discharge 5754
lb/day of ultimate CBOD and 6475 lb/day of NBOD at mile zero. Dissolved oxygen
deficits are calculated in accordance with equations 1 and 2 of Table 3 for the
CBOD and NBOD. With the stream velocity of 3.9 m/day, the carbonaceous and
nitrogenous decay rates of 0.41 and 0.26 per day and reaeration coefficient of
2.30 per day - all at the design stream temperature of 27C, maximum dissolved
oxygen deficits due to these sources amount to 2.73 mg/i. at milepoint 3.5 and
2.15 mg/i, at milepoint 4 for the CBOD and NBOD respectively (Table 1). Note
that the maximum deficit due to the NBOD occurs downstream of that due to
CBOD due to the slower reaction rate of the NBOD,
Upstream Boundary
Values of the five-day BOD of 1.0 mg/ and ammonia nitrogen of 0.2 mg/Jl,
measured during the 100 cfs survey (see preceding example), are assumed to be
the same for the 7 Q 10 flow of 30 cfs. It may be noted that this assumption
is reasonably valid as long as the masses of these constituents which enter
upstream of the STP are flow-dependent. If the primary source of these con-
stituents is another upstream point source, the assumption would not be appro-
priate.
The in-stream decay rates of the upstream CBOD and NBOD are assumed to be
the same as those of the STP. In some cases, the upstream constituents may be 
more refractory than the STP loads and lower reaction "ratesfor the upstream
sources should be assigned.
Dissolved oxygen deficits due to these sources are calculated as frac-
tions of the corresponding STP deficits (.equations 3 and 4, Table 3), since
k
John A. Mueller
5-28

-------
the reaction rates are the same. The combined maximum deficit due to both
sources amounts to 0.20 mg/Jl as seen in Table 1.
Initial Deficit
As in the previous example, the upstream waters are assumed saturated,
containing 8.0 mg/Jl of dissolved oxygen. The STP effluent is assumed to
contain 2 mg/Jl of dissolved oxygen. A mass balance of the upstream and STP
dissolved oxygen results in a calculated D.O. immediately downstream of the
STP of 5.77 mg/Jl (Table 3). Since the saturation concentration of D.O. in
the stream at 27C is 8.0 mg/Jl, an initial deficit of 2.23 mg/Jl is intro-
duced at x = 0. This initial deficit reaerates away according to equation
5, Table 3, becoming zero ten miles below the STP (Table 1)..
Benthal Demand
Present benthal deposits are calculated to exert an oxygen demand of
2
2 g/m -day over the two mile reach downstream of the STP. Thereafter, a
" 2
lower value of 0.8 g/m -day exists. Since the mass of BOD^ discharged by
the STP under future design conditions is approximately the same as that
being discharged presently (2877 lb/day vs. 2502 lb/day, preceding example),
the amount of suspended solids will be assumed to remain the same. Thus,
the present, level of benthal demand - primarily caused by settling of the
STP solids - will be used for the STP design conditions.
The higher benthal demand over the first two miles of stream bed causes
a maximum D.O. deficit of 0.90 mg/Jl at milepoint 2 (Table 3, equation 6a).
Downstream of this point the deficit is composed of a decreasing deficit due
to reaeration of the initial 0.90 mg/Jl deficit together with an increasing
2
deficit due to the benthal demand of 0.8 g/m -day (Table 3, eq. 6b). As seen
in Table 1, the peak deficit due to benthal deposits is 0.90 mg/Jl at mile-
point 2. At milepoint 10, the effect of the first two-mile deposit is insig-
nificant and an equilibrium value of 0.52 mg/Jl of deficit - due to the subse-
quent benthal deposits - is reached and this persists downstream.
Photosynthesis-Respiration
From light-dark bottles suspended in the stream during the 100 cfs sur-
vey, it is determined that the average daily photosynthetic oxygen production
5-29.

-------
rate CP) is 5 mg/Jl-day and the respiration rate (R) is 3 mg/-day. Thus the
net P-R of 2 mg/-day is a source of oxygen to the stream. These rates exist
for many miles downstream of the STP and are caused primarily by algae result-
ing from nutrient discharges in the STP effluent. Since nutrient discharges
will be increased under design conditions (ammonia nitrogen of 938 lb/day
present vs. 1439 lb/day design) it is probable that the algal biomass will
increase over present conditions and result in a higher P-R. Since P-R is a
source of oxygen, the present value of 2 mg/Ji-day will be assumed as a conser-
vative estimate with respect to its effect on the average daily D.O. concen-
tration.
Dissolved oxygen deficits, calculated according to equation 7, Table 3,
are seen to range from zero at the STP location to an equilibrium level of
-0.87 mg/ at milepoint 10 (Table 1). The negative sign indicates a "sink"
of deficit or a source of dissolved oxygen.
Total Deficit - Design Conditions
The total dissolved oxygen deficit due to the individual sources, i.e.
STP CBOD and NBOD, upstream CBOD and NBOD,'initial deficit, benthal demand
and P-R, is a linear summation of the deficits caused by the individual
sources. Values of the total deficit begin at 2.23 mg/ at milepoint zero,
increase to a maximum of 5.42 mg/Jt at milepoint 2 and decrease thereafter to
0.31 mg/ at milepoint 30 (Table 1). Note that the additional deficit due
to the benthal deposits has been largely offset by the negative deficit due
to net photosynthesis and respiration.
As indicated in Fig. 1, under design conditions of secondary treatment,
the daily average dissolved oxygen violates the standard of 5 mg/. over the
first ten miles of stream. The critical deficit of 5.42 mg/Jl occurs at mile-
point 2, resulting in a minimum dissolved oxygen concentration of 2.58 mg/Jl
well below the water quality standard of 5 mg/Jl.
Alternatives
As discussed in the previous example, secondary treatment with nitrifi-
cation would probably be the most cost efficient method of reducing the dis-
solved oxygen deficit in the stream. Thus, secondary with nitrification is
analyzed as the first alternative. Assuming a 90% reduction in the effluent
5-30

-------
NBOD, and no incremental reduction in CBOD below 30 mg/Jl, the total deficit
under alternative one equals the total deficit under design conditions minus
90% of the deficit due to the STP NBOD. Referring to Table 1, the total
deficit at milepoint 2 under alternative 1 would be 5.42 - 0.90 x 1.82 =
3.78 mg/Jl. A summary of the deficits for all locations is contained in
Table 2. As shown in Fig. 1, the dissolved oxygen concentrations have now
improved considerably - when compared to the design case - but violation of
the standard by a maximum of 0.8 mg/Jl still occur from milepoint 0.5 to
milepoint 4.5.
Examining the deficits by source in Table 1, the major remaining contri-
butors are the STP CBOD and the initial deficit due to the low dissolved oxy-
gen in the STP effluent. Assuming that further reduction in the CBOD (to an
effluent BOD^ concentration of approximately 20 mg/Jl) is less economical than
post aeration, alternative two consists of the addition of post aeration to
alternative one. Thus, resulting dissolved oxygen deficits are calculated by
subtracting the deficits due to the initial deficit (Table 1) from those of
alternative 1 (Table 2). Within a tenth of a milligram per liter, the mean
daily dissolved oxygen concentration now meets the required standard.
Minimum Daily Dissolved Oxygen
The presence of algae in the stream causes variations in the dissolved
oxygen throughout the day. Minimum D.O. concentrations occur in the early
morning and maximum values in the early afternoon. As indicated in the first
series of seminars, the difference between the maximum and minimum daily dis-
solved oxygen concentrations, A, is approximately related to the average
daily photosynthetic oxygen production rate, P, as follows:
where A = D.O. max - D.O. min, mg/Jl
P = Av. daily photosynthetic 02 irate, mg/2-day.
This approximation applies for streams having reaeration coefficients K <
cl
2/day, for photoperiods of one-half day and for regions of the stream a suf-
ficiently far distance downstream of the beginning of the algal presence
5-31

-------
( > A U/K ). In the region of the maximum deficit for alternative 2, these
3
conditions are reasonably fulfilled and one might expect
a - Hg/t-day) , 2.5 mg/
Assuming t.he maximum and minimum daily D.O. concentrations are one-half A
above and below the average daily D.O. - a reasonable approximation for reaera-
tion coefficients less than approximately 2/day, the minimum daily dissolved
oxygen would be 1.25 mg/Jl below the. daily average profile, as shown in Figure 1.
If the dissolved oxygen standard of 5 mg/I is a "never-less-than" standard,
requiring conformance at all times of the day, alternative two would not meet
the standard. Additional reductions in the deficits due to the STP CBOD or
benthal demands would be one way of achieving conformance. Another alternative
would be to reduce nutrients, and thus reduce the algal population with its
attendant diurnal dissolved oxygen swings.
5-32

-------
TABLE 1. DISSOLVED OXYGEN DEFICITS BY SOURCE FOR STP DESIGN CONDITIONS
X
STP
UPSTREAM
INIT.
BENTHAL
P-R
TOTAL
(mi)
CBOD
NBOD
CBOD
NBOD
DEF.



0
0.00
0.00
0.00
0.00
2.23
0.00
0.00
2.23
1
1.67
1.22
0.09
0.03
1.24
0.58
-0.39
4.44
2
2.43
1.82
0.14
0.04
0.69
0.90
-0.60
5.42
3
2.70
2.07
0.15
0.05
0.38
0.73
-0.72
5.36
3.5
2.73
2.13
0.15
0.05
0.28
0.67
-0.76
5.25
4
2.72
2.15
0.15
0.05
0.21
0.64
-0.79
5.13
5
2.61
2.12
0.15
0.05
0.12
0.58
-0.82
4.81
6
2.43
2.05
0.14
0.05
0.06
0.56
-0.84
4.45
8
2.04
1.85
0.11
0.04
0.02
0.53
-0.86
3.73
10
1.68
1.63
0.09
0.04
0.00
0.52
-0.87
3.09
15
1.00
1.18
0.06
0.03
0.00
0.52
-0.87
1.92
20
0.59
0.84
0.03
0.02
0.00
0.52
-0.87
1.13
25
0.35
0.60
0.02
0.01
0.00
0.52
rO.87
0.63
30
0.21
0,43
0.01
0.01
0.00
0.52
-0.87
0.31

Equa-
tion
Used
*
1
2
3
4
5
6a
6b
7

*
See
Table 3







5-33

-------
TABLE 2. DISSOLVED OXYGEN DEFICITS FOR ALTERNATIVES
X
(mi).
TOTAL
Design
D.O. DEFICIT
Altern. 1
(mz/SL)
Altern. 2
0
2.23
2.23
0.00
1
4.44
3.34
2.10
2
5.42
3.78
3.09
3
5.36
3.50
3.12
3.5
5.25
3.33
3.05
4
5.13
3.20
2.99
5
4.81
2.90
2.78
6
4.45
2'. 61
2.55
8.
3.73
2.07
2.05
10
3.09
1.62
1.62
15
1.92
0.86
0.86
20
1.13
0.37
0.37
25
0.63
0.09.
0.09
30
0.31
-0.08
-0.08
NOTES: Design = 11.5 MGD, 30 mg/Z BOD5, 15 mg/ NH^-N
Alt em 1 = Add Nitrification (BOD^. = 30 rng/Z, NH^-N = 1.5 mg/Z)
Altern 2 = Altern 1 + Post Aerate to D.O. = 8.0 rng/Z
5-34

-------
TABLE 3. DISSOLVED OXYGEN DEFICIT EQUATIONS
STP
0.41 x L
CBODU: D,
1 2.30 - 0.41
o . -0.1051x -0.5897x,
(e	- e	)
(1)
Lq = 5754/(47.8 x 5.4) = 22.3 mgH
K/U = 0.41/3.9 = 0.1051/mi
r
K /U = 2.30/3.9 = 0.5897/mi
a
NBOD:
0.26 x N
2 2.30 - 0.26
o , -0.0666x -0.5897x.
(e	- e	)
(2)
UPSTREAM
Nq = 6475/(47.8 x 5.4) = 25.1 mg/
K /U = 0.26/3.9 - " '-ii
n
CBODU: D3 = 0.0563 D^^
d3 = dl x lo(upstr)/lq(stp)
L CUPSTR) = 2.0 x 1.0 x 30/47.8 = 1.255 mg/J.
o
Lq(STP) = 22.3 mg/I
NBOD: D. = 0.0225 D.
4	2
(3)
(4)
D4 = D2 x No(UPSTR)/NQ(STP)
NqCUPSTR) = 4.5 x 0.20 x 30/47.8 = 0.565 mg/I
Nq(.STP) = 25.1 mg/1
NOTE: Reaction rates in the stream for upstream sources and STP
assumed the same in this analysis.
INITIAL DEFICIT
D.O.(STP) = 2 mg/J.
R) = 8.0 i
= 30 cfs x 8.0 mg/ft + 17.8 cfs x 2 mg/
D.O.CUPSTR) = 8.0 mg/I Csaturated = C )
s
D.O.
x=o
47.8 cfs
= 5.77 mg/X
Do = Cs - D-- x=o = 8- - 5-77 = 2-23 ms
D, = D e
5 o
-K x/u
a
D5 = 2.23 e
-0.5897x
C5)
5-35

-------
TABLE 3. DISSOLVED OXYGEN DEFICIT EUATIONS (cont'd)
BENTHAL DEMAND
0 ^ x < 2 mi
ij	-K x/u
D6-FH(1-e >
a
B = 2 g/m^-day
H = depth in meters - 2.2/3.281 = 0.671m
n 1 in/i -0.5897x.	.
D& = 1.30(1 - e	)	(6a)
D,I  = 0.90 mg/I
6|x=2 -	
2
x > 2 mi B = 0.8 g/m -day
D = 0.90 e--5897(x_2) + o.519(l - e-0-5897^-2))	6b)
0
P - R
P-R -Kax/U,
7 r(1 -e  >
a
P = 5 mg/Jl-day, R = 3 mg/S.-day
D? = -0.870(1 - e-0-5897x)	(7)
5-36

-------
ST?
Ql7.r cfS
B0&5 a 30 hd/i
b0.  0.0 h>j/L
UPSTR.
9=30 c-Rf
Bo>si.o.h y7-
NHj-Nr 0.1 Kj//
"b.0. = ?.0 Ihj//
-*> I	j &s o. ? j/h>l-
-J
o
ALT6RN.1
	
	S TP
A =2.5" m$jl ALTgRM.2
L.
10
T
\S : ftO
miles Downstream of 5TP
is
30
Fxs.l "5U30LVED oxygen PRoFiLej-Design + ALTeRNArvej
5-37

-------
"k
A Methodology for Estimating Future Benthal Demands in Streams
Deposits of organic material on the bed of a stream may be caused by
background sources and point sources. For the typical case of a single STP
on a stream, a natural level of benthal demand would exist upstream of the
plant, a higher value immediately downstream and an intermediate value above
the natural level further downstream. Since the mass rate of total suspended
solids discharged by the treatment plant into the stream is directly related
to the magnitude of the benthal demand above the natural background level, an
estimate of projected benthal demands can be made. Thus, the benthal demand
downstream of the point source is the sum of the naturally occurring value ,
B(BACK), plus the increment due to the STP, B(STP). This latter increment is
calculated as:
B(STP)I	_ = B(MEAS) - B(BACK)
|present
where B(MEAS) are from field measurements.
For future conditions, the benthal demand due to the STP may be estimated
from:
BCSTP)|	= BCSTP) I	x ^SS ^ -future
|future	|present Mass TSS present
Note that the time required to establish the new equilibrium value of
the benthal demand is in the order of one to several years - a function of
the annual hydrology of the stream and its flushing (scouring) characteris-
tics. It is assumed that a sufficient period would, elapse after STP up-
grading to allow the benthal deposits to reach the new equilibrium.
Example
The STP of the previous examples discharges 7.5 MGD at present and
11.5 MGD under future design conditions. For the original treatment train
of primary and trickling filters, the effluent TSS concentration is 60 mg/Ji.
The design treatment train of primary, activated sludge and nitrification re-
sults in an effluent TSS of 20 mg/I.
~
John A. Mueller and Robert V. Thomann
5-38

-------
As shown in Figure 1, benthal demands are calculated to be 0.4, 2 and 0.8
2
g/m -day, for locations upstream, in the vicinity of and downstream of the
STP, based on field measurements. Assuming the upstream benthal demand is
caused by background sources similar to those downstream, the naturally occur-
2
ring benthal demand would be 0.4 g/m -day for the entire stream. The calcu-
lated benthal demand due to the STP under present conditions immediately down-
2	2
stream is 1.6 g/m -day which is reduced to 0.8 g/m -day in the future (Fig. 1)
since TSS loads will be reduced 50%.
2
Estimated future benthal demands are then 0.4, 1.2 and 0.6 g/m -day, as
seen in Fig. 1. These lower values cause the peak dissolved oxygen deficit to
decrease from 0.90 to 0.54 mg/S. at milepoint 2.

-------
#eseiu)
B - o.t	(present)
ante
STREAM
H l-l'* 0.C71 M
U. = 3.9 fri/day
KV 1.3o/cUy  19*C
5 TP gFFme*T TSi"
PRfe^eNr 60
FlA.TU.fte 1.0
SENTH4 L bSMANdS	TO STp
PRESBN T
0 'Xia nc B(jtp) ca-0.^3 \.Gj/ni*-dr
Xa. B(stp) * oi-o.is o
where B(bacn) = 0.4 $/*v- Uy (uPrrR of :tp)
FU.TU.Re
05:9C * X
a
B(STp)=: l.G xAli5xOO-= 0.5^ = S.f^/lhWay
n n.sx co J
B(stP)=0.+ x( e.5 ) = 0-2. Ji/Ui.y
B= 0.+ dfa-tUy
B= i.a
B= o.c
(future)



i.o-
Vx

ft
031-


o


0-
PREJBN T
FUTURE
1	1	1	r
5-	10	15"	10
MILE'S BELOH/ JTP
15"
I
30
FICU.&E \ Es TIWATION OP PU-TuAe B6VTJML JeMANVr
5-40;

-------
CHAPTER 6
WASTE LOAD ALLOCATIONS
TREATMENT PROCESSES

-------
WASTE LOAD ALLOCATIONS
TREATMENT PROCESSES
Pag e
N urrbe r
I.	PRINCIPALS OF BIOLOGICAL TREATMENT
BIOLOGICAL TREATMENT	. 6-1
II.	SPECIFIC PROCESSES - BOD REMOVAL
SECONDARY TREATMENT PROCESSES	 6-9
A.	ACTIVATED SLUDGE PROCESSES		6-9
B.	PURE OXYGEN TREATMENT		6-15
C.	ROTATING BIOLOGICAL CONTACTORS		6-1 y
D.	CARROUSEL LOOP AERATION SYSTEM		6-19
E.	DEEP SHAFT SYSTEM		6-2 6
F.	COMBINED BIOFILM/SUSPENDED GROWTH PROCESSES....	6-28
G.	AEROBIC LAGOONS		b-28
H.	PACT PROCESS		6-28
TYPICAL EFFLUENT CONCENTRATIONS		6-32
OPERATIONAL PROBLEMS		6-37
III .VARIABILITY/RELIABILITY		6-38
IV.	NUTRIENT REMOVAL		6-5U
I.	MAJOR NITROGEN REMOVAL PROCESSES		6-50
INDUSTRIAL WASTES		6-61
II.	DENITRIFICATION		6-69
III.	PHOSPHORUS REMOVAL....		6-7U
V.	BIOLOGICAL NUTRIENT REMOVAL		6-71
BARDENPHO PROCESS		6-71
PHOSTRIP		6-71
VI.	COST OF TREATMENT		6-75
VII.PRIORITY	POLLUTANTS/TOXICS	 6-106

-------
BIOLOGICAL TREATMENT
Biological waste treatment essentially consists of
controlling environmental factors to enable a mixed culture of
microorganisms to employ the organic matter in the waste as a
food source for reproduction (synthesis) and energy
(assimilation) . In aerobic treatment systems, organisms are
suspended in a liquid medium with the waste to be treated.
Dissolved oxygen' is required by the culture and sufficient time
is allowed for the organisms to utilize the organics as a food
source. The suspended and colloidal organic matter measured as
BOD undergoes an initial reduction by adsorption to tne
organisms. Thereafter tne rate of BOD removal is generally
related to the BOD present and viable microorganisms- in the
system.
In the design of waste treatment facilities, the rate at
which these reactions occur, the amount of oxygen and nutrients
required, and the quantity of biological sludge produced in the
reaction must be determined.
The reaction constant in the BOD removal equation is
temperature dependent. It is possible to relate the effect of
temperature cn BOD removal by the following relationship:
k - k e(T-2y)
Kt " 20
where
= BOD removal coefficient at temperature
T (C)
= SOD removal coefficient at 20C
T = temperature in treatment system (C)
0 = temperature coefficient (1.U30 - 1.080)
In general, the system will approach some minimum BOD value,
rather than zero concentration, due to an equilibrium between the
bacteria and their liquor. The magnitude of the initial removal
is a function primarily of sludge concentration, acclimatization,
and waste composition. The' rate of reaction is a function of
temperature, nutrient level, concentration of waste, and sludge
composition .
Table 6-1 summarizes the reactions and information that must
be developed for the design of aerobic biological processes.
6-1

-------
TABLE 6-1
BIOLOGICAL TREATMENT REACTIONS
. cells
ORGANICS + NH3 + 02 	> C5H?N02 + C02 + H20
cell s
C5H?N02 + 02 	> C02 + H20 + NH3 + cells
cells
KINETICS
dS
dt
k SX
dS _ kX o >> k
dt
5
zero order
k' X S S << k
5
1st order
OXYGEN
02 Required
a' BODd + b" X
H
0 Transfer
Steady State
BIO SLUDGE PRODUCTION
SSp = aBOD^ - b X

-------
PROCESS DESIGN & CONTROL
Loading Rate
F/M
BOD^ (lbs/day) Applied
MLVSS (lbs)
Sludge Age
0 =	V X
a BOD rZ - bXV
o r
0 =	VX
wX + (Q-W)Xe
NUTRIENTS
60Dj- : N : P
100 : 4.5 : 0.3

-------
Figure 6-1 presents a schematic representation of the removal
of BOD by biological treatment as a function of the
microorganisms in contact with the wastewater (MLVSS), X and the
time of contact, t. At low Xt.values which would represent high
Food to Microorganism, F/M, ratios and low sludge age the BOD
remaining changes sharply with small incremental increases in Xt.
Under these conditions the system is unstable and it would be
difficult to design a plant to provide consistent performance in
this region. As Xt increases beyond this region effluent BOD
remain relatively constant and stable operation is obtained.
Figures 6-2 and 6-3 shows effluent cha r ac ter i s t i cs to trie
system, loading rate.
Figure 6-4 summarizes from a number of studies performed by
HydroQual the relationship between effluent soluble BOD.. and
system loading rates for a variety of industrial wastes.
6-4

-------
100
80
60
40
20
X t
UNSTABLE
STABLE
X t
FIGURE 6- I
BOD REMOVAL

-------
FILAMENTOUS AND	^	 WTHIF.CAT.ON
DISPERSED GROWTH OPTIMUM FLOC DISPERSION
FLOCCULA

noD isoLuiu.i ]
SLUDGE AGE
r-/M
FIGURE 6-2
EFFLUENT CHARACTERISTICS AS RELATED TO SLUDGE AGE AND F/M

-------
BOD
BODt
SS
SOL. BOD

-------
40
PHARM.
120
100
ORGANIC CHEMICAL
80
60
GRAIN PROCESSING
TANNERY
ORGANIC
CHEMICAL
40
TEXTILE
PULP 8 PAPER
20
SYNTH.
FUEL -
DOMESTIC
REFINERY 
TEXTILE
0.2
0.3
0.4
0.5
0.6
0.7
0 8
F/ M
FIGURE 6-4
INDUSTRIAL WASTEWATER TREATABILITY

-------
SECONDARY TREATMENT PROCESSES
A. ACTIVATED SLUDGE
The activated sludge process is a continuous system in which
aerobic biological growths are mixed and aerated with wastewater
and separated in a gravity clarifier. A portion of the
concentrated sludge is recycled and mixed with additional
wastewater. The process should provide an effluent with a
soluble BOD of 10-33 mg/1 , although the organic concentration of
the effluent in terms of COD may be as high as 500 mg/1,
depending on the' concentration of bioresistant compounds
originally in the wastewater. There are many impurities in
industrial wastewaters such as oil and grease, which must be
removed or altered by preliminary treatment before subsequent
activated sludge treatment can be considered.
Many modifications of this process have been developed over
the decades, the principal ones being shown in Figure 6-5. The
conventional process employs long rectangular, aeration tanks,
which approximate plug-flow with some longitudinal mixing. This
process is primarily employed for the treatment of domestic
wastewater. Returned sludge is mixed with the wastewater in a
mixing box or chamber at the head end of the aeration tank. The
mixed liquor then flows through the aeration tanks, during which
progressive removal of organics occurs. The oxygen utilization
rate is high at the beginning of the aeration tanks and decreases
with aeration time. Where complete treatment is achieved, the
oxygen utilization rate will approach the endogenous level toward
the end of the aeration tanks. The principal disadvantages of
this system for the treatment of industrial wastewaters are (1)
the oxygen utilization rate varies with tank length and requires
irregular spacing of the aeration equipment or a modulated air
supply; (2) load variation may have a deleterious effect on the
activated sludge when it is mixed at the head end of the aeration
tanks; (3) the sludge is susceptible to slugs or spills of
acidity, causticity or toxic materials.
In the completely mixed system the aeration tank serves as an
equalization basin to smooth-out load variations and as a diluent
for slugs and toxic materials. Since all portions of the tank
are mixed, the oxygen utilization rate will not vary with time
and the aeration equipment can be equally spaced.
Step aeration is a variant between the conventional process
and the completely mixed process and has been successfully
employed for the treatment of domestic wastewaters. Table S-2
and Figure 6-6 compare the impact of operational modes
(conventional vs step aeration) on removal and oxygen requirement
6-9

-------
INFLUENT
EFFLUENT
CLARIFIER
RECYCLE
AERATOR
CONVENTIONAL
EFFLUENT
INFLUENT
RECYCLE
STABILIZER
INFLUENT
CONTACT STABILIZATION
EFFLUENT
CLAR
AERATOR
RECYCLE
STEP AERATION
INFLUENT
EFFLUENT
cRATOR 1
RECYCLE
COMPLETELY MIXED
FIGURE 6-5
ACTIVATED SLUDGE SYSTEMS

-------
TABLE 6-2
COMPARISON OF OPERATIONAL MODES
AT ULTIMATE PEAK LOADS
Step Aeration Modes
Parameter
Flow, rngd
Conv entional
Mode
74. 6
BOD, 1,000 lbs/day	160
Recycle rngd	24.6
mg/1	12,000
F/M, lbs BOD/lb
MLSS-day	.52
X , gm/1	3.0
a
t, hrs. Q	3.9
Temp ( C)	30
Soluble BOD, mg/1 14
Oxygen Required
1,000 lbs/day
137.6 Total
Case I
Pass 1 Pass 2 Pass 3 Pass 4
37.3
80
24. 6
12,000
4.8
30
15
Distribution 103.9 14.4 9.9 9.9 65.3
Average DO, mg/1 0.5 2.5 2.4 2.4 1.0
Air Required
1,000 scfm
Di str10 ut ion
79-3 Total
55.2 10.3 7.1 6.7
37.3
80
0
0
0
0
0
0
0
Average .46
3.0 3.0
3.9 Total
30	30
22
16
142 Total
30
14
55.7
1. 0
11.6
3.0
9.4
5.0
37
84.9 Total
31.6 9.0
Case II
Pass 1 Pass 2 Pass 3 Pass 4
0
24.8
53.3
24. 6
12,000
6. 0
30
10
52.7
1.5
24. 9
53-3
0
24. 9
53-3
0
0
0
Average .39
4.0 3-0
3.9 Total
30	30
14
45. 9
1.5
22
150 Total
40.2
2.5
3.0
30
14
11.2
2.5
7.3
32. 1
96.9 Total
28.0 28.8 8.0

-------
1/20
l/SO -'
1/20 .
1/50
1/50
<= 6000
4000
3000
3000
3000
3000
3000
3000
3000
3000
300
_ 200 
UJ ~
-J \
CD	C
3	E
_l  100
O
if!
Q _
1
UJ \
O 
z -
uj O
O o
S2
o
z
UJ
o
>
X 	
o _
o ^
QJ ^
> e
o
l/l
v>
160
120


0


60
o

50
tr

40
->
u

o
#1

in
O
30
or
O


O

cr

20
<




10


0
AVG 0 0.* 2 ma / I
z
ZZ2
//A//A
300
200
100

12	3	4
160 
120
80
12 3 4
PASSES
AVG 00 * 2 mq / I
Z
777777
300
200
100 
160
120
80
AVG 0.0. s 2 mg / I
0
60
30
40
30
20
10
0
FIGURE 6-6
OXYGEN DEMAND AND AIR DISTRIBUTION ULTIMATE AVERAGE LOAD

-------
at a 75 MGD combined domestic and industrial wastewater treatment
pi ant .
In the extended aeration process, sufficient aeration time is
provided to oxidize a large percentage of the biodegradable
sludge synthesized from the BOD present in the wastewater.
The contact stabilization process is applicable to
wastewaters containing a high proportion of the BOD in suspended
or colloidal form. Since bio-adsorption and flocculation of
colloids and agglomeration of suspended solids occur very
rapidly, only short retention periods (15 - 30 minutes) are
required to effect clarification as shown in Figure 6-7. After
the contact period the activated sludge is separated in a
clarifier. A sludge reaeration or stabilization period is
required to stabilize the organics removed in the contact tank.
The retention period in the stabilization tank is dependent on
the time required to assimilate the soluble and colloidal
material removed from the wastewater in the contact tank.
Effective removal in the contact period requires sufficient
activated sludge to remove the colloidal and suspended matter and
a portion of the soluble organics. The retention time in the
stabilization tank must be sufficient to stabilize these
organics. If it is insufficient, unoxidized organics will be
carried back to the contact tank and the removal efficiency will
be decreased. If the stabilization period is too long, the
sludge will undergo excessive auto-oxidation and will lose some
of its initial high removal capacity. Increasing retention
period in the contact tanks will increase the amount of soluble
organics removed and decrease required stabilization time. A
large increase in contact time will negate the requirement for
sludge stabilization. In this case, the process becomes the same
as the conventional activated sludge process.
Increasing the biological solids level also decreases the
stabilization time requirements since the organic' loading for
unit solids becomes less. The total oxygen requirements in the
process are those required for synthesis of the organics removed
and for endogenous respiration. The split of this oxygen between
the contact tank and the stabilization tank depends on the solids
level carried in both units and on the retention period in each
tank. Increasing the contact tank solids level or retention
period will increase the percentage of total oxygen to that unit.
DOMESTIC SEWAGE
A distinction must be made when considering the activated
sludge progress for the treatment of domestic sewage as compared
to soluble industrial wastewaters, based upon the physical
6-13

-------
100
4 hr
90
CONTACT TIME
1% hr
80
70
OVEROXIDATION
60
50
MINIMUM
STABILIZATION
TIME
0
23
STABILIZATION TIME, hr
FIGURE 6-7a
SCHEMATIC REPRESENTATION OF
THE CONTACT-STABILIZATION PROCESS

-------
composition of the wastewaters and the resulting mechanisms of
removal. The organic content of domestic sewage consists of
three components, suspended organics resulting from ground
garbage, paper, rubber, etc., colloidal matter, and soluble
organics consisting mainly of carbohydrates and some nitrogenous
material. Most of the organics are in the form of particulates.
Investigators have shown 35%, 40% and 25% of the total COD was
present as suspended, colloidal, and soluble material,
respectively in American sewage.
Typical design criteria for the unit processes that' are
contained in most activated sludge plants are shown on Table 6-3.
Processes are selected and designed to be cost effective for the
treatment of specific wastewater characteristics and situations.
The design of a , total treatment system integrates the various
processes to produce the desired effluent quality. The "safety
factor" incorporated into a design is a matter of good
engineering judgment which should consider the specific needs,
type process, reliability, waste variability, and cost.
B. PURE OXYGEN TREATMENT
I.	General Design Considerations
F/M	- 0.5-0.9 lbs/day B0D5
lb MLVSS
MLVSS	- 4,000 - 8.000 mg/1
Stages	- 3 to 4
Oxygen Utilization - Avg. Load 90 + %
II.	Special Design Considerations (Industrial)
1. O2 Transfer
2 . A1 kal in i ty/pH
3.	Temperature
4.	Oxygen Utilization
5.	Solids Clarification
III.	Schematic - Figure 6-7b
IV.	Performance - Figure 6-8
6-15

-------
IMbLL l>"j
ACT 1 VATtu bLtliJbE
UUl'ltbliL W A S I t W A 11 rt
PKlKiAKY CLAK1F 1EKS
ACTIVATED SLUUGE
A  K A TI ON BASIN
TIME
FINAL CLAK1E1EKS
AIR hLUTAT1 UN
WAS
FLOAT SOLIDS
liKAVlTY THICKEN
PR IMARY
LlEWATEK 1N6 dUUlmtNl
UC b
hKP
BELT FlLlER PKESS
VACUUll F1LTKAT1UN
buL)
8UU-12UU gpd/sf 2(J-4U% 4U-/U*
2"5 HOURS	REMOVAL REMOVAL
U-2-U-4 E/ivt
4~8 HOURS
UK = bUlM2UU GPD/SF 5U mg/l 5U mg/l
FLUX = 2U-3u lbs/ft^/day
2-4 lbs/hr/sf
3~b%

CHEN 
HEEL)
CUNU1T-
SULiUS
POLYMER
1-2%
POL YMER
WU%
POLYMER
1-2%
CHEMICAL
2-b%
LAKE
CAPACITY SULILiS
2UU-4UU lbs/hr 5-1U%
2UU-4UU lbs/hr 12"14/o
5UU-4UU lbs/hr 12-14%
2-6 lbs/hr/sf 14-20%

-------
AERATION	GAS RECIRCULATION
TANK COVER
COMPRESSORS
AGITATOR.
OXYGEN
FEED GAS* ~
EXHAUST
"GAS
MIXED LIQUOR
eTfluENT TO
CLARIFIER
WASTE
LIQUOR
FEED
STAGE
BAFFLE
SPARGER
FIGURE 6-7b
SCHEMATIC DIAGRAM OF MULTI-STAGE
OXYGEN AERATION SYSTEM

-------
LIQUID PHASE
GAS PHASE
400
300
O 200
00
4
STAGE
20
3 
o
E
o
d
o'=.74lb0I/lb B0Dr
b'*.l2 Ibt 0|/lb MLVSS-d
I
2
3
4
STAGE
EQUIVALENT TOTAL
PLANT LOADINGS.
0' 105 mgd
w" 170,000 lbs B0Ds/day
 OBSERVED DATA (WITH RANGE)
	MODEL PREDICTION
FIGURE 6-8

-------
C. ROTATING BIOLOGICAL CONTACTORS
1.	Domestic Wastewaters
Organic Loading Rates - 1-3 lbs/day BODj-/l,000 sf
2
Hydraulic Rates	- 0.75-1.5 gpd/ft
2.	Variability
Fixed Film Process w/o Recycle
Subject to variability
Generally effl . variability ~ infl . variability
3.	Temperature Effects
May not be significant on overall removal .
a.	kinetic rate decreases 0 = 1.10
b.	Active film layer  increases due to increased
oxygen saturation
4.	Schematic - Figure 6-9
Design Relationship Domestic Wastewater - Figure 6-10
Sensitivity - Figures 6-11 to 6-13
D. CARROUSEL LOOP AERATION SYSTEM
The Carrousel system, originally developed in Netherlands is
basically a low rate activated sludge (extended aeration) process
that incorporates a mechanically aerated continuous channel.
Oxygenation and circulation of mixed liquor is provided by
conventional surface aeration equipment normally located at
influent end and at the turn point of the loop, depending upon
basin configuration. The system can be visualized to consist of
two sections: the aeration zone, which is essentially completely
mised, and the channel section, with a plug flow regime.
Due to the long sludge ages and the variable dissolved oxygen
that exists in the basin the Carrousel process can be utilized
for combined nitrification/denitrification . (See Figure 6-14).
6-19

-------
effluent to
SECONDARY .
CLARIFIER
COVER
INFLUENT
FROM
PRIMARY
TREATMENT.
RBC UNITS
A
=k
FLOW OVER BAFFLES
CONTOURED TANK FOR MULTIPLE RBC SHAFTS
INFLUENT
EFFLUENT TO	FROM HIGH
SEDIMENTATION	RATE OVERFLOW
ZONE OF TANK
CLARIFIER
FLOW UNDER BAFFLES
FLAT BOTTOM RBC TESTING TANK
FIGURE 6-9
RBC BOTTOM CONFIGURATIONS

-------
o
s
Q
O
CO
60
40
30
<
-
O
6 
UJ
P
10
INFLUENT SOLUBLE BOD. MG/L
160 120 100 90 80 70 60	60
46
40
35
 25
20
(5
S
o'
o
m
oo
D
_J
O
V)
t-
2
UJ
3
15 -
10 -
WASTEWATER TEMPERATURE > 55 "F
- 30
25
3	4	5	6
HYDRAULIC LOADING RATE, GPD/FT2
FIGURE 6-I0
DESIGN RELATIONSHIP FOR BOD REMOVAL FROM DOMESTIC WASTEWATER

-------
<
>
o
2
UJ
o:
m
Q
O
m
in
o
uj
in
<
UJ
CC
a
2
l-
2
UJ
U
CC
UJ
a.
0 = I 500 m3/day
T = 20C
INFLUENT
DISSOLVED OXYGEN
6 mg/l
3 mg/l
I m g / I
1
50	100	150	200
INFLUENT SOLUBLE BODj, mq/l
250
FIGURE 6-11
SINGLE STAGE PROCESS DESIGN CURVES RELATING
THE EFFECT OF DISSOLVED OXYGEN ON SBODg REMOVALS

-------
200
HYDRAULIC LOADING
(mVd/m2 )
I 80
0.4
160
I 40
I 20
100
D
80
60
LlJ
40
LlJ
20
0
20
40
60
80
100 120 140 160 I
INFLUENT SOLUBLE BODj, mg/l
FIGURE 6-12
SINGLE STAGE PROCESS DESIGN SOLUTIONS RELATING
EFFLUENT SBOD5TO INFLUENT SBOD5 AND HYDRAULIC LOADING

-------
u
2
O
o
z
UJ
o
>
X
o
o
UJ
>
o
o>
to
X X
/ \
/ \
W I NTER
SUMMER
/. X
ACTIVE FILM
ACTIVE FILM
FILM THICKNESS
FIGURE 6-13

-------
SLUDGE RECYCLE
CLARI FIER
INFLUENT
FIGURE 6-14
CARROUSEL PROCESS

-------
E. DEEP SHAFT EFFLUENT TREATMENT SYSTEM
The Deep Shaft Effluent Treatment System, originally
developed by Imperial Chemical Industries in Great Britain is
basically a high rate activated sludge process, employing
compressed air for oxygenation and circulation of wastewater.
The heart of the process is the Deep Shaft bioreactor where
aeration and substrate removal take place. A typical bioreactor
consists of a totally cased and grouted vertical shaft 300-800
feet in depth,, which is divided into a downcomer and riser
section by a partition or a concentric tube arrangement. Air
injection points are provided in both sections. The wastewater
is circulated around the shaft using the air lift principle.
During normal operation, the compressed air is injected in the
downcomer section, while the injection point in the riser is used
only for startup (Figure 6-15).
Sol id s-1 iquid separation is normally achieved by flotation in
the Deep Shaft system which makes use of the air entrained in the
biological floes as they emerge to the top of the riser.
Average loading rates for the Deep Shaft process are in the
range of 2 to 4 lbs BOD/lb MLVSS/day. Since the system is a very
high rate process relatively large amounts of sludge are produced
in treatment.
TYPICAL OPERATING PARAMETERS
. MLSS - 8,000-10,000 mg/1
Residence Time per pass - 2-6 min.
Retention Time - 1-4 hours
. F/M - 2-4 lbs BOD/lb MLVSS
6-26

-------
SLUDGE
RECYCLE
AIR
Compressor
OUTLET
START-UP AIR
PROCESS AIR
Downcomer
Riser
Shaft
Lining
FIGURE 6-15
DEEP SHAFT

-------
F.	COMBINED B I OF I LM/S US PENDED GROWTH PROCESSES (ABF)
Combined bio f i lm/suspended growth processes employ a biofilm
reactor upstream of a conventional activated sludge reactor. The
first-stage biofilter is used as a roughing filter to remove most
of the organics and buffer loadings to the aeration basin.
Typically, about half to two-thirds of the system stabilization
occurs in the biofilter, and the balance in the aeration basin.
Thus, most stabilization occurs in the relatively energy-
efficient biofilter and furthermore, net oxygenation efficiency
is improved in the aeration basin since load .fluctuations are
reduced. Figure 6-25 is a schematic diagram of the activated
biofilter process (ABF) which employs this concept. In this
case, mixed liquor settled in the secondary clarifier is recycled
and distributed over a horizonta1-media biofilter. Thus,
suspended growth microorganisms are combined with high-strength
wastes in the highly aerobic environment of the biocell.
Accordingly, the biocell is analogous to the contact basin in a
co ntac t-stab il i za t io n activated sludge process. However, the
biocell plays a dual role in the ABF, since a biofilm growth
develops also contributing to organic stab il i za t io n .
Aerobic conditions are maintained in the biocell through
relatively high surface wetting rates, 1.5-4 gpm/sq. ft., and the
horizontal media design. Performance of the ABF process is
comparable to activated sludge. It is particularly applicable to
h ig h-str eng th wastes and wastes with widely-fluctuating loadings,
since the contribution of the biofilter is accentuated in these
situations.
G.	AEROBIC LAGOONS
Aerobic lagoons are simple, mixed reacto.rs without recycle.
SRT- is equivalent to the HRT in this configuration, thus
relatively long HRTs are required to achieve reasonable
stabilization efficiencies. Typical detention times range from 1
to 10 days. Clarification is required to proyide good effluent
quality. Aerobic lagoons are used where simplicity is necessary
and land is abundant. Several industries use lagoon treatment
s ysterns.
H.	PACT PROCESS
The "PACT" process (Dupont patent) is an activated sludge
process employing powdered activated carbon (PAC) addition to the
aeration tanks. Figure 6-16 presents a flow diagram of the
process. Both virgin and regenerated PAC are added to the
primary effluent based on attaining a certain PC concentration in
the aeration tank. Cationic polymer is typically added to the
aeration tank effluent to insure adequate clarification in the
6-28

-------
flXfDHt
BlO-Clll
Al R AT ION
PROC! SS,
INUUl NT
FlOW CONTBOl
& SPUT T INC
BlO-CEll
mm station
RETURN SlUDCf
WASTE SlUOCE'
FIGURE 6-25
ABF PROCESS FLOW SCHEMATIC

-------
Virgin
PAC
"Cationic
Polymer"
"Pnmory
Se,Ce, Xe
Effluent
Xu ,Cu
Xu,Cu
<:	
Regeneration
Secondary
Clarifier
Aeration 
Tank"
x,xc,xB,s
FIGURE 6-16
FLOW DIAGRAM OF PACT PROCESS

-------
secondary clarifier. When economically feasible, thermal
regeneration is utilized which also provides destruction ofo the
waste activated sludge. Depending on the thermal regeneration
process, thickening and dewatering may be utilized prior to
regeneration. Acid washing of the regenerated PAC is also
practiced at the Dupont Chambers Works Plant to reduce ash
contents .
Process development was based on the ability to generate
better effluent qualities than activated sludge alone, meeting
more stringent effluent standards without separate granular
activated carbon systems.
Use of high sludge ages will significantly reduce the carbon
dosage required. Carbon dosages typically from 5 to 200 mg/1
have been utilized. The full scale Chamber Works plant uses ~130
mg/1 PAC with a portion regenerated by multiple hearth
incineration. A 6 mgd municipal plant at Vernon, Connecticut,
produces an effluent BOD of less than 5 mg/1 and SS less than 10
mg/1 after sand filtration. Virgin carbon feed is approximately
10 mg/1 with an additional 300 mg/1 of carbon recycled from wet
air oxidation regeneration.
CONCLUSIONS
1.	The PACT process will supply benefits over activated sludge
by increased priority pollutant removals, especially base
neutral and acid extractables. The PACT process also
provides some protection against upsets and quicker recovery
compared to activated sludge.
2.	Increased removals are due to influent PAC dose. The degree
of bioregeneration occurring in "PACT" units is relatively
insigni f icant.
3.	Wet air oxidation appears to be the best process for PAC
regeneration, allowing ~95% recovery of the PAC.
4.	Cationic polymer addition (1-5 mg/1) is required prior to
secondary settling to remove PAC particles from the effluent.
The PAC provides a weighting agent for the sludge allowing
higher mass loadings on secondary clarifiers than
conventional .
5.	The PACT process is more costly than activated sludge but
less costly compared to GAC. Above a certain size plant
depending upon the method and cost of sludge disposal- PACT
process has been reported less costly than activated sludge.
Carbon regeneration is not economical below carbon usage of
5,000 to 10,000 lbs/day.
6-31

-------
TYPICAL EFFLUENT CONCENTRATIONS
Table 6-4 puts typical effluent BOD results from various
treatment processes in properly operated and maintained treatment
works as reported by the EPA in the Process Design Manual for
Upgrading Existing Wastewater Treatment Plants, October, 1974 .
A study conducted for the EPA resulted in a report on
"Estimate of Effluent Limitations to be Expected from Properly
Operated and Maintained Treatment Works. This is a 3 part manual
illustrating development of data base from various types of
treatment plants, primary, conventional, contact stabilization
and extended aeration. Flow was normalized by dividing actual
flow by design flow. Based on data, the study generally shows
that up to design flow secondary treatment normally produces an
effluent of 30 mg/1 or less, and estimates the effluent which may
be expected at normalized thus up to double the plant capacity.
A typical curves showing data and estimated effluents for BOD and
SS for conventional plants are .shown in Figures 6-17 and 6-18.
As can be observed, typically plants produce effluent BOD and
SS less than 30 mg/1 up to design flow, however, for various
reasons attributed to poor operation, this level is exceeded.
6-32

-------
I'rtbLt b-M
LUWb 1 tKl'l AVEKA6E HEKfUKHANlt Uh wtLL UHLKAThU PLANTS
	lffluen r buli mg/l	
it Uh PLANiS
AC11 VrtTtlJ SLUUbE	KANGH AVERAGE SURVEYED
CUlMVtINi i 1 (JNAL
b
TO
3b
13
lb
STEP aEKAT1UN

TO
18
U
1^
CUNIACT S'l AB ILl ZA t 1UN (w/o





PRIMARY TREATMENT < 1 (J MGD)
1/
TO
3U
21
8
CUi'lHLETE I'lIX
b
TO
37
19
21
MUUlFlLU 'AEKA'I I UN
38
TO
bb
33
1U
2 STaGE (for ammonia oxidation)
4
TO
21
U
11
UXYlitN ACTIVATED SLUDGE HLAN1S
y
TO
2 3
13
19
TRICKLING F1L1EK PLANTS





LOW RATE
14
TO
bb
34
5
HIGH RATE

Tu
bb
39
b
REFERENCE : ESTIMATE OF EFFLUENT LIMITATIONS TO BE EXPECTED AT
PROPERLY OPERATED AND MAINTAINED TREATMENT WORKS,
epa-ci no- b8"Ul-43^9

-------
1 ABLE b-M
(CONTIN U E D )
LUNb
fEKi'i AVtKAbE HtKhUKl'IrtNCt Of" WELL UHtKaitU HLAl\ll'SU)
ADVANCED TREATi'lENl I'iEI'HUUS
AEROBIC POLISHING LAGOONS
1 BOD REMOVAL TF/AS EFFLUENTS : RANGE:
AVERAGE
M I CROSCREENS
SOLIDS REMOVAL AND BOD ASSOCIATED WITH
SOLIDS ON TF/AS EFFLUENTS:	RANGE:
INF  SS b TO ^>4 MG/L
2 TO 1!? mg/l
8 - b 9 %
5U"857o REMOVAL
EFF- SS
FILTER
I NFL UENT
BOD MG/L
F I L T E R
EFFLUENT
BOD MG/L
MEDIA FILTERS
SAND
1< ACTIVATED SLUDGE EFFLUENT	i2 ~ 2U	2 ~ 10
I- TRICKLiNG FILTER EFFLUENT	^(J " 45	b " 2b
MULT I MEDIA
ACTIVATED SLUDGE EFFLUENT	2 " lb
ACTIVATED CARBON COLUMNS
EFFLUENT BOD " 2~5 MG/L ON ACTIVATED SLUDGE EFFLUENT
(1) PROCESS DESIGN MANUAL FOR UPGRADING EXISTING WASTEWATER
TREATMENT PLANTS, EPA TECHNOLOGY, TRANSFER OCT- 1974-

-------
o
o
ffl
"r
60
50
40
30
20
10
QU ESTIOMABLE
~ OPERATION
 GOOD
. OPE RATION
0.1
0.2
NORMALIZED FLOW
Figure 4. Conventional Activated Sludge, BODS
 SUMMER (June  Sep)
 WINTER (Dec - Mar)
A OTHER MONTHS
NORMALIZED FLOW

<1.0


|> 1.0
Total
Summer
Winter
Annual Ave.
<60 mg/l BOD5
98'/.
83'/.
99 V.

< 50 mg/l
91%
83V.
83 V.
99V.
< 40 mg/I
78%
67V. ,
67 V.
75V.
< 30 mg/l
64 V.
507.
50V.
75 V. -
FIGURE 6- 17

-------
E
CO
O
3
o
CO
O
ui
o
2
UJ
a
	 questionable _
OPERATION
cooo
OPERATION
2.0
NORMALIZED FLOW
Figure 5. Conventional Activated Sludge, Suspended Solids
 SUMMER (June - Sep)
 WINTER (Dec - Mar)
A OTHER MONTHS
<1.0
>1,9
Total
Summer | Winter
Annual Ave.

<60 mg/l BOOj
99%



60%
< 55 mg/l



99%

< 50 mg/l
97V.

99%

20%
< 40 mg/l
94%
99%
93%
91V.

<30 mg/l
79%
75%
79%
82V.

FIGURE 6- 18

-------
OPERATIONAL PROBLEMS
Operational problems at wastewater treatment plants can be
oa-used by a wide variety of conditions including poor operation,
deficiencies in the plant, waste characteristics and
environmental conditions such as temperature. The most common
operational problems experienced at wastewater treatment plants
are generally related to the following :
(a)	Inadequate Sludge Wasting
high inventory of solids in clarifiers
hign MLSS
low F/ M
(b)	Inadequate Dissolved Oxygen
Other common process causes that contribute to poor performance
of pi ants incl ude
Hydraulic or Organic Overload
Shock Loadings
Inadequate Nutrients
Toxic i t y
Recycle Loads from Sludge Treatment
6-37

-------
VARIABILITtf/KELIALilLI i'Y
The ability of a treatment plant incorporating various
treatment processes to reliably produce an effluent which does
not exceed a maximum limit is determined by numerous factors some
of which are listed in Table 6-5. Surveys and analysis of actual
performance of treatment facilities have been done which clearly
indicate that to meet a maximum week or maximum month discharge
standard, the plant process must be designed to produce average
concentrations significantly less than the standard. Trie
selection of this value should be based on the risk and
associated costs invclveu . As environmental limits are lowered
and risk due to exceed iny these limits increases, greater
reliability is required which must be considered in the design
bases, and ultimately both capita] and operating costs. High
expectation in effluent quality results in a need for additional
or more so ph i s t ica ted aparatus, special control systems, and in
some cases increased treatment facilities including tertiary
trea tment uni ts .
Niku, et . al . (1) studied thirty seven activated sludge
plants and statistically analyzed one year's data. Table 6-6
illustrates the range in effluent BOD and solids concentrations
found. For the plants studies, and the variability in effluent,
to meet a given effluent limitation about 90% of the time, the
long term mean effluent value (design) would have to be about 50-4
of the effluent limitation for SS and BOD.
Analyses of operating plant data by Hovey, et . al . for
secondary treatment plants indicated that a plant would have to
be designed for a long term average BOD of 17 mg/1 in order to
meet the secondary treatment standards of 30 mg/1 as a MA30CD
(maximum average 30 consecutive day) and 45 mg/1 as a maximum /
day average. Figure 6-19 graphically presents this analysis.
Figure 6-20 summarizes operational data at a meat processing
plant (chicken) wen raw wastewater concentrations averaged about
l,2UiJ mg/1. The extended aeration treatment plant with primary
air flotation reduces BOD by mere than 90 i, nowever, roughly 3J
percent of the time based on 30 day averages the plant exceeds
permic limits. Generally the higher effluent concentrations
exist during the cold temperature periods. Consideration of
seasonal treatment is suggested when developing permit limits.
Figure 6-21 summarizes the performance of a lagoon treatment
system for a pulp and paper wastewater located in tne Soutn.
Treatment consists of a series of lagoons which provides greater
than days detention.
6-38

-------
TABLE 6-5
FACTORS AFFECTING PLANT PERFORMANCE
1. Related to Waste Characteristics
Variability
diurnal
long term
seaso nal
Industrial Contribution
si ug s
tox icity
difficult to treat organics
Infiltration/Inflow
Temperature
2. Related to Design
Specific Treatment Processes
Design Parameters - margin for overloading
Spare/Emergency Capacity
3. Related to Plant Size - O&i-l
Accidents
Level of Expertise of Operators
Downtime for Repairs, Availability of Spare Parts
Response to Upsets/Problems
Finane i ng

-------
N i k 11 c t j I
TABDE 6-6
TABLE VI! Percentile valjes of efPuent BOD concentration.
E/Huent DOD Percentiles
Nouniltied Percentile!
\cti\attvl SIikI^c
TABLE VIII. Percentile values of etUuer.t SS concentration
Kf'iuent SS Percentiles
Nornialued Pcrcennies
&Q
I1'
J I
to
o5
- n .|
II ~2
1 .'7
1 S.
J 7^
2 tJ5
A 0 .-
7 S"














Mv  nut

H
i:
1 1
17
?1
:s
- O 10
1 1) HI
" i 1
I J 7
I '>5
.'if
< 7r,
I l'urt 111jrtin

7
10
21
26
o 2
1:0
31
o 3''
0 :a
1 . i
3 Ma
;o si
(' lit( ,1 S ii r mi
 llt.l
rt
i <
lrt


(f
-0 tn
1 I 1
4 '5
W/. i
j M%|	

(i
ft
'i
11
14
to
- 0 ' 1
II OS
l i'2
1 7o
2 ft a
ft aJ
M 			

1 s
.\
t_

5 7
7(i
-(I J<>
II Ml
1 .'U
1 O.I
1
\ f;
r. mi .i s K
r.uiK nt o
1 >
i 5
2o
<
20
21
-ii : 2
o ;s
1 1')
1 si
2 4')
2 'M
(Mum,.,

I
:2
<0

Id
M
-II <5
l <.J
1 1')
3 _ |
( 05 J
4 f(s
(i ] ;
I M !.-on

l')
t0
So
(il
1 1 t
I5*
-u '2
u 15
! IN
1 71
\ >!
6 01
C lIlllM. t li.lt.1

i;
);
tit

41
(til
-  .'7
ll Ml
1 4<
1
\
2 0}
('.I		 H
.1(1
17
20
W>
To-
M,
1 IS
-0 27
(i U
0 'IS
1 ;a
4 1 *
7 ;o
II ,(t I

11
.*'
t.
;t i
7 i

-( 16
' tl
0 '1 l
4 l \
C iltiiiti t. M
iii2
19
2n
14
IS
'
i
-n 24
0 {ft
0 7S
1 4 *
4 7 J
7 20
I'l-. K . .1

i
J 1

w
5c>
?n2
-d ! 7
ti
( 77
1 11
2 46
115 1 |
( i Inii.t i 11
.u (
I 1
21
IJ
til
1 lo
21 1
- II Jo
0 JO
o 7 2
0 57
1 Hi
4 lo
') 2 1
7 OS
t.,,

Mi


(l ^
>;
171
- o: i
0 V>
i :i
1 7'i
1 o1;
0 (i t 1
S " 1
1 \ ! It I tl .1 %

1 S
2 5
to
o5
1 2 i
22 1
- o 2 5
0 1 s
1 (.0
3 f 1
( il nil] .1. >il r I|n 1


t;



M
- IM J
U S7
i :t
1 M.
2
1 >>h)ts>n C
>1
7o
101
l ;u
2 jo
(12
- <1 11
O <,s
\ 12
t 'If,
* (.1
S 7o
II 1 -[ 111^ <

14
: 2
in
r>
ir,
1 M
-0 J7
0 _M
0 7o
1 r.r.
4 7 \
- - 1
S s I 
I ll l.llj llifll 1
' .|Kfs
56
71
hO
'1 i
111
1.MI
-0 1 S
I) l.s
l 13
1 ft i
J V5
4 b7
1 --.f r.'t	

I ^
j"
JS
ii
i j

- <
ti l'i
1 Jm
1 ''I
\ r.]
S iM I
1 j l-l Mil. S

6
11
17
>0
7n
ls(.
..o i s
O II 1
ii it
I :o
1 /0
Id 01
1 .1-. ,

11
.;
;
w,
ti.'
*).
- i) \3
ll ol
1 IS
J IN

5 1 'I i
1 .Itt 1 1 I'.'tl'l.l ..
12
2>>
.'(.
\\
M
1 U.
- o . i
o ; i.
II Nt
i it
\ 01
lo .<
11	I.I I'.,k '

tf
i 
4 i
i i
* t
1\l
- (i
 1.'
0 '>1
1 7n
' -11
|H o I


10
J1
IS
40
7 S
1 1 >
- o . 
o (7
1 21
1 *o
\ 00
7 o7
11 in..!, r r h'k. h
1 ft

S \
7o
ins
17il
-o 17
(1 f 7
1 1 >
1 vVJ
l 4 2
1 [.iiiii\. r 1*.
rk \
2o
l<
o;
1 l'i
2 11
Si;
 (i >,
o 2 i
.. i, i
1 7o
1 (.'
10
I- -1..

S
('
n
I"1
l i
In
ii in
H 11
i : s
J II \
5 0 5
4 12 !
} l.mon r I'
('k M
15
l
71
Jf,
loo
2; i
- 0 ^
ii 2%>
1 <
1
i a7
(i 1;
\ ,i,,

1

J
>
 7
7
- (i (.a
(I 7r>
1
1 .'(1
< 0.
*01
I'.nii'.ii i

S

)
1 1
i <
2 \
ii 12
o ;o
1 2 S
I 51
' '';
2 ol
ooj
N... j'-t O.ik

I

1
4
4

-0
0
0 '/I

\ .'li nit i

1
3
7

11
2 2
- o 5;
1 2 7
- 2 
3 (i i
o ' s
I		 It. . h

Is
'
7

in
1 |
ii i"/
 <)
1 tit
117
' ?7
3 0'>
s HI Jom* C'
(U
i
c
ti
i
11
1 ;
-n.'j
t 71
I o5
1 0$
t On
* ; 2
W s v\" ( 			
\
7
1 1
1 t
15
KS
i
- n i 

- ll 0 i
0 7:
1 22
I
2
; o2
U s \\ I h.
li
4
t,
;

14
1 6
- u in
It 7 I
I \
U > U Ch.
. ... M
U
ft
lo
!
l.s
lo
- Ol -
O 2 l
i 
1 -.
i 1'
t <.t
) 1 7
U S \\ t ....
1)
I
;
$
7
U
In
- ii n.'
ii (.ii
1 1''
J <5
< 5 ?
4 I 1
4 2 o
\\ s \\ C I.i
v." 1
5

/
1 I
i:
2 '
-1' ;;
i .'j
i i.
v ,t. h
<
\
(t

i i
\ s
- tt .ii
H (.0
: i ^ 1
[ (:
3 \ 5
5 <>2
1*. h . I.-, }.,
7 i
I.i
1?
j I
to
17
01
-ll t.
n ^ 7
I '
1 ''0
i " 
\ i '
I). It i h..
1 .p 7 5
lo
2V
J s
o;
ii
2
- 0  
'0
l :
1 7o
< i'i
6 "1
I>< ll 1 lo.tl .1,
7
j
i:
li
I?
.'5
Jtt
- n M 1
ll (>7
I
Ol
t 0 J
; W
i 'j 
1 ' ita 1 mm
-I..., 7 i
lo
lo
2n
j(.
c i
1 SI
- o i 5
o <2
ool ]
i i i
* <1
til 'J.S
1 h ll t I..* -Kv
7<,
i:
\;


;
i t
- ! II'J
d (.-t
1
1 7 7
t ll
l>. 1'a Imu,
O.p 7S
ft
11
^ 7
21
2H
s;
- 0 20
H 0s
115 i
i
J ft"
(. >*"
t a i
I It i 1 "-.t-l,
7;
i.
r
j i
_;

, ^
-tl I.'
i  :>
1 i 
1 71
S 20 |
5 v> ;
\ 5
l>. It.. 1.--
7'
0
12
I 7
2 o
2o
lo
- O \l,
tl
1 17 .
O!
t lo
1 .a s( | , \

j

tn
] ;
lr.
J 4
- u mi
ii ~i
I MJ
1 77
3 in
i < 7
1 i. , loi
7 T
7
13
10
2>
i ^
o2
- o 2*7
O ?(,
(1 Ma I
. (, 7
4 ">
7 io
1 >>t 1 i -it. -

4
)
11
]>
;

-0 Is
ii S 5
i ;i

1 .st I .

'i
1 1
1 7
2''
2'>

- o i:
II (/'
121 1
 '
3 2 o
j /./,
K.- II.1!

'/
i <
17

41
M>
-<)
U J(
II 7 5
1 I ;
4 '}
4 r.j
2 <.< '
1 isl 1 Ill-ill.
. -s
ft
15
l'
2
to
S5
- o !>
0 7o
1 20 1
* t
J al
o > i
s-" i -	 C
l.lf.l
1 t
11
\ 7

If.
S||
-ii hi
() *>|
ij:
I a <
2 I I
k... ~y ii.::

ID
14
I..
W
2 I
in
-0 I'l
o oS
1 OO 1
(;
2 7 5
7 74
>i,l.i. 

1 (

1^
$ i
(.ii
Vt
-ii n
i>
i 11
.t)l
I "S
2
4	*>4 :
5	1
7

in i CI k t
22
tO
In
1 t
S2
1.2
- o ; t

lw
11
4"
-d I1)
(1 hi
i h
2 >"
SltllM >

Id
'o
<3
; s
7a
1 ! 1
- 0 .M
0 >0
0 <> I l
(.0
< l *
I..P.L.

:$
4 i
f'
7u
1 5 ^
24*
- II 1
u 4(>
i 
-0 10
0 (..)
1 Jo 1
13* 2
Ml
* ot
' ^'
K. nt.hi

5
1 1
1 i
17
.'D
.' 1
-u.u
(1 ')l
2
2 4
3 05
1 llpl k.l

21
5o
fto
11 >
177
Jo I
- n
ll S l
I -
l 73
0ft
s.hi lit rn irilui.i

.'ti
J'l
J 7
4 1
5 S
1 .'ll
- 0 11,1
0 70
tl .' ^
1
1 n11
2 r.'.
 25
7 7 S '
Rt at. nt

0
lo
1 2
11
22
27
-tl ti
0 To
122 1
7 l
3 ftii
5 lo






U
r
-0 .'1
UM
I ; 3

b i.i lit.in uOmu
14
<5
41
>7
5ft
<>1
 u u
1 US
\ VJ 1
"l
 <><;
2











- . *> (






\%<
r.i^i
- o 2 5
I) k2
I "S 1

t pi
o '>3
pernntiks	ol ilit. sianil.irtj norma' tji-
Ifil'ti (i..ii (hit is (lu nuinlu-r .>f standard <1 
s > 11 tons 11\ %\ lii< h \  t r< >>11 11><- m< .i m
Valtu s of i!it ( \) R J or t fllui n [ r'ii i n t r.i 11..11 a
lor  <.1 win  11> >n .i( I> 11 < rt n I
lex i K of 11li.il.ilt I \ an v i ii i ii I .i Mi \
I In. h mi!i -.Ii.ih n hi ! .Mi V 11 i \ i* ,i si^(iiii
I'anl poUniiit .lpplti .Mli.n in I'lsi^u \ ilun
of ( (' A' \  a in I .iI'N V ina\ In usi > |rin .i
Cer |.on r I i.i In [i (\ I Ik.' 111< ih * i ('ii I ol \ .i r i.i t >oii
f>>r elll.ui.t t ..ii, v n (i ,i I ion sIi.miI.I In i st i ni.i 11 .1
Si U i t iwit (> t l.t ppr -pi mU l i	s .ilni. < ' l>\
(  X /Ml ll tl I Ol V^'lltloll I I III If I ll I'.IM I <v. rati) ! ht> m.w Lv
doiit from p.ist i \ | k r k m. f or iisiii^ tin.' rc-ulla
from oilier similar Ir<..x(mi ni pliuis \ ilix s
ol co iti(11111 ol variation (or ii'luvtu
s? lor soiiu* (rutiiHtil plants are ^i\'ii tit
TaMe {( I tuplir.itioixs <|i rM .1 irm l.tl.U \
 If. l>t(	I r\ .III IS.IIllpIt
1 o hj \ Vj't rt Ii.il m)i 11 tli.it 11.) in ii t not i
 oiu i ii t rj 11, .ii i > 1.1| u.i! (ooflishilitn i i i r
f .ii n ii ,i ihl.i ril V, ii lu n I \ Ii .r l I.i plau i is
i stiui.iUi) to t>i 0 70 (hi plant slii' 12 i l.t
ilivpiul for tin nii.wi \ i I Hi upi.d ( <>i
liss l)iJil 0 U V, (If \, U) inn I,
tliin average Mol) U 1 J . *0 - 1 o
ing/l or !c> Similarly, for a Ii ss stringent
standard <( \. = 4LI	.i x r i^t l.itii
 0 43 X 40 = I 7 1 iiij;/' ,r I*
;\b Mould i'X|c<" ti i
v ,i r i.i ( ioi i mi tllluini ioiu i ii(r.iln>n
/ fli n I.i It. .'is|n|-i iii l.ihlt \ i.im Ik uiucd
in .i sli^'idv 111; 11 r<.111 uiiili'M	ji-iiImil;
I al'lc \ I Hr tin fr.u (i-ni.il f11i.ilnlit\ t< r
ililui til t mil i ii t r.i lu.n is |ifiMii!l t> .i luiti-
tioii of I \ ,i ill (In rin tn lo >i.iiiil.iri' i<>n
I  11(1 I tied ! i tlo (Moll' t Ii j t t In a I .1 t li Is i ; ll.ll
tn t '< 'A' \ .Jui si /,', -.iiJis fro/n i il'! \ I if .ii
I i 11 i  I (.  < at i m.t (t i hi 11li.il .|| i ..I ,i 11 < ,.i
incnt pl.tn( under operation if rhc nu.in .uul
alattil.ird ill i i.i 11   11 I r (hi jilml u kmnni
I or i\.iinplv, ilu-ri' is , f <. lu I.il 11 \ in .i pl.mt
opt ruling illi a ini.ui \aliu- nt 0 0 ami
a l'\ 0 70 In iiilur u..r>!i nt a ti>^ run
opera t ion. a I hi u t If, ol t hi . .1 m 'i  i j i ill in n t
v i r i iMi % w on l< I t m 11 il "1 im1 I in a pi in (
opiratinu with mu ,o- v.tliti ol l> in^ I an
journal Wl'CK, Vol 51. N'o 12.
Itoilur It)T
-------
CT>
J,
o
Si
cc
I-
z
LU
o
z
o
o
NPDES
ACTUAL OPERATING
DATA-HOVEY ET AL
''O
17mg/l
4.2 mg/l
100
365
LOG TIME (days)
FIGURE 6-I9

-------
30
JAN. 79 -AUG. 80 DATA
30-DAY AVERAGES
15 
10 
5 
-fc A A
A-A A
DISCHARGE LIMITATION I4mg/I
A A
J	L
J	L
2	5 10 20 30 40 50 60 70 80 90 95 98
% OF TIME EQUAL TO OR LESS THAN
FIGURE 6-20
VARIABILITY IN EFFLUENT BOD AND SS

-------
9
E
in
O
O
CD
2
UJ
n
_i
L_
Ll
UJ
25
.20
10
SUMMER

TEMP =28C
PERMIT LIMITS - B0D5
 FLOW : 46 mgd
MONTHLY AVG.= 3500 Ibs/d
B0D5 : 5.8 mg/ 1
DAILY MAX.: 7000 Ibs/d


AV0. PERMIT LIMIT -J
/
y
II II 1 I 1 1 1 1 1 II 1 1
20 30 40 50 60 70 80 90 95 98 99
o
E
in
o
O
CD
t-
Z
UJ
3
_l
Li.
U.
Ul
o>
o
Q
o
co
ui
3
_l
li.
U_
Ul
SPRING AND FALL
TEMP - 23C
FLOW - 39 mqd
B0D5 :7.3mg/l
ftVG PERMIT LIMIT
20 30 40 50 60 70 80
90 95 98 99
WINTER
TEMP = I4C
FLOW = 3lmgd
B0Ds= 10.8 mg/ I
AVG. PERMIT LIMIT
5 10 20 30 40 50 60 70 80 90
PERCENT LESS THAN OR EQUAL TO
98 99
FIGURE 6-21
EFFLUENT B0D5 BY SEASON
JUNE I, 1979  MAY 31,1980

-------
A Statistical Documentation of the Performance of Activated
Sludge and Activated Stabilization Basin Systems Operating in the
Paper Industry by the National Council of Air and Stream Impact
29th Purdue Industrial Wastes Conference 1974 was conducted.
This study looked at 53 treatment systems in 7 manufacturing
processes classifications. Figures 6-22 and 6-23 summarize the
ratio between long term average effluent and 30 day average and
maximum, day for which permit standards are typically set.
The recently requested GAO survey of 242 randomly selected
municipal plants found that 87% of the plants violated their
NPDES permit for at least one month in the year, and 31% were in
serious violation (exceeded permit limit in at least one category
BOD TSS or fecal coliform for more than 4 consecutive months) .
Non-compliance was attributed to various factors including
deficiencies in design (inadequate capacity) operation and
maintenance, and equipment, and overloading by
infi 1 tration/inf 1 ow or industrial wastes. Non compliance was not
related to potentially unreal i st ical 1 y low permit limitations.
While the serious violations undoubtedly should be rectifiable,
more consideration might be given to the problem of the
occasional violation, and its significance with respect to effect
on a receiving stream and the cost to increase reliability to the
point that such violations are rare. This would be part of
realistic overall .allocation of loads based on water quality
requirements, treatment capability, cost factors and various
other tangible and intangible factors effecting treatment
performance.
A study conducted for the EPA, "Evaluation of Operation and
Maintenance Factors Limiting Biological, Wastewater Treatment
Plant Performance" (EPA 4002-79-078 ) reviewed thirty plants to
determine causitive factors of limited performance. Table 6-7
presents actual performance data for the plants studied.
Numerous problems in areas of design capacity, operation and
maintenance were identified. Major problems were improper
operator application of concepts and testing to process control,
infiltration and inflow and industrial loading. It was estimated
that compliance with NPDES permit limitations could be
significantly increased as a result of implementing improvements
in operational practices. Figure 6-24 from this report related
0/M unit cost to size of plant.
6-'4 4

-------
2.
2 .6
2.4
2.2
2.0
1. 8
1.6
1. 4
1.2
1.0
e r	
i
J f DATA AT

1 / 3.28,. 910

/ 3.65, .936

/ 3.90,.960
-
J 6.21,.985
1 J

ui
 1
 /
1 j
O
 /
or

>
j
-i *
.'7
__ <
/
z
J
<
/
s
j
o
/
o
//
K) ,
j
s
(
	 IL /

0 /

o j

V- /

a J r
jy

/
FIGUPE 3
/ 
BI'O-TREATflENT
/ *
EFFLUENT QUALITY
/ 
VARIABILITY
/

/ 
RATIO OF MAX. DAY '
/ i
1 1 1 1 1 1
TO MA30CD
I I , I , I I I I I J.
10. C
9 .C
..01 .10
.50	.80 .90 .95 .98 .99 .995
FRTOIT.MCY or OCCURRENCE (CUflDLE DISTRIBUTION)
. 999
2 . 0 _
1.0
DATA AT
11.1..985
FIGURE 4
BIO-TREATMENT
EFFLUENT QUALITY
VARIABILITY
(M)
RATIO OF MX. DAY
TO Al!:i. AVG.
.50	.80 .90 .95 .98 .99 .995
FREQUENCY OF OCCURRENCE (OUMrtLE DI KTR111UT I ON )
.999
FIGURE 6-22

-------
2. I
2.6
2. 4
2.2
2.0
1. 8
1. 6
1. 4
1.2
1. 0
DATA AT
3.	45, .960
4.	22,. 985
FIGURE 5
BIO-TREATfiENT
EFFLUENT DUALITY
VARIABILITY
dD
RATIO OF HA30CD
TO Af'H. AVG.
I N I i I  I I
2 .
2 .
.01 .10	.50	.80 .90 .95 .98 .99 .995
frequency of occurrence (gumdle distribution)
.999
2.2
2. 0
1.
1. 6
1.4
1. 2
1.0
8			
1
-
data at
6 -
1
/ 3.25,.910

/ 3. 4 5, . 9 3G

/ 3.90,.960

/ 5.fiO,.985
4 -

2 
1 * /
o
  /
u
* /
ro
,/
Z
./
>- e
 J
/
>
/
/
o
I
2

3 /
2 J

 < :J

5 /

u. /

 /

O [

t- [
& /

/
 a: J

J 
/ 
_ / i
FIGURE 6
/
/
BIO-TRCAThENT

EFFLUENT DUALITY
'/
VARIABILITY
 r~
ME AN
(sT)
-
RATIO OF flAX. DA
1
1 I 1 I 1 1
TO MA50CD
11,1,11 III 1
.01 .10	.50	.80 .90 .95 .98 .99 .995
FREQUENCY OF OCCURRENCE (CUDDLE D I STRI DUT I ON )
.999
FIGURE 6-23

-------
o
4a
Plant
So.
Average
Flow (mJ/t!)
TABLE. 6-7
TWt:fi=iS-. CURRENT WHIAL F.FFLIIT.'.'T CHARACTERISTICS OF PRELIMINARY EVALUATION PLANTS
Average
Flow fmgd)
Average
BOPg Cone.
(ixjl/1)
Average
BOO- Load.
(Kg/day)
Average
BOP5 Load.
fib./day)
042
1 , 520
0. 55
23
36
SO
057
1 .950
0.51
16
- *>
70
102
(N'/A)
(N/A)
(V\)
(N/A)
(N" / A)
005
570
0 15
14
9
20
0S6
1. -180
0. 59
30
4 5
100
052
1 I,560
5.0
i:
136
50
059
54.820
9. 2
32
1 , i 1 *
2,455
024
4 .920
 1 5
ir
34
1 S5
03S
17,030
1 5
95
1 ,617
3, 565
093
22.350
5 9
2 2
:^0
1 ,030
082
4 , 240
1 12
16
(>S
150
005
:, 080
0 35
22
4 5
ion
0JS
15,350
4 . 05
35
5 35
1 , 130
0S9
1,4 00
0. 57
13
20
4 5
095
1 , 140
0. 50

J 1
90
120
11,500
2.72
5
5 -
115
054
1.210
0. 32
(i
27
60
06S
1 ,850
0.4 9
S
16
35
071
4 , 550
1 15
10"
4 65
I ,025
077
4,540
1 . 2
29
132
290
021
3, 350
0.SS'
0
20
45
026
24,980
0.6
w
9 23
2,035
046
910
0.24
30
:7
60
114
40,500
10.7
7
284
6 25
106
11,310
3. 12
25
295
650
053
8,330
 2
> 7
134
403
074
2,460
0. 65
33
9 5
205
0S5
33,4 20
S. 83
12
401
885
066
1. 250
0. 35
15
IS
4 0
07S
3, 530
0. 38
25
84
1S5
Average
S. S. Cone .
(mg/1)
52
18
(VA)
55
53
21
55
IP
57
11
26
21
"59
4 7
24
10
50
21
50
19
?
62
19
in
44
"> r
25
25
21
15
Average
S. S. Load
(Kg/day)
68
95
(VA)
18
IS
2 38
1.218
2-13
630
9 1 '1
127
13
905
66
21
105
56 .
59
152
86
25
1 ,549
17
<10-1
519
209
56
836
25
50
Average
S. S Load
(lb./day)
150
205
C'-VA)
10
105
5:5
:,6ss
535
1 ,590
2,015
2 SO
95
J ,95
145
60
231
SO
S6
290
190
50
3,'115
33
890
1 , 145
124
1 , 84 2
55
110
S'PPCS Permit
Comp1i anee
BOO S.S
^ es
Yes
Ye?
Yes
\'o
No
\ OS
>	cs
"10 5
^ e
>	cs
N'o
'i e<
\o
es
^ c-
^ e
\0
Yes
U-s
Yes
"i es
les
Yes
Ye 5
No
Yes
Yes
Yes
No
'.0
No
So
No
\'o
No
NO
\ e s
c*
No
No
U-N
> c?
1 L'S
U'S
"ICS
Yes
Yes
No
1 CS
Ye*
\o
Yes
.No
Yes
Yes
2^2.5 20
72.0
20.8
, 294
16,080
32 .0
S.72S
19,235

-------
O ACTIVATED SLUDGE
B TRICKLING FILTER
SIZE OF PLANT (MGD)
FIGURE 6-24
RELATIONSHIP BETWEEN OPERATION
AND MAINTENANCE EXPENDITURES AND DESIGN PLANT FLOW

-------
Re fer ences:
(1 ) Performance of Activated Sludge Process and Reliability rfased
Design, JWPCF, Dec. 1979 .
JWPCF Monitor-GAO Survey Finds Extensive Treatment Plant
Non-compliance, p. 137, February 1981.
6-49

-------
NUTRIENT REMOVAL
I. MAJOR NITROGEN REMOVAL PROCESSES
The major processes considered in this manual are
nitrification-denitrification , breakpoint chlor ination (or
supe r chl o r ina t io n) , selective ion exchange for ammonium removal,
and air stripping for ammonia removal (ammonia stripping). These
are the processes which are technically and economically most
viable at the present time.
Biological N itrification-Denitrificotion
Biological nitrification does not increase the removal of
nitrogen from the waste stream, over that achieved by conventional
biological treatment. The principal effect of the nitrification
treatment process is to transform ammcn i a-n i t r og en to nitrate.
The nitrified effluent can then be denitrified biologically.
Nitrification is also used without subsequent biological
denitrification when treatment requirements call for oxidation of
ammonia-nitrogen in the secondary stage or is removed by anotner
process. Nitrification can be carried out in conjunction with
secondary treatment or in a tertiary stage; in both cases, either
suspended growth reactors (activated sludge) or attached growth
reactors (such as trickling filters) can be used.
Biological den i tr i f ica t io n can also be carried out in eitner
suspended growth or attached growth reactors. As previously
noted, an anoxic environment is required for the reactions to
prcce^d. Overall removal efficiency in a nitrification-
den itrification plant can range from 70 to 95 percent.
Breakpoint Chlorination
Breakpoint chlorination (or superchiorination) is
accomplished by the addition of chlorine to the waste stream in
an amount sufficient to oxidize ammon i a-n i tr og en to nitrogen gas.
After sufficient chlorine is added to oxidize the organic matter
and other readily oxidizable substances present, a stepwise
reaction of chlorine with ammonium takes place. The overall
theoretical reaction is as follows:
3CI2 + ^Nil^	> N 2 + 6HC1 + 211
In practice, approximately 10 mg/'l of chlorine is required
for every 1 mg/1 of ammonia-nitrogen. In addition, acidity
produced by the reaction must be neutralized by the addition of
caustic soda or lime. These chemicals add greatly to the total
6-50

-------
dissolved solids and result in a substantial operating expense.
Often dechlorination is utilized following breakpoint
chlorination in order to reduce the toxicity of the chlorine
residual in the effluent.
An important advantage of this method is that ammonia-
nitrogen concentrations can be reduced to near zero in the
effluent. . The effect of breakpoint chlorination on organic
nitrogen is uncertain, with contradictory .results presented in
the literature. Nitrite and nitrate are not removed by this
method .
Selective Ion Exchange for Ammonium Removal
Selective ion exchange for removal of ammonium from
wastewater can be accomplished by passing the wastewater through
a column of clinoptilolite , a naturally occurring zeolite which
has a high selectivity for ammonium ion. The first extensive
study was undertaken in 1969 by Battelle Northwest in a federally
sponsored demonstration project. Regeneration of the
clinoptilolite is undertaken when all the exchange sites are
utilized and breakthrough occurs.
Filtration prior to ion exchange is usually required to
prevent fouling of the zeolite. Ammonium, removals of 90-97
percent can be expected. \ Nitrite, nitrate, and organic nitrogen
are not affected by this process.
Air Stripping for Ammonia Removal
Ammonia in the molecular form, is a gas which dissolves in
water to an extent controlled by the partial pressure of the
ammonia in the air adjacent to the water. Reducing the partial
pressure causes ammonia to leave the water phase and enter the
air . Ammonia removal from, wastewater can be effected by bringing
small drops of water in contact with a large amount of
ammonia-free air. This physical process is termed desorption,
but the common name is "ammonia stripping."
In order to strip ammonia from, wastewater, it must bp in the
molecular form (NH^) rather than the ammonium ion (NH^) form.
This is accomplished by raising the pH of the wastewater to 10 or
11, usually by the addition of lime. Because lime addition is
often used 'for. phosphate removal, it can serve a dual role.
Again, nitrite, nitrate, and organic nitrogen 1 are not affected.
The principal problems associated	with ammonia stripping are
its inefficiency in cold weather,	required shutdown during
freezing conditions, and formation of	calcium carbonate scale in
the air stripping tower.
6-51

-------
The effect of ccld weather has been well documented at the
South Lake Tahoe Public Utility District where ammonia stripping
is used for a 3.75 mga tertiary facility. The stripping tower is
designed to remove 90 percent of the incoming ammonium during
warm weather. During freezing conditions, the tower is shut
down. One mechanism of scale formation is attributed t the
carbon dioxide in the air reacting with the alkaline wastewater
and precipitating a-s calcium carbonate. In some instances,
removal with a water jet has been possible; in other applications
the scale has been extremely difficult to remove. Some factors
which may affect the nature of the scale are: orientation of air
flow, recirculation of sludge, pH of the wastewater, and chemical
makeup of the wastewater.
Other Nitrogen Removal Processes
In addition to the processes listed above, there are other
methods for nitrogen removal which might usefully be discussed.
Most are in the experimental stage of development or occur
coincidentally with another process.
Use of anionic exchange resins for removal -of nitrate was
developed principally for treatment of irrigation return waters.
Two major unsolved problems are the lack of resins which have a
high selectivity for nitrate over chloride and disposal of
nitrogen-laden regenerants.
Oxidation ponds can remove nitrogen through microbial
denitrification in the anaerobic bottom layer or by ammonia
emission to the atmosphere . The latter effect is essentially
ammonia stripping but is relatively inefficient due to a low
sur face-vol ume ratio and low pH. In a study of raw wastewater
lagoons in California, removals of 35-85 percent were reported
for wel 1 - ope r a ted lagoons.
Nitrogen in oxidation ponds is assimilated by algal cultures.
If the algal cells are removed from the pond effluent stream,
nitrogen removal is thereby effected. Methods for removal of
algae are summarized in the EPA Technology Transfer Publication,
Upgrading Lagoons.
It was noted previously that in secondary biological
treatment and in nitrification, some nitrogen is incorporated in
bacterial cells and is removed from the waste stream with the
sludge. If an organic carbon source such as ethanol or glucose
is added to the wastewater, the solids production will be
increased and a greater nitrogen removal will be effected.
Disadvantages are that large quantities of sludge are produced
and that difficulties occur in regulating the addition of the
6-52

-------
carDcn source, with high effluent BOD^ values or high nitrogen
levels resulting .
Summary
Table 6-8 summarizes the effect of various treatment
processes on nitrogen removal. Shown is the effect that the
process has on each of the  three major forms: organic nitrogen,
ammonium, and nitrate. In the last column is shown normal
removal percentages which can be expected from that process.
Overall removal for a particular treatment plant will depend on
the types of unit processes and their relation to each other.
For example, while many processes developed for nitrogen removal
are ineffective in removing organic nitrogen, incorporation of
chemical coagulation or multimedia filtration into the overall
flowsheet can result in a low concentration of organic nitrogen
in the plant effluent. Thus, the interrelationship between
processes must be carefully anlyzed in designing for nitrogen
removal .
6-53

-------
TABLE 6-8
EFFECT OF VARIOUS TREATMENT PROCESSES ON NITROGEN COMPOUNDS

Lffect on constituent
Hemov.-jl of
total nitrogen
Treatment process
Organic N'
NH3/NII4
NO3
entering process,
perron;''
Conventional treatment processes
Primary
Secondary
1 0-20% removed
15-2 5% remover^
urea NH3/NH4
no effect
1 0%, removed
no effect
nil
5-10
1 0-20
Advanced wastewater treatment processes
nitratlonc
Carbon sorption
Electrodialysis
Reverse osmosis
Chemical coagulation0
30-95% removed
30-50% removd
1 00% of suspend
organic N removed
1 00% of suspend
organic N removed
50-70% removed
nil
nil
40% removed
85% removed
nil
ml
nil
40% removed
85% removea
ni)
20--10
10-20
35-45
80-90
20-30
Land application
Irrigation
Infiltration/percolation
. NH3/KH4
NH3/NH4
NO3
-* plant N
-* NO3
-* plant N
 n2
40-
-------
4.	Martin, D.M., and D.R. Goff, The Role of Nitrogen in the Aquatic Environment.
Report No. 2, Department of Limnology, Academy of Natural Sciences of Phila-
delphia, 1972.
5.	Sepp, E., Nitrogen Cycle in Groundwater. Bureau of Sanitary Engineering, State of
California Department of Public Health, 1970.
6.	McCarty, P.L., et al, Sources of Nitrogen and Phosphorus in Water Supplies. JAWWA,
59, pp 344 (1967).
7.	Sylvester, R.O., Nutrient Content of Drainage Water for Forested, Urban, and
Agricultural Areas. Algae and Metropolitan Wastes, Robert A. Taft Sanitary Engineer-
ing Center, Tech. Rep. W61-3, 1963.
8.	Reeves, T.G., Nitrogen Removal: A Literature Review. JWPCF, 44, No. 10, pp
1896-1908 (1972).
9.	Nitrogenous Compounds in the Environment. Hazardous Materials Advisory Com-
mittee (to the EPA), EPA-ASB-73-001, December, 1973.
10.	Kaufman, W.J., Chemical Pollution of Ground Waters. JAWWA, 66, No. 3, pp 152-159
(1974).
11.	Weibel. S.R., Anderson, R.J., and R.L. Woodward, Urban-Land Runoff as a Factor in
Stream Pollution. JWPCF, 43, p 2033 (1971).
12.	American Public Works Association, Water Pollution Aspects of Urban Runoff.
FWPCA Report No. WP-20-15, January, 1969.
13.	Bum, R.J., Krawezyk, D.F., and G.T. Harlow, Chemical and Physical Comparison of
Combined and Separated Sewer Discharges. JWPCF, 40, pp 1 12 (1968).
14.	Avco Economic Systems Corporation, Storm Water Pollution From Urban Land
Activity. EPA Report No. 1 1034 FKL 07/70, July, 1970.
15.	Weibel, S.R., et al.. Pesticides and Other Contaminants in Rainfall and Runoff.
JAWWA, 58, pp 1075 (1966).
16.	Dept. of Biological and Agricultural Engineering, North Carolina State University at
Raleigh, Role of Animal Wastes in Agricultural Land Runoff. EPA Report No. 13020
DGX 08/71, August 1971.
17.	California Department of Water Resources, Nutrients From Tile Drainage Systems.
EPA Report No. 13030 ELY 5/71-3, May 1971.

-------
Biological Nitrification
NH4 + 2 + HC03 	> c5H7n02 + H2 + N03 + H2C03
1.	Oxygen Required ^ 4.5 lbs O^/NO^-N produced
2.	SIudg e Yield
Nitrosomonas 0.04 - 0.13 lbs VSS/lb NH^ ox id.
Nitrobacter	.02 - 0.07 lbs VSS/lb NO^ oxid.
3.	Alkalinity Destroyed
7.14 mg A1 k. per mg NH^-N oxidized
4.	pH	> 6.5 to 8.5
5.	Temperature
k = k e1"20
T 20
9 = 1.1 t0 1.3 Activated Sludge
6.	Sludge Age - (Figure 6-26)
6-10 Days @ 20cC
Nitrification of municipal wastewaters can readily be
accomplished in single or 2 stage activated sludge plants and in
low rate trickling filters. Figures 6-27 and 6-28 show the
treatment of 32 mgd in a single stage activated sludge plant and
of 4 mgd in a low rate trickling filter plant at Flint, Michigan.
Nitrogen balances developed during a 30 day evaluation Deriod i
shown on Table 5-9.
6-56

-------
25
20
\ '5
CTi
s
+ *
1
s
K
2
ki
-J
li-
lt
ki
10

1 ^   f  	I" ' ~"l "
|
1~

/



PERCENT REMOVAL


_
1


-
1 /-EFFLUENT AMMONIA

-
-
V -
	1	L_ 1
1
1
10	15	20	25
DESIGN SOLIDS RETENTION TIME, DAYS
30
100
90
80
70
35
S
Uj
o
Ct
Uj
0.
>.
O
60 S
50 t
vu
40
30
20
10

O
K
n
o
ct
FIGURE
EFFECT OF SOLIDS RETENTION
CONCENTRATION AND NITR
6-26
TIME ON EFFLUENT AMMONIA
I FI CATION EFFICIENCY

-------
100,
UJ
o
O
tr.
t-
o
2
<
<
>
o
5
UJ
T
30- DAY
DESIGN
oi	0 2	0.3	0.4	0.5
F/M (gm B0D5/gm MLSS-doy )
30
z
I
m
I
Z C
H \
Z V
LJ E
3 
_l
L-
U.
UJ
2 5
20
1.5
1.0
0.5
30-DAY
F/M  0 125
EFF KIHj-N= 0 08 mg/I
I
DESIGN F/m= 0 2
EFF NHj-N < 0 2 mg/l
# /

 r	.
01	0.2	0 3
04	05
F/M (gm BODj/gm MLSS-doy)
06
FIGURE 6-27
AMMONIA REMOVAL CHARACTERISTICS
ACTIVATED SLUDGE

-------
100
<
>
o
2
UJ
cr
2
I
K)
X
4 0 6.0 8.0 10 0 12 0 14 0 16.0
BOD LOADING (lbs/day / 1000 ft3)
18 0 20 0
5.0
INFLUENT BOD/DETENTION TIME (mq/l/dav)
FIGURE 6-28
AMMONIA REMOVAL CHARACTERISTICS
TRICKLING FILTERS

-------
TAB LE u-y
NITROGEN BALANCE
(3 0-Day Average)
N i trogen
(1)
Org anic
Amm.on ia
Nitrite
Nitrate
(2)
(mg/1)
(mg/1)
(mg/1)
(mg/1 )
R aw
y. 5
12.0
0 . 0
0 . 0
(3)
Pr imary
Effluent
13.1
13.5
0 . 04
0.0 7
f r i c kl l ng
Filter
Effluent
1.8
1.1
0 .05
13.5
Ac t i v a ted
Siudg e
Effluent
i . a
0 .08
0 . 02
14.4
Tctal N (mg/1)	21.5	26.7	16.6	15.3(4)
Total N (Ibs/d)	-6,560	y,Q8 5	5 50	4,4 30
1.	Nitrogen species; concentrations expressed as nitrogen.
2.	Computed as the difference between TKN and NH-^-N.
3.	Sludge return streams not included in Raw.
4.	Concentration in microstrainer washwater and soluble component of
sludge waste streams. At a flow of 4.2 mgd , this is equivalent to
570 lbs N/day.

-------
INDUSTRIAL WASTES
Nitrifying autotrophic organisms are more sensitive to
environmental conditions and toxic inputs than are the
heterotrophics. However, many industrial wastewaters can be
nitrified.  Table 6-10 summarizes information developed from
studies performed by HydroQual on a variety of wastes. All wer'e
designed as single stage activated sludge systems except Case F
and I where 2 stage systems were required due to toxicity effects
of raw waste. Toxic materials were removed in the first stage
system. Figure 6-29 presents the removal rate of TKN and ammonia
for the latter case.
Figure 6-30 shows the hydrolysis of organic nitrogen to
ammonia and the oxidation to nitra.te developed from a batch
laboratory experiment on an industrial wastewater.
Ammonia is oxidized to nitrite and then to nitrate. The rate
limiting step is generally the oxidation to nitrite, hence the
effluent from a nitrification process is predominantly nitrate
witn little nitrite.' In some cases with industrial wastes
containing high concentrations of unoxidized nitrogen oxidation
proceeds only to the nitrite form. This appears to be due to
inhibition caused by un-ionized ammonia concentration. Limited
information is available and further investigation is necessary
to confirm these observations (Figure 6-31) .
Rotating Biological Contactors (RBC)
Nitrification in RBC systems can be shown from an analysis of
the Gladstone, Michigan treatment plant. The plant was operated
as a six stage unit in series. The physical dimensions of the
plant are as follows:
1.	Bio-surf Media Diameter, D = 3.6 meters
2.	# layers/stage	= 95.2
3.	Wetted surface area/stage
(SURF)	= 4.3,000 ft2
4.	Rotational speed, u	= 1.65 rpm
Figure -6-32 presents the observed BOD , oxygen and nitrogen
profiles through the plant. Figures 6-33 aVid 6-34 are calculated
profiles of the biological distributions and mechanisms of
nitrogen removal through the plant.
6-61

-------
TALSLt 6-iU
EXAMPLES UF BlULUblCAL HIIKIFICrtTIOW







U1 1 Krt1E AND









hi 1 r K1 IE
HVEKhuE
trFLuEN1



--INFLUENT--

LOADING KAIE
SLUUbE
PHULiUCTI ON

UO^-N


BUU
OKbANlC N
NH^-N
HI DAY bOU
Abt
rfN/UMY
nH^-n
ull^-N
^STE source aiju strength

(mg/l )
(mg/l )
(mg/l)
W1LSS
(UaYS)
ti rILSS
(mg/l)
(mg/l)
. DOMESTIC WASTES
150-220
12-18
15-20
0-1-0-3
b-18
U-02-0-03
o-l
12-20
I. INDUSTRIAL WASTES









A  ORGANIC ACIDS

300
3-8
25
0-12
11 -2b
0-01
LOW
30
B- PHARAMCEUT1CAL AND ORGANIC
CHEM1CALS
250
80
25
0-05-0.1
>20
0-01
2
54
C- SYNTHETIC FIBERS AND POLYMERS
1, ouo
80
LOW
0-15
>20
0- 0U3
5
18
D- SYNTHETIC FIBERS

5, 000
700
50
0-17
30 +
0-U17
2
5u0 +
 NYLON

2,850
200
50
0-15-0-2
>10
0-012
'2
23U
F- PHARMACEUTICAL AND ORGANIC
CHEM1CALS
1 200
75
625
0-02
>20
0-05
50-100
3uu-'iuu^
G- INORGANIC WASTES

10
0
500-100U
0
>3U
0-2
<1
5U-100U
H- SLAUGHTER HOUSE " BEEF

400
30
50
-05
>30

<1
bU
" CHICKEN

500
20
30
 1
>3U

<1
4U
I- ORGANIC CHEMICAL/PESTICIDE
MFR  1
500

100
<0-1


<5
8U
1-SECOND	STAGE OF TWO"S T AGE SYSTEM
2-PHEDOHINANTLY	NU2

-------
16
to
10
>
_l
2
s
w
z
<
>
o
2
UJ
CC
Z
st:
I-
.14
.1 2
.10
.08
A AO
A A A.
V A
.06
AP
4
A

A A
.04
.02 -
.00
FIRST ORDER
ZERO ORDER
A	A
A
PHASE n- PILOT STUDY
AVG. T = 2IC
A DAILY DATA
A WEEKLY AVERAGE
O DAILY BENCH UNIT DATA
10 20 30 40 50 60 70 80 90 100 NO
EF FLUENT NHj-N (mg / I )
.1 6
o
i
to
CO
>
x
z
<
>
o
5
UJ
QC
z
o
5
<
.1 2
A A
*A
.02
.00
FIRST ORDER
OAr-
A A
ZERO ORDER
A A
A
J	L
10 20 30 40 50 60 70 80 90 100 NO
EFFLUENT NH^-N (mg/l)
FIGURE 6-29
TKN AND AMMONIA REMOVAL

-------
400
INITIAL ORG -N = 41 MG/L
MLSS - 2200 MG/L
O
Q
O
O
~ INITIAL ABSORPTION
* .+
200
200
c
"0
H
>
100 m
4	6
TIME -HOURS
10
0
80
INITIAL 0RG-N = 41 MG/L
T = 2 0 C
60

S 40
(S>
o
cr
h
0 33 GM 0RG-N
GM S5-Doys
Z
0.034 GM NH,-N
20
GM SS- Days
0RG-N O
TIME -HOURS
FIGURE 6-30
BATCH EXPERIMENT
SYSTEM No. I

-------
A
A
INHIBITION
NOz >> I mg /1
o7
NO2< Img/1
.008
.004
LEGEND:
O- DOMESTIC WASTE
A- INDUSTRIAL WASTE
0.2
0.4 0.6 0.8 1.0	2.	4. 6. 8. 10. 20
TOTAL AMMONIA, mg/l (N)
40 60 80 100
FIGURE 6r 31
UNIONIZED AMMONIA - NITRITE EFFECTS

-------
60



f, =2.0

~ 50


s.
II
t
*
6 40
r\ Sim=50
s
o>

J\
e
 30
~ \s
z
O

1
CD
\

. 20
 T
+ *
_j
\ (J)
X
o

z
OT 10



B~"~ J-i n

0
l i l I i i i

o>
E
UJ
o
>
X
o
o
LlI
>
_1
o
V)
V)
12
10
8
6
4
2
0
2 3 4
STAGE
= 0.02

a | = o. 8

b , =0.15

S3 m =

fT^
n
X
1 ! 1 I I
= 0.04
o 20
"> 10
STAGE
0 = 0.89 gpd /ft2
TEMP. = 15.4 C
2 3 4
STAGE
FIGURE 6-32
PRELIMINARY CALIBRATION - DATA SET 2

-------
100
80
z
o
3
m
cc
60
HETEROTROPHS
h-
CO
Q
40
AUTOTROPHS
x
i-
i 20
o
tE
O
STAGE
Q = 0.23 MGD
Q = 0.89 gpd / f t
T = 15.4 C
FIGURE 6-33
GROWTH DISTRIBUTION FOR DATA SET 2

-------
AMMONIA STRIPPING
o>
DEN! TRIFICA TION
NET GROWTH
I
5
3
4
2
6
STAGE
FIGURE 6-34
DISTRIBUTION OF TOTAL SOLUBLE NITROGEN REMOVAL
FOR DATA SET !

-------
II. DENITRIFICATION
The biological process of denitrification involves the
conversion of nitrate nitrogen to a gaseous nitrogen species.
The gaseous product is primarily nitrogen gas but also may be
nitrous oxide or nitric oxide. Gaseous nitrogen is relatively
unavailable for biological growth, thus d en i t r i f i ca t i o n converts
nitrogen which may be in an objectionable form, to one which has
no significant effect on environmental quality.
Denitrification is a two-step process in which the first step
is a conversion of nitrate to nitrite. The second step carries
nitrite through two intermediates to nitrogen gas.
An,organic carbon source is required as an energy source in
the reaction. BOD in the wastewaters or an external source such
as methanol can be utilized.'
6-69

-------
III. PHOSPHORUS REMOVAL
Tne Chemical Removal c. f phosphates from wastewaters
essentially involves two steps: (1) insolubilization or
precipitation of the phosphate species by the addition of a metal
salt, and (2) separation of the resulting chemical sludge.
Wnereas the choice of coagulant and point of application are
mainly dictated by economic factors, the conditions of proper
coagulant dosage, and pH range are governed by the relevant ionic
equilibr ia.
The degree of inso 1 ub il i za tic. n of phosphates is controlled by
the concentration or applied dosage of metal ion (Law of Mass
Action) . In otner words, the greater the quantity of metal
coagulant added, the more phosphate will be removed from solution
v until some minimum (non-zero) concentration is attained.
The second factor which control the extent of phosphate
precipitation is the pH or hydrogen ion concentration. The pH is
an extremely important consideration in the chemical
precipitation of phosphorus since hydrogen and/or nydroxyl i^ns
may enter into either the primary (in the case of Ca T)
in so 1 ub il i za t io n reaction or other competitive precipitation or
complexation reactions. As a result the coagulant may be
partially or completely consumed by these competitive reactions
and the phosphorus removal efficiency accordingly reduced.
Implicit in the foregoing considerations is tne fact that the
selection of coagulant, proper dosage, and optimum. pH is strongly
influenced by the ionic composition of a given wastewater. As a
consequence, these factors must be independently determined in
each case .
6-70

-------
TAB Lo 5-11
Ca
+ +
Fe
+++
Al
+ + +
Fe
+ +
TYPICAL CHEMICAL COAGULANTS
FOR
PHOSPHORUS REMOVAL
Typical Dose
1-3
1-3
2-3
1-3
(1 )
Optiirum pH
11
5.3
6.0
Sludge Prod
variable
2-3
3-5
2-3
(1)	Moles cf Metal/Mcle cf P
(2)	ing Sludge/rrg Metal

-------
BIOLOGICAL NUTRIENT REMOVAL
BARDENPHO PROCESS
Bardenpho Process was developed by James L. Barnard and its
initial use occurred in South Africa. Several installations have
been built in this country. The process basically provides
biological removal of BOD, nitrification, denitrification and
phosphorus without the additions of chemicals. The process is
schematically shown on Figure 6-35. Basic principals to
highlight are:
1.	Anaerobic zone required to obtain subsequent P uptake by
biolog ical sol ids .
2.	Anoxic zone which receives high recycle of nitrified waste.
BOD of raw waste waters provide organic carbon for
denitr ification.
3.	Nitrification F/M ~ 0.1.
4.	Further denitrification if low NO^ is required in effluent.
Table 6-12 presents a cost comparison prepared by Bendick and
Dallane on the Bardenpho process and several advanced waste
treatment processes for a 1.4 mgd plant.
PHOSTRIP
Descr ipt ion
"Phostrip" is a combined biological-chemical precipitation
process, Figure 6-36, based on the use of activated sludge
microorganisms to transfer phosphorus from incoming wastewater to
a small concentrated substream for precipitation. The activated
sludge is subjected to anaerobic conditions to induce phosphorus
release into the sub-stream and to provide .phosphorus uptake
capacity when the sludge is returned to the aeration basin.
Settled wastewater is mixed with return activated sludge in the
aeration tank. Under aeration, sludge' microorganisms can be
induced to take up dissolved phosphorus in excess of the amount
required for growth. The mixed liquor then flows to the
secondary clarifier where liquid effluent, now largely free of
phosphorus, is separated from the sludge and discharged. A
portion of the phosphor us-rich sludge is transferred from the
bottom of the clarifier to a thickener-type holding tank: the
phosphate stripper. The settling sludge quickly becomes
anaerobic and, thereupon, the organisms surrender phosphorus,
which is mixed into the supernatant. The pho spho r us-r ich
supernatant, a low volume, high concentration substream, is
removed from the stripper and treated with lime for phosphorus
precipitation. The thickened sludge, now depleted in phosphorus,
is returned to the aeration tank for a new cycle.
6-71

-------
SLUDGE
( P REMOVAL)
RETURN SLUDGE
RECYCLE
2 HRS
2 HRS
6-10 HRS.
8 HRS
2 HRS.
CLARIFIER
ANAEROBIC
DENITRI F.
NITRIF 8
P- UPTAKE
DENITRIF.
POST
AERATION
FIGURE 6-35
BARDENPHO PROCESS

-------
TABLE 6-12
BARDENPHO PROCESS
COST COMPARISON
BASIS:
FI ow	= 1.4 irgd
Effluent Criteria -
BOD	= 5 rrg/1
SS	=5
Nitrogen = 3 mg/1
P	=1 rpg/1
To tal
Annual Cost
gVl'JOa gal
75
6 3.4
56 . 5
Capital Cost	O&M
Process * gVlUQU gal	g^/l 00 gal
1.	Conventional AWT
2 Sludge + Chem . 41.7	33.3
2.	RBC + Filtration 27.9	35.5
3.	Bardenpho + Sand Filter 3U.0	26.5
Ref :
Burdicke & Dallaire, Florida Sewage Treatment Plant
First tc Remove Nutrients with BACTERIA ALONE, Civil
Engineering, Oct. 1978 .

-------
FLOW PIAGRA.V
Lime Storage
and Feed
Secondary
Sludge
P-Rich
Sunematant
Precipitator
Stripper
Chemical
Sludge
Return Anoxic
Sludge to
Aeration Tank
FIGURE 6-36

-------
COST OF TREATMENT
Figures 6-37 and 6-33 show total construction cost and
operation and maintenance costs for secondary treatment plants.
Costs in January 1978 were obtained from the EPA document
Construction Costs for Municipal Wastewater Treatment Plants:
1973-1977.
Figure 6-39 shows comparative capital costs of alternate
secondary treatment processes (1978 Basis) .
Table 6-13 presents a summary of cost estimates prepared by
HydroQual for an 8 mgd industrial treatment facility where
activated sludge, pure oxygen and RBC systems were considered.
The following analysis considered the cost of treatment of
municipal wastewaters to produce various effluent qualities. The
significant increase in costs (capital and O&M) with advanced
treatment can be seen particularly as activated carbon is added.
Degree of Treatment vs Cost
The liquid process trains chosen for analysis are enumerated
in Table 6-14. These cover a range of treatment efficiencies
from conventional primary treatment to advanced schemes with
carbon adsorption. Raw influent pumping is included as a common
baseline that would usually be necessary for discharge of
wastewater even with no further treatment.
Literature data are ad justed to 1977 values using the
following price index levels: EPA Sewage Treatment Plant
Construction Index (STP.) = 2 75 , Engineering News-Record
Construction Cost (ENR) = 2,666, Wholesale Price Index (WPI) =
194, Consumer Price Index (CPI) = 182. All liquid treatment
schemes include raw pumping, preliminary treatment (for screens,
comminutors, grit removal, and- flow metering), prethickening of
sludge, and disinfection by chlcrination. Processes with lime
addition include dewatering and recal cination of lime sludge.
Capital expenses are amortized over 20 years @ 6-5/8% interest.
Costs for land acquisition are not included.
Figure 6-40 presents total annual costs for liquid treatment
processes (excludes sludge treatment costs) of the various
process trains in relation to the percent of SS they may be
expected to remove. Processes utilizing chemical coagulants
demonstrate higher costs for similar removals than do those
without chemical addition. The breakdown into capital and
operation and maintenance costs in Figure 6-41 shows the
difference between the total cost curves is due principally to
differences in operating costs with smaller differences evident
in capi tal costs .
6-75

-------
CO
rr
700
<
60.0
_i
50 0
_j
40.0
0
0
30.0
b.

O
20 0
CO

z

0
10 0

_J
9.0

8.0

70

60
2
50

40
H
co
3.0
0

0
2.0
2

O

h-
10
( >
0.9
1
0 8

0 7
ir
h-
0.6
co
0 5
2
0.4
O

0
0 5
_j
0 2
<

O

(

j .'.COST VS DESIGN FLOW 4_U_
SECONDARY TREATMENT- NEW CONSTRUCTION
NATIONAL
- J -J.

! FIGURE 6
. - J i t-
. . i __i- ) 4...
, . i , j ; L
I
I" "
J .. ...
.it
4+
i !
I.
1 _._Ll4_
M
1978 COST "J
J	L
O.OI
005
0.1
0.5	1.0	5.0 10.0
DESIGN FLOW IN MGD
(1000 M3/DAY = MGD/0.264)
500
1000
500.0
_d
1000.
FIGURE 6-37

-------
TOTAL 0 & M COST VS. ACTUAL FLOW
SECONDARY TR EATM ENT-ACTIVATED SLUDGE
NATIONAL
IOOO
5.00
I 00 -
0 50 - -
QIO -
005
0.01
8 25 x ! 0 Q -
.-li-i ill*
1978 COST
1.0	5.0	10.0
ACTUAL FLOWCMGD)
( 1000 M 3 = 3.785 MGD )
FIGURE 6-38

-------
5.0
in
a:
<
o
o
u.
o
in
z.
o
TRICKLING
/ 	 FILTER
PURE OXYGEN
CONVEN'
ACT. SLUDGE
0.1
Ref. INNOVATIVE AND
ALTERNATIVE TECHNOLOGY
ASSESSMENT MANUAL
JLL
0.2
1.0
10.0
PLANT FLOW, 'MGD
FIGURE 6-39
CAPITAL COST
BIOLOGICAL PROCESSES

-------
TABLE 6-1 J
COST COMPARISON - INDUSTRIAL WASTEWATER
BASIS
Raw Waste
Flew
BOD.
SS
Permit - Effl
BODr
ss 5
Ave rag;
8.3 mgd
88,000 lbs/day
20,800
90% Removal
100 rrg/1
Max in>um
10.5 rr.g d
114,500 lbs/d
3 5,000
80%
200 mg/1
Primary plant exists
Capital Cost"
O&M Cost1
COST TREATMENT PROCESS
Act . SIudqe	Pure Oxygen
$7 ,000,000
$870,000
$7,000,000
$y36,000
R8C
$15 , 000, 000
$54 0,000
1 - Sludge Dewatering and Disposal (Thickening, Dewatering
& Landfill) not incl. These costs were an additional
Capital Cost = $4.7 million
O&M	= $0.y million

-------
TABLE 6-14
ALTERNATIVE TREATMENT STRATEGIES EVALUATED IN STUDY
	Unit Processes	
Process # Name	Physical-Chemical Biological Advanced
P Raw Pumping Only	-	-
1	Conventional Primary	3	- -
2	Polymer Primary	PS+FS	- -
3	Alum Primary	AL3
4	2 Stage Lime Primary	TLS
5	High Rate Activated Sludge	S	HRAS
6	Conventional Activated Sludge	S	CAS
7	Two Sludge Nitrification	S	HRAS+NO^
8	Three Sludge System	S	HKAS+NO^+N^
9	Advanced Lirne,
Ammonia Stripping	S	CAS	TLS+NH^
10	Conventional Activated Sludge
with Filtration	S	CAS	KM
11	Conventional Activated Sludge
and Advanced	S	CAS	FM+CAD
12	Chemical Primary, Biological
and Advanced
13	Physical-Chemical	TLS	-	FM+CAD
and Advanced	L3	N0^+N2	FI'i+CAD
ALS
= al urn addition + sedimentation
N2
; biological denitrification
CAS
= conventional activated sludge
NHn :
: ammonia stripping
CAD
= carbon adsorption
NO^ :
: biological nitrification
FM
= multimediun filtration
PS :
: polymer addition + sedimentation
FS
= fine screens
3
= primary sedimentation
HRAS
= high rate activated sludge
TLS :
= two stage lime addition +
LS
= lime addition + sedimentation

sed imentation
Note: All Processes include raw pumping, preliminary treatment and
prethickening. Processes with lime addition (4, 9, 12, 13) include
recalcination.

-------
b5
fuA.i I fcc \t Y . 'I 00 (V-nVj
cobri (ADiy^re
(.fS^D
%-
COSTS njoT i W CLUjPCD.
6i-ODdi
p _T-?-^"h-7-
/ ye/S/?/jvjz>i>7~~ ^v>-v	35i>c. i t '. e - j
	O ^'-f' |V-'NJ'T
s

' !
r~'" 'El
^ ' i ii I
- - . V
'
, I, i  1
-O i !
\
l i

 : ; 1 ;

-------
>-

pUAvt^T	i foo
1 i i I 1  '
._co5rs_.ftqju5^EP ,TP._ 1.3.1 ?_
-15.

\3
Cos'rs u
0-r IWCLUDSD


-10 \a
-
(3 m o .'t
/
/

.0'
% SS REMOVAL
T
fe'O
a
a
 i
1 i i
t	i	r
70 | 8o
I	i	I	.
1	i	!   - i
X
"llo
v5
L.o*
t/t
o
VJ
o.
loo
FIGURE 6-41.CAPI TAL AND 08M CC j; FOR LIQUID TREATMENT PROCESSE

-------
Sludge is the highly concentrated by-product of wastewater
treatment. It can be composed of material removed directly from
the waste; as in primary settling, or the biomass generated
during secondary treatment, or a combination of a chemical
additive and the contaminants it has removed. The nature and
quantity of the sludge depends on the contaminants present in the
influent and the processes used to remove them. The sludge
treatment options selected for study are incineration, ocean
disposal, land application, and landfill. Total annual costs are
shown on Figure 6-42.
Schuckrow and Culp (19) have evaluated the comparative
economics of a number of treatment systems including activated
sludge, GAC, PAC and PACT. Table 6-15 indicates that the PACT
system, at plants >5 mgd is somewhat more expensive than
conventional activated sludge or single stage nitrification.
Physical-chemical systems with both granular and powdered carbon
are sig ni f icantl y more expensive. The effluent qualities from
the various processes is given in Table 6-16. The PACT process
quality is anticipated to be somewhat greater than the activated
sludge but lower than single stage nitrification. For the PACT
process, 120 mg/1 PAC dose was used with wet air oxidation
requiring 17 mg/1 makeup carbon. Multiple hearth incineration
would have been significantly more expensive.
In comparing the cost of the activated sludge to the single
stage nitrification, capital costs are greater due to tne greater
costs for secondary clarifiers (400 gpd/ft compared to 600) .
Also, WAO and chemical feed system costs for the. "PACT" process
are greater than the reduction in vacuum filtration and
incineration costs (primary only versus primary and secondary) .
The "PACT" plant in Vernon, Connecticut, @ 600 gpd/ft provides
an average effluent SS of 24 mg/1 prior to filtration, thus the
cost differential in secondary clarifiers should be negligible
reducing the capital costs differential by ~30%. A cheaper
sludge disposal alternative other than incineration would make
the activated sludge costs significantly cheaper than the PACT
co sts .
The economic evaluation by Dupont (31) comparing GAC (->34
million) to the "PACT" process ($25 million) showed the costs for
the carbon columns, initial carbon inventory and incinerator for
the sludge to be the major cpst differential. The PACT clarifier
was designed at 950 gpd/ft compared to 640 for the activated
sludge providing another significant cost savings. From the full
scale results, the median SS effluent concentration was somewhat
greater than 30 mg/1 but values as high as 900 mg/1 at times
occurred providing a mean of 87 mg/1.
6-83

-------
FIGURE 6-42.T0TAL ANNUAL COSTS - LIQUID + SLUDGE TREATMENT
t* -
IS -

COrA<> KDJUSfEO
TO 1^77	J I	. j
I	! 1	^i
-R^UST; ' OF '5i,UDG,;'	r.oyj c, lNDCf, l,," j"
i L-fjjhJt' Chsr-C /Kl' .uUOC'o! f^fC	T>&ri^C:-/T'oNL>i
1
. o
\A- -
\1

o

-------
\
UJ
IV
% SS REMOVAL
' 40. Sb
Vo SS REMOVAL
7
-------
DESIGN FLOW, MGD
FIGURE 6-44. EFFECT OF PLANT DESIGN FLOW ON UNIT COST

-------
TABLE 6-15
COMPARATIVE ECONOMICS OF VARIOUS PROCESSES(19}


Costs/1,000 gallons
(Dollars)

Activated Sludge 1
mgd
5 mgd
10 mgd
25 mgd
50 mgd
Conventional
1. 02
0. 49
0. 38
0.29
0.24
Single Stage Nitrification
1. 10
0.51
0.41
0.31
0.26
Two Stage Nitrification
1.21
0.59
0.46
0.35
0.29
Conventional with Coagula-
1.49
0.71
0.55
0. 44
O.'if
tion & Filtration*





Granular Carbon Systems*





1,500 lbs carbon/mg
1.84
0.73
0.58
0.46
0. 40
750 lbs carbon/mg
1.75
0.66
0.52
0. 40
0.35
200 lbs carbon/mg
1.72
0. 64
0. 48
0.36
0.31
Powdered Carbon Systems





Eimco* - "PAC"





Basic Process
2.08
0. 94
0.77
3.62
0. 56
Single Stage
1.96
0.89
0.73
3.60
0.54
Two Stage with 100 ing/1
1.89
0.72
0.57
'J. 42
0.37
Carbon





Two Stage with 300 rng/1
1.68
0.81
0. 68
3.53
0.46
Throwaway (5lb) Carbon





Battelle* - "PAC"




;
Basic Process
1.70
0.97
0.87
0.78
0.71
200 mg/1 Carbon,
1.18
0.55
0.46
0.39
0.35
125 mg/1 al uin





200-mg/1 Carbon
0.96
0.48
0.41
0.36
0.33
without Filtration





Bio-Physical - "PACT"





Basic Process
1.46
0.55
0. 43
0.33
0. 29
Carbonaceous Criteria
1.43
0.52
0.39
0.30
0.26
Effect of 50% Reduction in





Carbon Price on Basic Process





Eimco
2. 02
0.88
0.71
0. 56
0. 50
Battelle
1.58
0.85
0.75
0.66
0.59
Bio-Physical - "PACT"
1. 44
0.53
0.41
0.31
0. 27
Effect of Multiple Hearth





Regeneration on Basic Process





Eimco
2.21
1. 00
0.81
0.65
0. 60
Battelle
1.66
0. 91
0.78
0.72
0.67
Bio-Physical - "PACT"
1. 66
0. 6j
0.50
0. 38
0.33
F iltration
0.22
0. 07
0. 05
0.034
0.024
These processes include effluent filtration.

-------
TABLE 6-16
ESTIMATES PROCESS EFFLUENT QUALITY CHARACTERISTICS
Primary Activated
Treatment
BOD (rng/1)
Suspended
Solids (mg/1)
Total P
(mg/1)
Total N
(mg/ 1)
NH^-N (mg/1)
140
70
9.8
32
25
25
25
6.7
25
23
Activated
SI udge
Sludge N itrification
no3-n
15
15
6.7
25
1
23
Activated
Sludge and
Coagulation
and Filtration
15
0.5
0. 1
25
23
Physical-Chemical Processes
Granular
Carbon
System
20
0.3
25
23
"PAC"
Eimco
Process
20
10
6. 7
25
23
"PAC"	"PACT"
Battelle Bio-Pysical
Process Process
20
10
b.7
25
23
20
20
6.7
28
3
18

-------
O&M Costs have been extracted from the I&A Technology Manual
to show approximate costs for nitrification, denitrification and
phosphorus removal. Approximate adjustments for 1981 costs are
shown allowing for increased power (2-3), labor (1.5) and
chemical costs (2) . Figure 6-45 presents this information.
6-89

-------
( ) APPROX. COST ADJUSTMENT
TQ 1981
Ref. I a A TECHNOLOGY MANUAL
1978 COST BASIS
o,i	I	I	I MINI	I	I	I MINI
I	10	100
DESIGN FLOW, MGD
FIGURE 6-45
NUTRIENT REMOVAL
0 a M COST

-------
Process Design Manual for Nitrogen Control - EPA Technology
Transfer .
Process Design Manual for Phosphorus Removal - EPA Tecnnology
Transfer.
PACT Process State of Art Review - HydroQual internal
document .
Biological Waste Treatment - Manhattan College 1931 Summer
Institute in Water Pollution Control.
Performance of Activated Sludge Processes and Reliability
Based Design - Niku, et. al., Journal of Water Pollution
Control, December 1979.
Stability of Activated Sludge Processes Based on Statistical
Measures - Niku, et. al., Journal of Water Pollution Control,
April 1981.
Innovative and Alternative Technology Assessment Manual, EPA
430/9-78-009.
Results of Various Industrial & Municipal Wastewater
Treatment Studies - HydroQual, Inc.
Florida Sewage Treatment Plant First to Remove Nutrients with
Bacteria Alone, Burdick, et . al., October 1978 . Civil
Engineering - ASCE.
Biological Nutrient Removal Without the Addition of
Chemicals, Barnard, J. L., Envirotech.
Grieves, G. G., Stenstrom, M. R., Walk, J. D., and Grutscn,
J. F., "Powdered Carbon Improved Activated' Sludge Treatment,"
Hydrocarbon Processing, Vol. 56, 125-120, Oct. 1977.
Crame, L., "Activated Sludge Enhancement: A Viable
Alternative to Tertiary Carbon Adsorption," presented at 2nd
EPA-API-NPRA-UT Forum, Tulsa, Oklahoma, June 6-9, 1977 .
Kehrberger, G., "Nitrification Study for LaPorte, Texas
Plant, E. I. Dupont de Nemours & Co., Inc.," Hyd rose ience,
DUPO0600 , May 1978 .
Mulligan T., "Process Evaluation Studies of the Cone Mills
Dye Waste Disposal Plant, Greensboro, N. C. ," Hydroscience,
Inc ., June 1976 .
6-91

-------
REFERENCES (Continued)
15.	Shuckrow, A. J. and Culp, G. L., "Appraisal of Powdered
Activated Carbon Processes for Municipal Wastewater
Treatment," EPA-600/2 -77-156.
16.	Zimpro, Inc., "Carbon Impacts Vernon," REACTOR, publication
of Zimpro, Inc., August 1979.
17.	Singley, J. Beaudet, B., Ervin, A., and Zegel, W., "Use of
Powdered Activated Carbon to Reduce Organic Contaminant
levels," from Environmental Science & Engr., Inc., May 10,
1979.
18.	Grutsch, J. F. and Kloeckner, D. C., "Application of
Industrial Treatment Technology to Municipal Wastewater,"
presented at the 52nd Annual WPCF Conference, Houston,
October 1979.
19.	Hutton, D. and Temple, S., "Priority Pollutant Removal:
Comparison of Dupont PACT PROCESS and Activated Sludge," 52nd
WPCF Convention, Houston, Texas, October 1979.
6-92

-------
TREATMENT OF TOXIC WASTEWATERSa
1	2
By Thomas J. Mulligan, M.ASCE, James A. Mueller, M. ASCE,
0. Karl Scheible, A.M. ASCE
INTRODUCTION
Congress has enacted more than two dozen statutes regulating
potential routes by which certain chemicals or chemical usages
can threaten human health and environment. The Clean Water
Amendments of 1977 address in particular the control of toxic
material discharge to natural water systems. Section 304
stipulates that technology-based effluent limitations are
required for all pollutants, including toxic substances, from
point source discharges. Although past effluent standards
dealing with broad, non-specific parameters such as biochemical
oxygen demand (BOD^) and suspended solids will continue to be
important measures, limits are now being promulgated for specific
chemical compounds. This will place new and complex demands on
pollution control technology since removals of priority
pollutants will be required to much higher levels than have
generally been accomplished by conventional treatment systems.
Toxic pollutants are presently defined as the priority pollutants
identified in the National Resource Defense Council (NRDC) vs.
Train Consent Decree. There are a total of 129 substances
presently on the list, including 114 organics, 13 metals,
cyanide, and asbestos. The following presents a discussion of
alternate treatment processes capable of removing these priority
pollutants from, wastewater. No attempt is made here to be all
inclusive, but those processes that have in general the widest
potential application have been selected for inclusion in this
d isc ussion .
a. Presentation at the May 11-15, 1981, ASCE International
Convention and Exposition,' held in New York City, N.Y.
1.	President, HydroQual, Inc., Mahwah, N.J.
2.	Staff Consultant, HydroQual, Inc., Mahwah, N.J.; Associate
Professor Environmental Engineering and Science Program,
Manhattan College, Bronx, New York, N.Y.
3.	Principal Engineer, HydroQual, Inc., Mahwah, N.J.
6 -93

-------
ACTIVATED CARBON
The ability of activated carbon to function effectively as a
practical adsorbent is due to an extremely large active surface
per unit mass. Carbon adsorption is generally favored for
compounds of a hydrophobic nature, i.e., low water solubility.
Since the solubility of organics will typically decrease with
increasing chain length, adsorption is greater for higher
molecular weight compounds.
The quantity of sorbate that can be adsorbed by a given
weight of activated carbon is related to the concentration of the
sorbate in the external liquid phase. Adsorptive capacity
increases with liquid-phase concentration. An adsorption
isotherm is the relationship (at constant temperature) between
the equilibrium concentration of sorbate in solution and the
quantity adsorbed per unit weight of carbon.
Dobbs et . al.,(l) have computed data on carbon adsorption
isotherms for a number of toxic organics. Carbon adsorption
capacities were determined at an equilibrium concentration of 1
mg/1 and neutral pH utilizing pulverized Filtrasorb 300. When
considering the priority pollutants, the pesticides, acid
extractable phenolic compounds, and most of the base/neutral
extractable organics were found to adsorb reasonably well on
activated carbon. The purgeable organics are typically poorly
adsorbed. The nitrosamines and haloethers, depending on the
particular compound, may or may not exhibit good adsorption onto
carbon.
The influence of pH depends on the physico-chemical
properties of the individual organic. Adsorption decreases with
increasing ionization and with increasing polarity of compounds.
Adsorption will generally be enhanced at pH levels below the pk
values of the compounds. Non-destructive regeneration of
activated carbon has been practiced using an acid or alkaline as
the regenerant and is applicable when the adsorbed chemical is
ionized by a change in pH. This method is particularly
attractive when considering chemical recovery.
Interaction between components in a mixture can reduce the
adsorption of some components well below that which would exist
in a single solute waste stream. As an example, consider a
wastewater mixture of two compounds, p-nitrophenol and phenol.
Of the two compounds, p-nitropenol is the more favorably
adsorbed. As schematically illustrated on the upper display of
Figure 1, phenol is prevented (time = t ) from adsorbing onto the
carbon at the influent'end of the colunrn due to competition from
the favored p-nitrophenol for adsorption sites. But it adsorbs
without inhibition at downstream positions. As the bed becomes
6-94

-------
TIME = t,
TIME= t
2
_i
o
o
o
CD
K
<
O
PHENOLy
p-NITROP
x
(-
a
LlJ
Q
PHENOL
p- NITROR-
X/M	X/M
Schematic of solid phase loading with depth,
2.0
O PHENOL
A p- NITR0PHEN0L
500
1000	1500	2000
TIME (MINUTES)
2500
3000
Figure 1. Breakthrough curves illustrating
competitive adsorption of organics.

-------
saturated (time = t ), p-nitrophenol advances through the column
and contacts carbon which had been exposed only to phenol.
Displacement of the phenol by p-nitrophenol then occurs. This
can result in the effluent concentration of the displaced organic
actually rising above the raw waste concentration.
This phenomenon is confirmed in the lower display of Figure
3, which presents actual breakthrough curves for the binary
system of phenol and p-nitrophenol (2). The feed solution
contained equal molar concentrations of each compound (1 mmol/1)
and was pumped at a constant rate to a system with a large
inventory of carbon. The system was able to accumulate a
significant amount of phenol. As the more readily adsorbed
material (p-nitrophenol) saturates the carbon, phenol displace-
ment occurs and effluent phenol concentrations actually increase
to levels well above feed concentrations.
Thus although solute isotherm analyses are important and
provide information on the potential of activated carbon as a
treatment process for the removal of a specific compound,
compound interactions are an important element in defining carbon
adsorption capacities for the priority pollutants. Continuous
flow laboratory or pilot studies should be performed in order to
develop design criteria. The use of mathematical models to
simulate the competitive adsorption of organics in carbon columns
can effectively reduce the amount of pilot study required to
evaluate and design an activated carbon adsorption system for a
given wastewater.
CHEMICAL OXIDATION
Classifying the chemical oxidizability of organic compounds
is difficult because of the interaction of many variables. Large
molecule organics, such as the PCB's, pesticides and other cyclic
organics are generally not amenable to chemical oxidation, except
under certain catalyzed conditions. Polar, low molecular weight
organics such as acetic acid are also generally resistant.
Process selection for chemical oxidation is usually based on
economics, which in turn rely on waste volume'- and character ics,
reaction stoichiometry, and kinetics. The completeness cf the
oxidation reactions and the formation of by-products are also
being addressed now with increasing importance.
The oxidants in wide use today are chlorine, ozone, and
hydrogen peroxide. Permanganate and chlorine dioxide have had
limited applications. Chlorine dioxide has been shown to be a
selective oxidant with particular application to cyanide, phenol,
sulfides and mercaptons.
6-96

-------
100
CHLOROFORM
DICHLOROETHYLENE
80
NAPTHALENE
60
_J
<
>
O
5
UJ
CE
Q = 0.37 m /min
k, a = 50 /hr
20
DDT
0
25
50
75
100
125
G/Q
Figure 2. Effect of gas to liquid flow ratio
on air stripping of priority pollutants in packed towers.
100
CHLOROFORM, G/Q = 25
80
_)
<
> 60
O
NAPTHALENE, G/Q- 50
2
UJ
cr 40
o-
20
Q = 0.37 m /min
5	30	4 5
PACKING HEIGHT ( m ) '
6.0
Figure 3. Effect of packing height
on stripping efficiency.

-------
Optimization of chlorination often requires strict control
pH, since the aqueous chemistry of chlorine is pH dependent. The
pH dependence of the organics to be oxidized is also a critical
element in control of the reactions. Generally, oxidation rates
are highest when the organic compound is present as the
disassociated species.
Chlorination under alkaline conditions has long been an
accepted practice for the destruction of cyanides and is an
effective oxidant of phenols at high pH, where the hypochlorite
ion is favored. Recent work has also centered on the control of
the chlorination process to allow step-wise oxidation of mixtures
by manipulation of pH. A study reported the chlorination of
methylamine, emphasizing the importance of pH control for optimum
reaction rate and selective reaction pathways (3) .
Hydrogen peroxide has had little direct application to the
destruction of priority pollutant organics. It is effective in
oxidizing phenols and cyanides (alkaline pH) and has the
advantage of adding minimally to the dissolved solids of the
solution. Generally, peroxide has been used in conjunction with
a ca talyst .
Ozone is an allotropic state of oxygen and is significantly
more active because it delivers elemental oxygen. As with
chlorination, care must be exercised in controlling the pH at
which ozonation reactions occur. Ozone is typically ineffective
under acidic conditions.
Fochtman and Eisenberg(4) reported on the treatability of
several priority (or similar) pollutants by ozonation. Compounds
which were found to readily react with ozone were 1,1-diphenyl-
hydrazine, beta-naphthylamine, and 4 , 4-me thyl ene-bi s (2-chlo ro-
aniline) . Naphthalene was found to react slowly with ozone,
while dimethylnitrosamine was resistant to ozone oxidation.
Nebel , et. al . (5) reported the application of ozone oxidation to
phenolic effluents and indicated that high pH (optimum pH = 11.8)
values favored oxidation of phenol by ozone.
ULTRAVIOLET PHOTOLYSIS AND CATALYZATION
Chemical oxidation utilizing the primary oxidants described
above can be significantly enhanced by employing the synergistic
and/or catalytic effects of ultraviolet light energy.
Ultraviolet photolysis can in itself provide pretreatment by
detoxifying certain compounds, particularly chlorinated organics.
This is accomplished by cleavage of the chlorine-carbon bond.
The altered compounds may subsequently be amenable to biological
treatment. Banerjee, et . al . , (6) reported the photodegradation
of 3, 3-dichlorob'enzid ine utilizing ultraviolet energy in a pure
6-98

-------
solute. The decomposition of TCDD was reported by Batre, et. al .
(7) Ultraviolet photolysis was also utilized to destroy dioxin
contained in a waste sludge by-product. (8)
Prober, et. al., (9) reported the impact of ultraviolet
energy on the ozone oxidation of f er r ic yan ide . The synergistic
effects of ozone and ultraviolet caused the rate of reaction to
increase by an' order of magnitude over what would result with
either one individually. Meiners, et. al., (10) studied the
effect of ultraviolet radiation on the rate and extent of
chlorine oxidation of organic material in a highly nitrified
effluent. They determined that ultraviolet increased the rate of
oxidation by a factor of 3 to 10, with maximum rates occurring at
pH 5.
AIR STRIPPING
Since approximately 35% of the organic priority pollutants
are volatile to some extent, air stripping is a viable process
for significant organic removal. A number of equipment
conf ig urations can be utilized for this purpose. Conventional
aeration tanks used in activated sludge wastewater treatment,
employing either diffused or mechanical aeration, can obtain
significant stripping of volatile organics. The most effective
type of air stripper for the highly volatile compounds are
countercurrent packed towers. Cross flow towers can be utilized
when high gas to liquid flow ratios are required for the less
volatile compounds.
A quantitative evaluation of air stripping may be obtained by
applying basic gas transfer principles. The rate of air
stripping across a liquid-gas interface can be simplistically
related to resistance in two films; one on the gas side of the
interface and the other on the liquid side. Gases with high
Henry's Constant values, such as oxygen, are relatively
insoluble, and liquid film controls the transfer rate. Gases
with low H values, such as ammonia, are highly soluble and the
gas film controls the transfer rate. Ftp r the toxic organics,
both phases can be important depending on the compound. The more
volatile compounds, where liquid film controls, can be easily
removed by stripping.
Mass balance equations for both liquid and gaseous phases can
be solved at steady state to evaluate the capabilities of
specific, air stripping systems for removal of toxics. For
co un te rc ur r ent packed tower strippers, the height of a packed
tower is related to the chacter istics of the packing medium, and
hydraulic loading rate. Both affect the gas transfer coefficient
and Henry's constant for a particular toxicant. The height is
also related to the ratio of the gas and liquid flow rates, a
major design parameter.
6-99

-------
Figure 2 shows the results of a packed tower air stripping
analysis using a 2.5 cm Raschig ring packing medium. Four toxic
organics were chosen representing a range of volatilities. Those
compounds more volatile than chloroform will have greater than
90% removal at relatively low G/Q values of 25. Intermediate
volatile compounds such as napthalene will be markedly affected
by the G/Q ratios, requiring values, of 50 or greater for
substantial removals. The low volatility compounds such as DDT
will require extremely high G/Q values for significant removals.
The DDT curve is linear, indicating that removal is completely
controlled by G/Q and not markedly affected by transfer
coefficient. Thus, gas phase saturation for the low volatility
compounds is reached quickly, requiring high gas flow rates for
significant removal. Further analysis (Figure 3) would
demonstrate that the height of packing has a slight effect on
removals in the range of 1.5 to 3.0 meters and substantially no
effect when greater than 3 meters. Detention time (total tower
volume) varies from 4 to 8 minutes for the 1.5 to 3.0 meter
col umn.
Upper limits of G/Q exist for ccuntercurrent flow columns to
prevent flooding the column. In this situation, the liquid
cannot flow downward but is pushed out the top of the column due
to an excessive gas flow rate. To attain significant removals
for the low volatility compounds, either cross flow stripping
towers or surface aeration with high G/Q values must be used.
Figure 4 presents the expected removal efficiencies by air
stripping in aeration tanks. Diffused aeration systems have the
lowest removal efficiencies due to the gas flow limitation per
diffuser. The lower gas flow (G/Q = 2-5) range would be
typical of fine bubble dome or disc type diffusers having
transfer efficiency (E ) values near 20%, while the higher gas
flow range would be typical of the coarse bubble units with lower
transfer efficiencies (6 - 10%). The higher removal efficiencies
attained by the surface aerators are due to the capability of
blowing relatively large amounts of air across the surface.
Significant removals of the low volatility compounds such as DDT
can be attained at these high gas flow rates. These rates are
similar- to those used in ammonia stripping.
An important design parameter for the surface aeration system
is the power per unit flow rate, hp/Q. Analysis indicates that
at hp/Q levels above 0.08 kWh/m (400 hp-hr/MG), little
additional removal capability is attained. Staging the reactors
to attain more of a plug flow system may improve removals. At
intermediate removal efficiencies for the volatile compounds
(chloroform, G/Q = 25) , removals may be increased by 10 to 20% by
using 3 to 4 stages instead of 1. There is little impact from
staging for the low volatility compounds since the major effect
is the G/Q ratio.
6-100'

-------
100
1000 hp/MG
200 hp/MG
80
N0 = 3.0 lb 02/hp-hr
DICHLOROETHYLENE
60
_J
<
>
O
2
NAPTHALENE
SURFACE
AERATION
lU
or
40-CHLOROFORM
DIFFUSED
AERATION
DDT
20
DETENTION
TIME= 6 hrs.
500
100
200
20
50
G /Q
Figure 4. Effect of gas to liquid ratio on air stripping
of priority pollutants in aeration basins.

-------
Table 1 summarizes the characteristics of field air stripping
systems and their measured organic removal efficiencies (11, 12) .
The field systems were designed for decarbonation and ammonia
stripping at Water Factory 21 in Orange County, California, and
ammonia	stripping	at	Palo	Alto.
TABLE 1. CHARACTERISTICS OF FIELD AIR STRIPPING SYSTEMS
Packed Towers
Countercurrent Crss Flow	Mechanical
Flow	Fans On Fans Off Aeration
Location	Orange Cty, Ca . Orange Cty, Ca . Palo Alto, Ca .
Design Purpose Decarbonation Ammonia Stripping Ammonia Stripping
G/Q
22
2700
225
430
hp/Q hp-hr/MG
69
690
140
2770
t , m in_.
1.5
50
50
340
Ka, hr 89
(CHC1
3) 3 . 2 (NH 3)
~~ 
2 . 5 (CHCL )
Removal Efficiencies, %
Te trachloro ethyl en e


95
99
Trichloroethylene



99
Chlo robenzene
--
96

--
1,1,1-Tr ichloro-




ethane

--
91
--
Chio ro fo rm
79
83
79
92
Bromod ichl oro-




methane
85

--
94
Dibromochloro-




methane
71

82
82
1,3-Dichlorobenzene
--
--
83
94
1,4-Dichlorobenzene

97
92
92
1,2-Dichlorobenzene

--
88
91
1,2, 4-Tr ichloro-




ben zene
--


92
nh3
 
81
2 5

BIOLOGICAL TREATMENT
Given the prevalence of biological systems for wastewater
treatment, they must be regarded as a critical element in the
1 control of priority pollutants. This would be relative to direct
applications for the removal of priority pollutants, or to the

-------
impact of priority pollutants on subsequent biological processes.
Design of biological systems for specific industrial wastewater
applications requires a high degree of process evaluation,
especially for wastewaters containing compounds toxic to the
organisms, or compounds generally resistant to biodeg radation-.
Process modifications to minimize these impacts have been
successfully applied, notably the completely mixed activated
sludge and extended aeration processes. Microbial populations
may also be successfully adapted to specific wastewaters and
achieve efficient oxidation.
Three mechanisms can describe the removal of priority
pollutants in a biological process: b iod eg r ada t ion , adsorption,
and volatilization. Biodeg radation is the only true treatment
mechanism, resulting in a decompo si t ion of the material to stable
by-products. Adsorption and stripping remove the material from
the wastewater to the solid and gas phase, respectively. These
are legitimate mechanisms, but it must be understood that the
subsequent impact of the compounds on the plant sludges and air
quality need to be fully understood and properly accounted for.
Should these removal mechanisms result in an environmentally
incompatible sludge or in unsafe air quality conditions,
alternative processes would be required to remove and/or treat
the mater ial .
Results on the biodegradabi1ity of ninety-six priority
pollutant compounds have been presented (13). Of the ninety-six
tested, twenty-three were found to be resistant to degradation.
All but four of these are halogenated, with a significant degree
of halogen substitution. Generally, the results imply that the
majority of the priority pollutants are treatable by biode-
gradation. Such results, however, must be used with caution.
Acclimation often entails concentration levels which are high
enough to be available in the organic matrix. Low levels in
certain systems render the compound non-competitive to more
degradable material and may never be amenable to adaptation, thus
passing through the plant.
A survey of POTW's for the removal of priority pollutants
has been an ongoing EPA sponsored study. In an interim report
(14) on 20 plants, preliminary analysis indicates the POTW's to
be capable of significant organics removal. Net losses for total
priority organics in 5 plants ranged from 26 to 76%. These
losses were attributed to both volatilization and b iod eg r ada t ion .
System design for the biological treatment of the
biodegradable priority pollutants can generally follow normal
process evaluation procedures and analysis. Laboratory
investigations should be carried out which evaluate loading rates
to achieve a desired effluent quality to determine maximum
6-103

-------
permissible concentrations before inhibition sets in; and to
assess the degree of variability which would be acceptable to the
process. Generally, in systems which must achieve removal of
substances which are resistant to biodegradation, the design
incorporates low loadings and extended sludge ages.
The "PACT" process (duPont patent) is an activated sludge
process employing powdered activated carbon (PAC) addition to the
aeration tanks for adsorption of non-degradable organics. Hutton
(15,16) described removals in-, the duPont Chambers Works "PACT"
plant which treats 136,000 m /day (36 mgd) of chemical plant
wastewater, using an average PAC dosage of 126 mg/1 (37 percent
regenerated) . Of 36 organic priority pollutants found in the
feed to the wastewater treatment plant, 90% removal or greater
was achieved for 28. The overall removal of dissolved organic
carbon at the plant was 81% while color removal was 64%. Thus
most of the priority pollutants were removed to a greater extent
than the overall organic carbon or color.
1.	Dobbs, Richard A., Cohen, Jesse M., Carbon Adsorption
Isotherms for Toxic Organics, EPA-600/8-80-023, April 1980.
2.	Famularo, J., "Binary Characterization of Wastewater
Adsorption," presented at the 52nd Annual WPCF Conference,
Houston, Texas. October 1979.
3.	Exner, Jurgen H., Fox, Robert D., Parmili, Charles S., and
Mayer, John R., "Chlor ination Effects on Typical Organic
Chemical Plant Effluents," Presentation at the Conference on
Water Chlor ination, Gatlinburg, Tenn. October 31 , 1977 .
4.	Fochtman, Edward G. and Eisenberg, Walter, Treatability of
Carcinogenic and Other Hazardous Organic Compounds, Municipal
Environmental Research Laboratory, U.S.E.P.A. EPA-600/2-
79-097, Cincinnati, OH, August 1979.
5.	Nebel, Carl, Gottschling, Ronald	G., Holmes, John L.,
Unangst, Paul C. , "Ozone Oxidation of Phenolic Effluents"
31st Industrial Waste Conference,	Purdue University, Ann
Arbor Science, 1976.
6.	Banerjee, S., et. al., "Pho todeg radation of 3,3-dichloro-
benzidine, Environmental Science and Technology, V12, No. 13,
December 1 978 .
6-104

-------
7.	Batre, C., et. al " TC DD Solubilization and Photode-
composition in Aqueous Solutions," Environmental Science and
Technoloqy, Vol 12, No. 3, March 1978.
8.	IT Env irosc ience, "Destroying Dioxin; A Unique Approach,"
Waste Age, October 1980.
9.	Prober, Richard, Melnik, Peter B., Mansfield, Lee A.,
"Ozone-Ultraviolet Treatment of Coke Oven and Blast Furnace
Effluents for Destruction of Fe r r ic yan id es" 32nd Industrial
Waste Conference, Purdue University, Ann Arbor Science, 1977.
10.	Meiners, A.F., Lawler, E.A., Whitehead, M.E., and Morrison,
J. I . , An Investigation of Light-Catalyzed Chlorine Oxidation
for Treatment of Wastewater, NTIS PB-187757, December 1968.
11.	McCarty, P.L., Sutherland, K.H., Graydon, J., and Reinhard,
M., "Volatile Organic Contaminants Removed by Air Stripping",
presented at AWWA Conference, San Francisco, Ca., June 1979.
12.	McCarty, P.L., "Removal of Organic Substances From Water by
Air Stripping," submitted to EPA, October 1980 .
13.	Tabak, J., Quave, S.A., Mashini, C.I., and Barth, E.F.,
" B iod eg r ad ab il i ty Studies with Organic Priority Pollutant
Compounds" U.S.E.P.A., Office of Research and Development,
Cincinnati, OH., April 1980.
14.	Feiler, H. Fate	of Priority Pollutants in Publicly-Owned
Treatment Works, Interim Report, U.S.E.P.A., EPA-440/1-
80-301 , October 1 980 .
15.	Hutton, D.G., "Removal of Priority Pollutants by the DePont
PACT Process," presented at the 7th Annual Industrial
Pollution conference, WW MA, Philadelphia, June 1979.
16.	Hutton, D.G., "Removal of Priority Pollutants with a Combined
Powdered Activated Carbon-Activated Sludge Process,"
presented at the 179th ACS meeting, Houston, Texas,' March,
1980 .
6-105

-------
PRIORITY POLLUTANTS
I PURGEABLE ORGAN1CS
H BASE NEUTRAL
NITROS AMINES
HI ACID EXTRACTABLES
PHENOLS
JK PESTICIDES & PCB
3ZI METALS
HALOETHERS
POLYNUCLEAR AROMATICS
PHTHALATE ESTERS
CHLORINATED HYDROCARBON
NITROBENZENES
BENZIDINES
3ZT MISCELLANEOUS

-------
ACTIVATED CARBON
FACTORS AFFECTING ADSORPTION
SOLUBILITY
IONIZATION & POLARITY
SURFACE TENSION
PH
TEMPERATURE

-------
SOLUBILITY
MOLECULAR WEIGHT
CLASSIFICATION
Figure I. General adsorption
characteristics of
priority pollutants.

-------
1000
PENTACHL0R0PHEN0L
 p H 3
 pH 7
A pH 9
ortho-anisidine
 p H 3
 pH 7
A pH 9
01	0.1	1.0	10.
RESIDUAL CONCENTRATION (Cf), mg/l
Figure 2. pH effect on activated carbon adsorption,
100

-------
MECHANICAL AERATION
DIFFUSED AERATION
AIR
BLOWER
- INFLUENT
AIR
INF
1 J- FAN r
NF.
PACKING	AIR
EFF
(EFFLUENT
PACKED TOWER	CROSS FLOW TOWER
Figure 6. Air stripping process configurations.

-------
100
80
<
> 60
O
5
UJ
CC 40
20
0
0	0.08	0.16	0.24
hp/Q ( k W h / m3)
Figure 13. Effect of aerator
mixer power in closed tank.
CHLOROFORM
napthalene
DDT
6/0 = 500

-------
100
80
<
> 60
O
2
UJ
o: 40
20
0
chloroform,
G/O:25
DDT.
DDT, 6/0 = 500
hp/Q= 0.24 kWh/m3
12 3 4 5
STAGES (n)
Figure 14. Effect of staging
on stripping efficiency
in closed tank.

-------
CLARIFICATION	AERATION CLARIFICATION
^ WASTE
ACTIVATED SLUDGE
BIOCONCENTRATION ON ACTIVATED SLUDGE
COMPOUND
FACTOR
ACENAPHTHENE
24
1, 2 DICHLOROBENZENE
7-8
1,3 DICHLOROBENZENE
5-28
FLUORANTHENE
15-45
NAPHTHALENE
8-29
N-nitrosodi-n- PROPYLAMINE
100
Bis ( 2-ETHYLHEXYL) phtholate
30-76
BUTYL BENZYL PHTHALATE
172
Di-n-butyl PHTHALATE
15-21
Di-n-octyl PHTHALATE
22
DIMETHYL PHTHALATE
6
BENZO (a) pyrene
48
BENZO (k) fluoranthene
20
CHRYSENE
20
ACENAPHTHYLENE
100
FLUORENE
9-30
PHENANTHRENE
23-31
TETRACHLOROETHYLENE
6
TOLUENE
48
PYRENE
31

-------
CHARACTERISTICS STRIPPING SYSTEMS
PACKED TOWERS
COUNTERCURRENT
CROSS FLOW FAN
MECH.

FLOW
ON
OFF
AERATION
(1)
LOCATION ORANGE CITY
(2)
ORANGE CITY
(2)
PALO ALTO
G/Q
22
2700
225
430
HP/Q HP-HR/MG
69
690
140
2770
T0 , M1N
1.5
50
50
340
REMOVAL EFFICIENCIES %
TETRACHLOROETHYLENE


95
99
TRICHLOROETHYLENE



99
CHLOROBENZENE

96


1, 1, 1 -TRICHLOROETHANE


91

CHLOROFORM
79
83
79
92
BROMODICHLOROMETHANE
85


94
DIBROMOCHLOROMETHANE
71

82
82
1,3- DICH LOROBENZENE


83
94
1,4- DICHLOROBENZENE

97
92
92
1,2- DICHLOROBENZENE


88
91
1,2,4-TRI CHLOROBENZENE



92
nh3

81
25

DESIGN POSPOSE -
(1)	DECARBONATION
(2)	AMMONIA STRIPPING

-------
C495A.5 (I)
APPENDIX A
Simplified Analytical Method
for
Determining NPDES Effluent Limitations
for POTWs Discharging into Low-Flow Streams
	, 0	
NATIONAL GUIDANCE
Monitoring Branch
Monitoring and Data Support Division
Office of Water Regulations and Standards
September 26, 1980
I. INTRODUCTION
A. General
A simplified analytical method for determining effluent limi-
tations for publicly-owned treatment works (POTWs) discharging into
low-flow streams has been developed for nationwide use. This method
should help ensure that proposed construction grant projects have
adequate water quality justifications based on technically sound water
quality analyses, and that construction grant funds are used in a
cost-effective manner.
The analytical techniques which are used in water quality
modeling should be the simplest possible that will still allow the
A-3

-------
C495A.5 (I)
water quality manager to make confident and defensible water pollution
rr?*?:1 decisions. In many cases, where similar and relatively simple
conditions exist, simplified modeling efforts that have less extensive
manpower and data requirements (than normal, more comprehensive
efforts) are often adequate to make such decisions. Dse of simplified
efforts, when appropriate, can result in both substantial savings in
State and EPA resources and cost-effective and technically sound
effluent limitations that will protect designated water uses and allow
water quality standards to be achieved.
This simplified analytical method has been developed because of
the large number of relatively small municipal sewage treatment
facilities discharging into low-flow streams, and the need for more
cost-effective yet technically sound water quality analyses for these
cases. For example, this simplified method may be applicable to over
50 percent of the existing construction grant projections in Region V.
Additionally, this method will help ensure that similar dischargers in
similar situations will receive consistent consideration.
It should be noted that the analytical techniques described below
are intended to represent minimum levels of analysis acceptable to EPA
as justification for treatment beyond secondary. Water quality
analysts may, of course, employ more rigorous techniques incorporating
detailed intensive surveys and more complex models. EPA, however,
will not accept further simplification of the methods described below.
A-A

-------
C495A.5 (I)
unless such simplifying assumptions are adequately supported by a
technical justification.
B.	Modifications to the Region V Technology
The simplified method discussed below is based on the approach
originally proposed by Region V. and on comments and suggestions
received in response to the Region V proposal. Though generally sup-
portive of the overall approach* comments revealed some concern
regarding some details on calculating rate constants* DO targets* and
permit conditions. Consequently, several modifications have been made
to the Region V proposal.
C.	Needs for Additional Data and Future Modifications
The simplified method described below is based on the information
and data available to date. The data bases for many of the
recommendations are quite limited* and should be expanded. Users of
this method (as well as others) are strongly encouraged to develop
their own specific rates and other factors* and to submit this
additional data and other information, along with suggested improve-
ments for the method, to:
Chief* Waat.eload Allocations Section
Monitoring Branch
MDSD/OWRS (WH-553)
U.S. Environmental Protection Agency
401 M Street, SW
Washington, DC 20460
(202) 426-7778
A-}

-------
C495A.5 (I)
This additional data and other information is needed so that
arrr?riate improvements to the Method can be made periodically.
Areas in the method that require additional research and/or
data include:
	K-rates (reaeration, CBOD, NBOD), including relating them to
vaterbody characteristics, levels of treatment, etc.
	CBODu/BODj ratio
	diurnal fluctuation factors
	methods for performing the sensitivity analysis
	sediment oxygen demand ratest including relating them to
stream bottom characteristics, levels of treatment, etc.
II. APPLICATION AND CONSTRAINTS
This method may be applied only if all of the following
conditions are met:
1)	The discharger must be a publicly-ovned treatment works
(POTW) receiving predominantly sanitary wastewaters. Any
nonsanitary wastewaters in the treatment plant's influent
must exhibit essentially the same characteristics (e.g.,
reactions) as sanitary wastes.
2)	The discharge must be to a free-flowing stream in which the
design low flow (usually the 7-day, 10-year low flow) is
approximately equal to or less than the design discharge flow
from the POTW.
3)	The design discharge flow from the treatment plant must be 10
MGD (15.5 cf8) or less.
4)	There is no significant interaction between the discharger
being analyzed and any other upstream or downstream
_ discharger.
A-6

-------
C495A.5A (I)
Water quality in this type of system is highly dependent on
effluent quality. Hence, upstream quality is less significant here
!^an in systems where the upstream design flow is much greater than
design effluent flows. This method can also be applied to simple
systems where the upstream flow is greater than the POTW's discharge
flow, provided the upstream water quality and reaction kinetics are
well documented.
III. PROCEDURE
In order to determine the level of treatment required for a POTW,
the following analytical steps are recommended:
(a)	gather necessary data
(b)	perform an ammonia toxicity analysis
(c)	perform a dissolved oxygen analysis
(d)	perform a sensitivity analysis
(e)	interpret the results, and determine the final effluent
limitations.
These five steps of the Simplified Method are discussed below.
A. Data Requirements
The data required for the Simplified Method, and some of their
possible sources are listed below:
1) stream design flow-sources include USGS low-flow publi-
cations; drainage area yields; measurements during low-flow
periods.
A-7

-------
C495A.5 (I)
2)	upstrpani water quality-including the necessary DO, BOD,
ammonia, pH, alkalinity, temperature and other data needed
for this Method. Sources include historical data (e.g., in
STORET); State, EPA, or other water quality monitoring;
sewage treatment plant monitoring; transferable data from
similar streams.
3)	stream physical characteristics-including stream slope,
depth, etc. Sources include field measurements; DSGS topo-
graphic maps; special Corps of Engineers or county project
maps; stream gazetteers.
4)	time of travel/velocity-sources include dye studies;
direct velocity measurements; calculations based on field
measurements of widths, depths, etc.; estimates based on
slope/velocity relationships.
5)	effluent design flow-sources include State or local agency
population projections; Step 1 applications.
6)	characteristics of design eff1npnt-including the necessary
pH, alkalinity, temperature, and other data needed for this
Method. Sources include treatment capabilities for different
levels of treatment, presented herein; other data can be ob-
tained from State, E?A, or other water quality/effluent moni-
toring; sewage treatment plant monitoring; transferable data
from similar treatment plants.
Direct field measurements of time-of-travel/velocity, upstream
quality, stream physical characteristics (such as depth, type of
bottom, benthic deposits, etc.), and other data should be employed for
each segment studied, most notably for those where post-filtration of
the sewage treatment plant effluent is considered. Since these data
are readily obtainable by means of short duration, low resource
surveys, efforts should be made to obtain the data through State
agency monitoring programs or as part of the 201 grant process. When
such data are not available, estimates can be made from some of the
suggested sources listed above. The impact of. less site-specific data
A-8

-------
C495A.5 (I)
should be considered in the sensitivity anlysis. Time-of-travel
studies provide the most useful data when the upstream flow and
existing sewage treatment plant flow are equivalent to the sum of the
upstream	and the treatment plant design flow. If flows in
the immediate range of the design flow are not encountered during the
time-of-travel studies, a second 6tudy at a different flow will permit
extrapolation of the data to the design flow.
As a minimum* all modeling efforts must include: (1) a search
for all applicable historical data and information (e.g.. in STORET,
old modeling or water quality study reports* treatment plant records*
etc.) to support the current modeling work, and (2) a general on-site
reconnaissance visit to visually observe the system to be modeled (to
gain a better intuitive understanding of the system).
B. Ammonia Toxicity Analysis
A mass balance analysis will be used to determine whether the
nitrification unit process is required on the basis of instream
ammonia toxicity. The total ammonia-N limitation for the proposed
discharge will be determined by using the applicable water quality
standards (WQS)* upstream flow and background concentration* and
design effluent flow as follows (2):
A-9

-------
C495A.5 (I)
CD = ^CWQS^D+^U^ " CoQu^D	^E<1* ^
where = allowable design discharge concentration of total
ammonia-N for POTW,
Cyog = water quality standard limit of total ammonia-N
(usually based on un-ionized ammonia-N standard and
selected pH and temperature).
Cg = upstream or background concentration of total ammonia-N(
Qd = design POTW discharge flow rate,
Qjj = upstream design low-flow.
The allowable instream total ammonia-N concentration (C^qg)
will normally be based on the water quality standard for un-ionized
ammonia-N and the expected values of pH and temperature downstream of
the discharge (if an applicable total ammonia-N standard is specifiedi
Cyqg will equal that standard). The value of Cyqg can be deter-
mined from a table or graph which relates the toxicity of un-ionized
ammonia-N to pH and temperature (such a table and. graph is presented
in Exhibit 1). When selecting C^qg. one should be sure to use ap-
propriate values for the expected downstream pH and temperature con-
ditions during the design season* after mixing of the discharge and
the receiving stream. If no un-ionized or total ammonia-N standards
are available for use, the following criteria are recommended:
	0.02 mg/1 un-ionized ammonia for freshwater cold water
habitat
	0.05 mg/1 un-ionized ammonia for freshwater warm water
habitat.
A-10

-------
u
BC
UJ
a.
Ui
<
<
z
o
5
5
<
Q
Ui
N
Z
o
100.0
80.0 -
60.0 -
20.0 -
10.0 _
z
8.0 ^
o


6.0 -
<
tr
4.0 -


Z

UJ
o
2.0 -
z

o

CJ
1.0-
<
0  -
z
o
0.6 -
2
5
0.4 -
<

_i

<
0.2-
H

O



UJ
0.1 -
Z
0.08 
t-
0.06-
U.
O
0.04-
0.02-
0.01
TEMPERATURE (C)
Note: Redrawn from William T. Willingham, Ammonia Toxicity,
USEPA 908/3-76-001, Feb. 1976
Percent un-ionized ammonia in aqueous ammonia solutions*
Timptr-
pH Value
atura
(C)
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
10.0
5....
0.013
0.040
0.12
0.39
1.2
3.8
11.
28.
56.
10....
0.019
0.059
0.19
0.59
1.8
5.6
16.
37.
65.
15 ....
0.027
0.087
0.27
0.86
2.7
8.0
21.
46.
73.
20....
0.040
0.13
0.40
1.2
3.8
11.
28.
56.
80.
25 ....
0.057
0.18
0!$7
1.8
5.4
15.
36.
64.
85.
30....
0.080
0.25
0.80
2.5
7.5
20.
45.
72.
89.
*[Thurtton, at al. (1974)]
Exhibit 1. Percentage of un-ionized ammonia in ammonia-water solution
at various pH and temperature values.
A-ll

-------
C495A.5 (I)
The expected values of pH and temperature downstream of the dis-
charge should be based on the pH and temperature of the POTW effluent
and of the upstream vaters. If sufficient temperature data are avail-
able or can be estimated for the POTW and for the stream (upstream of
the discharge point) the expected downstream temperature can be cal-
culated as follows:
tr = 
-------
C495A.5 (I)
should be conducted in this area. Vhen actual stream or POTW data are
limited or not available* data from similar nearby streams and P0TWst
or equilibrium water temperature data* may be used as design condi-
tions and to help establish the range for a sensitivity analysis. In
this analysis. the pH and temperature values which are used should be
supported by one or more of the means described above. Any deviations
must be supported by a sound technical justification.
This mass balance analysis should be used to determine whether
the nitrification unit process is required solely on the basis of
instream ammonia toxicity. Since nitrification in sewage treatment
plants is generally an "all or nothing** process* the water quality
analyst should be aware that* in terms of treatment capital costs*
there may be no difference between an ammonia effluent limitation of*
say* 2 mg/1* and 8 mg/1. For example* the cost of building a
treatment plant to produce an effluent quality of 2 mg/1 ammonia-N*
may not be substantially different from that for a treatment plant
designed to produce an effluent quality of 8 mg/1. For further
details see the discussion below on treatment capabilities.
In light of the above discussion* this mass balance approach
should be used to estimate in6tream un-ionized ammonia concentrations
with and without nitrificaiton at the treatment plant. In cases where
it appears that only marginal violations of the instream ammonia
standard will result without nitrification at the plant, the decision
to provide nitrification can be deferred until the dissolved oxygen
A-14

-------
C495A.5 (I)
(DO) analysis (Step C, belov ) has been completed. The DO analysis
may indicate the need for a reduction of ultimate oxygen demand (DOD),
which would also support the need for the nitrification unit process
at the plant (a process known to be more economical than filtration)
for UOD removal. However, the latter conclusion is based on the
implicit assumption that all of the instream ammonia will exert an
oxygen demand in the stream segment under consideration, i.e., that
nitrification occurs instream.
In situations where the DO analysis does not indicate a need for
advanced treatment levels, but the ammonia toxicity analysis predicts
toxicity problems, consideration shall be given to using pH adjust-
ments (i.e., pH reductions) of the effluent during critical conditions
to control ammonia toxicity in lieu of requiring nitrification. This
consideration should include a determination of whether the temporary
lowering of pH and increase in total dissolved solids (TDS) concen-
tration would have any significant instream ecological or other
effects.
In addition to this mass balance analysis, a qualitative if not
quantitative assessment of nonpoint source contributions of ammonia
must be made. This assessment may reveal that nonpoint source pol-
lution may be of sufficient magnitude to preclude attainment of water
quality objectives in terms of ammonia concentrations. An example
which illustrates this point would be a treatment plant discharge
located in a predominatly agricultural watershed that has significant
A-15

-------
C495A.5 (I)
nonpoint source problems. Because nitrification alone may not solve
an ammonia toxicity problem, nonpoint source controls must also be
considered before nitrification is chosen. National guidance for non-
point source analysis related to facility planning is presently being
developed and is expected in the near future.
C. Dissolved Oxygen Analysis
A simplified Streeter-Phelps (3) analysis will be used to
determine the effluent dissolved oxygen (DO) and BOD limitations for
the POTW. This approach incorporates both carbonaceous (CBOD) and
nitrogenous (NBOD) oxygen demands in the analysis. The equation used
to calculate the DO deficit downstream from the point source is shown
below:
*
D = D0 exp (-K2t)	(Eq. 3)
+ [KX CB0Do]/[K2-Kj][exp (-Kj t)- exp (-K21)]
+[3 OT0Do]/[K2-K3](exp(-K3t)-exp(-K2t)]
+ S/HK2l-ej(p(-K2t>]
where D = the DO deficit (mg/l)
Dq = mixed initial DO deficit (at discharge point) (mg/1)
CBOD = mixed ultimate CBOD concentration at discharge point
(mg/1),
NBODq = mixed NBOD concentration at dischage point (mg/1).
The magnitude of the NBOD should be based on the total
ammonia concentration, and can be estimated using the
following stoichiometric relationship: NBOD = 4.57
(nh3-n).
A-16

-------
C495A.5 (I)
K1
= CBOD reaction (decay) rate (base e)
(1/day),
K2
= reaeration rate (base e) (1/day)

K3
= NBOD reaction (decay) rate (base e)
(1/day).
t
= travel time below discharge (days).

S
= sediment (benthic) oxygen demand (gm/m /day).
H
=. stream depth (meters).

The instream average DO concentration at a given point downstream
of the discharge point is calculated by using the following equation:
D0AVG = D0SAT~ D	(Eq. 4)
where DO^^ = instream average DO concentration (mg/1).
DO^i = saturation DO concentration at specified water
temperature (mg/1). This can be determined from
Ekhibit 2,
D	= as defined above.
Calculations using the above equations and a specified set of co-
efficients and assumptions apply for a given uniform stream reach. It
is important to subdivide the stream into individual uniform' reaches
wherever any significant system changes occur (e.g.* changes in chan-
nel geometry> significant tributary inflows, etc.) so that appropriate
coefficients and assumptions that adequately represent each reach can
be applied to the respective stream reaches when the model calcula-
tions are made.
A-17

-------
C495A5.T CI)
Exhibit 2. SOLUBILITY OF	OXYGEN	IN FRESHWATER (AFTER STREETER)
Dissolved Oxygon (mg/1)
(t normal atmospheric	pressure,	760 na	Hg)
T
(C)	0.0	0.1	0.2	0.3	0.4	0.3	0.6	0.7	0.8 0.9
0	14.62	14.58	14.54	14.50	14.46	14.42	14.39	14.35	14.31	14.27
1	14.23	14.19	14.15	14.11	14.07	14.03	14.00	13.96	13.92	13.88
2	13.84	13.80	13.77	13.73	13.70	13.66	13.62	13.59	13.55	13.52
3	13.48	13.44	13.41	13.38	13.34	13.30	13.27	13.24	13.20	13.16
4	13.13	13.10	13.06	13.03	13.00	12.97	12.93	12.90	12.87	12.83
5	12.80	12.77	12.74	12.70	12.67	12.64	12.61	12.58	12.54	12.51
6	12.48	12.45	12.42	12.39	12.36	12.32	12.29	12.26	12.23	12.20
7	12.17	12.14	12.11	12.08	12.05	12.02	11.99	11.96	11.93	11.90
8	11.87	11.84	11.81	11.79	11.76	11.73	11.70	11.67	11.65	11.62
9	11.59	11.56	11.54	11.51	11.49	11.46	11.43	11.41	11.38	11.36
10	11.33	11.31	11.28	11.25	11.23	11.21	11.18	11.15	11.13	11.11
11	11.08	11.06	11.03	11.00	10.98	10.96	10.93	10.90	10.88	10.86
12	10.83	10.81	,10.78	10.76	10.74	10.71	10.69	10.67	10.65	10.62
13	10.60	10.58	10.55	10.53	10.51	10.48	10.46	10.44	10.42	10.39
14	10.37	10.35	10.33	10.30	10.28	10.26	10.24	10.22	10.19	10.17
15	10.15	10.13	10.11	10.09	10.07	10.05	10.03	10.01	9.99	9.97
16	9.95	9.93	9.91	9.89	9.87	9.85	9.82	9.80	9.78	9.76
17	9.74	9.72	9.70	9.68	9.66	9.64	9.62	9.60	9.58	9.56
18	9.54	9.52	9.50	9.48	9.46	9.44	9.43	9.41	9.39	9.37
19	9.35	9.33	9.31	9.30	9.28	9.26	9.24	9.22	9.21	9.19
20	9.17	9.15	9.13	9.12	9.10	9.08	9.06	9.04	9.03	9.01
21	8.99	8.98	8.96	8.94	8.93	8.91	8.89	8.88	8.86	8.85
22	8.83	8.81	8.80	8.78	8.77	8.75	8.74	8.72	8.71	8.69
23	8.68	8.66	8.65	8.63	.8.62	8.60	8.59	8.57	8.56	8.54
24	'	8.53	8.51	8.50	8.48	8.47	8.45	8.44	8.42	8.41	8.39
23	8.38	8.36	8.35	8.33	8.32	8.30	8.28	8.27	8.23	8.24
26	8.22	8.20	8.19	8.17	8.16	8.14	8.13	8.11	8.10	8.08
-27	8.07	8.05	8.04	8.02	8.01	7.99	7.98	7.96	7.95	7.93
28	7.92	7.90	7.89	7.87	7.86	7.84	7.83	7.81	7.80	7.78
29	7.77	7.75	7.74	7.73	7.71	7.70	7.69	7.67	7.66	7.64
30	7.63	7.61	7.60	7.59	7.57	7.36	7.35	7.54
T
(c)
Dissolved Oxygen
(mg/1)
T
(C)
Dissolved Oxygen
(mg/1)
31
7.5
41
6.5
32
7.4
42
6.4
33
7.3
43
6.3
34
7.2
44
6.2
35
7.1
45
6.1
36
7.0
46
6.0
37
6.9
47
5.9
38
6.8
48
5.8
39
6.7
49
5.7
40
6.6


Note: correction for barometric pressure B (an Hg) multiply by B/760; correction for
salinity S (chloride,, mg/1) multiply by [l - (S/100,000)] .
A-19

-------
C495A.5 (I)
The universe of possible coefficients and assumptions that can be
used in tne moaei may vary over a wide range, and can result in sig-
nixicantly different predictions of instream DO. It is extremely
important that the best possible estimate of these parameters be
obtained for each case to ensure that they adequately represent the
stream system to be modeled. Site-specific data should be used
whenever possible. When a comprehensive field survey is not feasible*
appropriate data described-in the literature or available transfer
data may be used. However, if literature data or transfer data are
used, it is strongly encouraged that a general reconnaissance visit of
the site to be modeled be made in order to qualitatively evaluate the
applicability and reasonableness of the data being used. The coeffi-
i
cents and assumptions to be used and minimum site-specific data
requirements for this Method are discussed further* in the next sec-
tion. It is important to ensure that the coefficients and assumptions
which are used in the model do adequately represent the conditions in
each uniform stream reach, and that they are changed in the model, as
appropriate, between the stream reaches being modeled to reflect any
system changes' between the reaches (e.g., make appropriate changes in
coefficients, travel time, etc., to reflect significant changes in
slope, channel geometry, benthic characteristics, etc.)
After the appropriate assumptions are made and coefficients
selected, the location of minimum DO concentration (i.e., the sag
point) is to be determined. This can be accomplished by applying
A-21

-------
C495A.5 (I)
incremental time periods in Equations 3 and 4 and noting where the
minimum DO concentration occurs. The number of trial-and-error
iterations can be minimized by first using the following equation to
determine the approximate location of the sag point:
= [l/(K2"KB0D)J [ln(K2/KB0D^D	^
[i-W^ODM^BOD 0B0Do)]
-	approximate time (and. hence, distance) to the sag
(critical) point*
= reaeration rate*
= BOD reaction rate (for CBOD, NBOD, or average of
two rates; see text, below)*
= mixed initial DO deficit (at discharge point).
-	initial ultimate BOD concentration (at discharge
po int).
Where CBOD and NBOD have different rates* the sag point can be bounded
by assigning first the lower and then the higher rate to the total
ultimate BOD* or approximated by averaging the two rates.
The next overall step in this Method is to establish the allow-
able loading rates needed in order to meet the water quality standards
at the critical sag point. This can be accomplished by applying* in
an iterative manner, successively lower CBOD and NBOD values until the
DO standards are met at the sag point. An alternative to this "trial
and error method for dissolved oxygen is to separately calculate the
dissolved oxygen deficit due to each BOD source (e.g.. upstream BOD*
sediment demand* plant carbonaceous BOD* and plant nitrogenous BOD).
t
c
where t
c
^BOD
D
o
UBOD
,-22

-------
C495A.5A (I)
By knowing the relative contribution of each BOD source to the total
deficit when using this alternative approach, and since the various
"""a-.- deficits are additive (see Equation 3), it is an easy task to
identify the combinations of wastewater BOD reductions that will
achieve water quality standards and to select the combination that
will be the most cost-effective.
As stated above, it is extremely important that the best possible
estimate of the parameters' used in the model be obtained for each
case, and that they adequately represent the system being modeled.
The next several subsections discuss recommended parameter values and
assumptions to be used with the Simplified Method. The following
points are addressed:
	flow regime
	target DO
	treatment capabilities
	rate constants
	inital deficit determination
	conversion from CBOD to BODc
u	5
	post-aeration
	nonpoint sources.
The recommendations made below are intended to help the Simplified
Method user to develop modeling results that are consistent with the
applicable water quality standards.
1) Flow Regime. Both low-flow and high-flow conditions should be
assessed to determine the critical conditions. In some cases, severe
t
non-point source pollutant contributions during high-flows might
A-23

-------
C495A.5 (I)
preclude attainment of desired water quality objectives. If the high-
flow condition is found to be critical, further analyses of nonpoint
sources should be conducted.
The flow regime to be used in the Simplified Method is the design
low-flow specified in the applicable water quality standards. This
flow will, in most cases, be the 7-day, 10-year low-flow (yQjg).
If no design flow is specified, the yQ^g should be used for.design
purposes. If any flow value other than those specified above is used
in the analysis, a sound justification must be provided to support the
use of this value.
2) Target Dissolved Qxvypn. DO standards are often presented as a
minimum at all times: some States include an average value along
with the minimum. Outputs (the DO simulation) from steady-state
models are based on the averaging period for input loadings; they,
therefore, represent the average DO conditions likely to prevail at
the flow condition being simulated. The two major factors that can
cause the actual minimum DO to be considerably lower than the average
predicted by steady-state model computations are: (1) diurnal varia-
tions in loadings to and from the contributing waste treatment plant,
and (2) diurnal variations of instream DO caused by algal photosynthe-
sis and respiration. The magnitude of these variations is likely to
differ from plant to plant and from stream to stream. The problem is
further complicated by the fact that prevailing fluctuations in a
A-24

-------
C495A.5 (I)
scream may be radically altered under construction of a larger treat-
ment plant with higher levels of treatment* and that quantification of
these fluctuations through intensive field investigations may not ac-
curately define these future conditions. For this reason* users of
this Method are urged to obtain additional field data so that instream
responses can be better correlated with different levels of treatment,
and that better estimates under projected conditions can be made.
When modeling* the following DO targets should be used:
(a)	If the DO standard is expressed as an average and a minimum
requirement (e.g.* an average of 5 mg/1 and a minimum of 4
mg/l) the average number (e.g.* 5 mg/1) should be used as
the target.
(b)	If the DO standard is expressed only as a minimum (e.g.* a
minimum of 5 mg/1 at all times)* the target DO may be
obtained by adding one-half of the diurnal variation to the
DO standard (e.g.* for a total diurnal variation of 1 mg/1*
then the target is 5 mg/1 = 0.5 mg/1 = 5.5 mg/1). In the
absence of adequate site-specific or transferable data* 0.5
mg/1 should be added to the DO standard. If any other
values (either lesser or greater than 0.5) are used, they
must be supported by adequate data.
There is not a strong quantitative basis for using the
recommended value of 0.5 mg/1 to compensate for diurnal variations;
the choice is based in part on the acknowledgement of the existence of
such variations and on the need to allow some reasonable compensation
in the absence of an adequate data base. However* Thomann (19) feels
that there is a basis for using the 0.5 mg/1 value* but this value is
associated more with random, rather than just photosythesis/respira-
tion* fluctuations. Additional field studies should be conducted to
either support or modify this value.
A-25

-------
C495A.5A (I)
3J Trpafmpnt Capahi 1 irips. For typical domestic wastewaters, the
following effluent concentrations should ordinarily be assumed for
modeling purposes. These values are 30-day averages that would be
expected during warm summer months (i.e., during conditions similar to
those being modeled).
Effluent Concentration (mg/1)
Trpafmpnt
Influent
Secondary
Nitrification (single
stage or two stage)
Oxidation Ditch
Nitrification plus
Tertiary Filtration
m5
100 - 300
30 (or 85Z
removal)
5 - 8**
10 - 15
3 - 5**
MLj-il
12 - 35
10Z less than raw
concentration
1.0 - 1.5
1.0 - 1.5
1.0 - 1.5
**(See Appendix A2 for clarification.)
The values selected from the ranges given above should depend on the
influent concentrations (e.g., lower values should be used for lower
influent concentrations).
4) Rate Constants
(a) Reaeration RatpfK^. The critical values in DO analyses of
small streams are the reaeration rate, and to a lesser extent, the
CBOD and NBOD decay rates and effluent DO levels. Many formulations
have been developed for predicting stream reaeration rates based on
A-26

-------
C495A.5A (I)
physical characteristics such as stream width, depth, velocity, and
slope (4,5). Recent work by Rathbun (6) and by Grant and Skavroneck
(8) indicates that the Tsivoglou formula (7,20), in which is
calculated by Equation 6, tends to most accurately predict stream
reaertion. Presently, the data base on which most reaeration
equations and recommendations are based is quite limited. Additional
data collection efforts and research are needed in this area.
The Tsivoglou formula, presented below, should be used for
computing reaeration rates on small, shallow streams:
K2 = CVS at 20C	(Eq. 6)
where	= reaeration rate (1/day)
V	= stream velocity (ft/sec)
S	= stream slope (ft/mi)
C	= proportionality constant with the values shown below:
C = 1.8 for 1< Q <10 cfs
= 1.3 for 10
-------
C495A.5A (I)
separate DO calculations using both the higher and lower C values
so that lover and upper limits of predicted DO can be established.
If this range of predicted DO is found to be relatively large, it
is recommended that additional work, including field measurements,
be performed to help reduce the uncertainty in the reaeration rate
to be used.
O'Conner's reaeration formula, presented below, may be used for
larger, deeper streams with more uniform channel geometry or those
with significant pooling (4):
K2 = 12.9 v0,5/H1,5	at 20?C	(Eq. 7)
where V	= stream velocity (ft/sec).
H	= average stream depth (ft).
The values of V and H used in the above equations should be based
on actual field measurements so that the uncertainty in the rate can
be reduced. The value of S can be determined from field measurements
or from appropriate maps.
Any other applicable reaeration prediction methods may be used in
lieu of the above methods only if these alternative methods are
supported by an adequate technical justification that includes
sufficient field data collected from the area.
(b) CBOD Decay	a review of reaction rates measured on
low flow streams with similar characteristics showed that CBOD rates
generally range from about 0.2 to around 3*0 or more (10. 11. 12.
13. 21) depending in part on depth and degree of treatment (see
A-28

-------
C495A.5A (I)
Exhibit 3). The minimal data available for small* low flow streams
with treatment greater than secondary suggest that the CBOD rates
under these conditions typically fall between about 0.2 and 0.5 (at
20C). Adjusting CBOD rates by depth as proposed by Hydroscience
(13) suggests 0.3 to be a representative value for these low flow
streams with a mostly stable fairly rocky bottom, and about 0.2 for
streams with a primarily unstable sediment bottom.
Using this approach. CBOD then becomes (14):
Kj= C (H/8)"0*434	for H <8 ft.	(Eq. 8)
= C	for H > 8 ft.
where	= CBOD decay rate (1/day),
H	- average stream depth (ft).
C = 0.3 for streams with mostly stable fairly rocky
bottoms.
C =0.2 for streams with primarily unstable Bediment
bottoms.
It should be noted that Equation 8 generally represents an average of
a range of possible values at any given depth. Based on limited data
presented in the literature (11. 13. 21) and elsewhere (10. 12; also
see Exhibit 3). the following ranges of the CBOD rate are presently
being suggested:
A-29

-------
C495A5.T.(l)|
Exhibit 3. REACTION RATES MEASURED ON LOW FLOW STREAMS**
River
CBOD Rate
Measured
Depth
Adjusted
NBOD*
Rate
Treatment
Level
Flow (cfs)
River STP Depth (ft)
Upper Olentangy, Ohio (7)	1.24	0.43
Patuxent River, (8)	0.30	0.3
Maryland
West Fork of Blue
River, Indiana (9)
Hydroscience (10)
0.5-0.79 0.2-.32
.37-.96 .19-.42
Recommended Values	0.3
Depth Adjustment K  K (Measured) (D/8)
.434
.27-.50
0.5
.42
D < 8 ft
AST - No nitrification 2.3 3.0	0.7
AWT - Nitrification with 31 6.8	
microscreens
AST - Secondary with	4 1.4 0.9-1.2
rapid sand filters
Highly treated effluent	1-3
nitrification
~Reaction rates are at 20C.
~~Submitted by EPA Region V.

-------
C495A5.T (I)
Exhibit 4. CBOD/BODj DATA*




Percent
Number
Ultimate



Flow
Industrial
of
CBOD
State
Plant
Type
(MGD)
Flow
Samples
bod5
Ohio
Lakewood
Activated
Sludge
11.7
0Z
1
3.27
Ohio
Mansfield
Activated
Sludge
10.6
32%
1
3.43
Oh io
Shelby
Activated
Sludge
1.2
0 Z
3
3.21
Ohio
Lorain
Activated
Sludge
14.1
14Z
4
3.13
Ohio
Coshocton
Activated
Sludge
2.3
39Z
1
4.34
Ohio
Conneaut
Activated
Sludge
2.6
OX
1
2.61
Ohio
CRSD Easterly
Activated
Sludge
136.0
12Z
2
5.10
Minnesota
Minneapolis-St. Paul
Activated
Sludge

27Z
13
3.18
Wisconsin
Fall Creek
Trickling
Filter


2
3.40
Uiscons in
Neenah-Menasha
Activated
Sludge

40Z
2
3.20
Wisconsin
Town Menasha East
Activated
Sludge

22Z
1
1.80
Wisconsin
Town Menasha West
Activated
Sludge

42Z
2
3.10
Wisconsin
Heart of the Valley
Act. and 1
filters
5
< 10Z
2
2.75
Wisconsin
Depere
Activated
Sludge

20Z
1
3.00
Average





3.2
~Submitted by EPA Region V.

-------
C495A.5 (I)
T.ovpI of Treatment
CBOD Rate (K^**
Minimum	Maximum
Secondary treatment
0.3
1.5
Greater than secondary
 streams with mostly
stable fairly rocky
bottoms.
0.3
0.5
 streams with primarily
0.2
0.4
unstable sediment
bottoms.
(Note: These ranges are based on a very limited data set; they are
subject to modification, as necessary* as additional rate data
are submitted to EPA Headquarters. Users are urged to
collect site-specific rate data whenever possible.)
**-(l/day. base e. at 20C)
Equation 8 may be used to estimate the CBOD rate vithin the ranges
specified above. Users of this approach should note that* at best,
the above equation is a crude* though rational, -empiricism, based on
a limited data set. A much larger data set consisting of accurate
Kj measurements for different levels of treatment and types of
streams is needed before a more precise empirical correlation equation
can be developed. Towards this end. States and EPA Regions are
urged to expand relevant data bases, and to submit these data and
suggestions to EPA Headquarters to assist in the refinement of the
above approach and ranges. Post-construction intensive surveys to
measure Kj (and K^) below AST and AWT plants would aid this
A-35

-------
C495A.5 (I)
effort significantly. Users are encouraged to collect site-specific
data or to use transferable data to help reduce the uncertainty in the
CBOD rate to be selected. Any deviations from the above approach must
be supported by an adequate technical justification.
(c) NBOD Decay Rate	Several environmental factors have
been shovn to influence the rate at which nitrification occurs. Among
them are pH, temperature* 'suspended particle concentration, hydraulic
parameters, other pollutants that inhibit the nitrification process
(e.g.. some toxics), and the benthos of the receiving waters. While
no attempt is made in this Method to quantify the effects of these
factors on K^. users are expected to determine qualitatively whether
or not nitrification is likely to occur in the subject stream. If so,
users must determine whether or not conditions are optimal for
nitrification. For example, several researchers have shown that a pH
in the range of 8.4 to 8.6 is optimal for nitrification, with a rapid
decrease in nitrification outside the range of 7.0 to 9.0. Because
most State water quality standards require a pH in the range of
between 6.5 or 7.0 and 9.0. it is unlikely that the pH factor greatly
influences the occurrence of nitrification. However, consistent pH
observations in the range of 8.4 to 8.6 indicate that this factor is
conducive to maximum nitrification. Nitrification is also a function
of available benthic surface area for nitrifying organisms to attach
themselves. For example, if a stream bottom is completely devoid of
A-36

-------
C495A.5 (I)
surfaces (such as rocks. eCc.) on which nitrifiers can attach
themselves, it is likely that nitrification will not be a significant
factor in the DO analysis. Conversely* a shallow stream with a rocky
bottom is likely to have a high nitrification rate.
A site inspection will indicate the likelihood of nitrification,
and should be conducted. Based on the observations which are made
during the inspection* the user must estimate the applicable NBOD rate .
value. In view of the tenuous nature of this rate selection
procedure, particular care should be taken in evaluating the effects
through sensitivity analyses. Another point to consider is the
outcome of the ammonia toxicity analysis. If it was determined
previously that ammonia removal is required on the basis of ammonia
toxicity considerations, then the role of in the overall DO
I
analysis becomes somewhat less critical. On the other hand, if the
ammonia toxicity analysis does not clearly indicate the need for
ammonia removal, then the decision to provide nitrification at the
treatment plant will hinge solely on the DO analysis. This makes the
determination of the value much more critical. The water quality
analyst must then carefully assess stream conditions, and assign
reasonable rate coefficients, accordingly.
Based on limited observations of NBOD decay rate (2; also see
Exhibit 3), it appears that, where instream nitrification is found to
occur, most values range between about 0.1 and 0.6. In thp
A-37

-------
C495A.5 (I)
absence of applicable site-specific data, a value within the
range of 0 to 0.6 is to be selected. This selection should be based
part on a site inspection (as stated above), and on any appropriate
available transfer data. Generally, a value of around zero
should be selected only if strong evidence suggests a lack of instream
nitrification occurring under the projected conditions. Otherwise,
the values which are selected might be roughly 0.2-0.3 for
deeper streams with a primarily sediment bottom, around 0.4 for
shallower streams with a moderately rocky bottom, and about 0.6 for
shallow, rocky streams. The user is strongly encouraged to collect
site-specific data, and data from similar sites, whenever possible to
support the selection of the NBOD decay rate.
(d) Sediment (Benthic) Oxygen Demand (S). Sediment oxygen is a
factor that is often significant in the DO analysis. For the types of
situations applicable to this Method, Thomann (19) suggests that the
following benthic demand rates be used when simulating stream DO
response to various treatment levels:
S(gm/m^/day of 02at 20C)
Vicinity	Downstream
Treatment Level	of Outfall	of Outfall
Poor Secondary Trt	2-4	0.5-1
Secondary Trt	1-2	0.3-0.7
Greater than Secondary	0.2-0.5	0.1-0.2*
~(Even with high levels of treatment at the point source, there"will
usually be at least a minimal benthic demand present, e.g., due to
"background" or other sources).
A-38

-------
C495A.5 (I)
For the purpose of this analysis, the becthic demands should be
considered to be at a minimum under future conditions* unless
site-specific circumstances indicate a continued presence of
substantial benthic deposits in the future (e.g.* from nonpoint
sources). The applicable rates suggested above should be used in the
analysis* unless site inspections indicate that higher or lover values
should be used.
When selecting the benthic demand rate for future conditions,
consideration should be given to the fact that there might be
continued other sources of benthic demand* such as from nonpoint
sources. Therefore* a site inspection should be conducted to
determine the characteristics of the stream bottom and the areal
extent and magnitude of the benthic demand* and to reveal any possible
continuing benthic demand problems.
(e) Temperature Corrections of Reaction Rates. Temperature effects
on the various reaction rates can be approximated by the following
equations:
 for the Sediment Oxvypn Demand Rate!
(SB)
T
(SB)20(1.065)T'20
(Eq.. 9)
where (SB)^.
adjusted benthic demand rate for specified stream
temperature*
= selected benthic demand rate (for stream
temperature of 20C),
A-39

-------
C495A.5 (I)
T = specified stream temperature (*C),
T-20	(Eq. 10)
- -T..S1^_E2J_aiisLE3: KT = K20 d
where	= adjusted K-rate for specified stream tenperature.
^20 = selected K-rate (for stream temperature of 20C),
T = specified stream temperature (C),
g = 1.047 for K^t
= 1.024 for Kj,
= 1.1 for K^.
(5) Initial Deficit: (D^) Determination. When performing a
DO analysisi the initial dissolved oxygen deficit (Dq) must be known
(see Equation 3). In order to calculate Dq, the resultant mixed DO
concentration at the discharge point must first be calculated. This
can be accomplished by performing the following mass balance:
DO
o
= [douqu+dodqd]/[qu+ qd]	(e<- n)
where D0q = mixed instream dissolved oxygen concentration at
discharge point (mg/1).
D0u	=	upstream dissolved oxygen concentration (mg/l)t
DOjj	=	POTW discharge dissolved oxygen concentration (mg/1).
Qu	=	upstream design low flowt
Qp	=	POTW design discharge flow rate.
Then the saturation DO (DOg^j) concentration must be determined
using the resultant water temperature downstream of the discharge
A-40

-------
C495A.5 (I)
(Tr) which was calculated using Equation 2 (in the "Ammonia Toxicity
Analysis" section). This can be determined from Exhibit 2. By using
and DOsAT* C^e	mixed dissolved oxygen deficit (Dq)
can be calculated as follows:
Do = DOSAT-DOo	(E<' 12 >
(6) Cnnvprsion from CBOD^to BOD.-. Data submitted by
Region V (see Exhibit 4) indicate that the ratio of CBOD^ to BOD^
should be about 3.0. Other limited data presented in the literature
suggest that this ratio is about 1.5 to 2.0. It is suspected that
many of the lower ratio values were established using older data from
older, less efficient treatment plants* and that the Region V data is
generally from newer more efficient plants.
When evaluating secondary treatment discharges* vater quality
analysts should use a ratio in the range of 1.5 to 2.0* unless
applicable long-term BOD tests indicate some other value. The value
of 1.5 should generally be applied to "poorer" secondary plants, and
2.0 should probably be applied to the "better"* more efficient
secondary treatment plants. A ratio in the range of 2.5 to 3.0 should
be used for plants with treatment levels greater than secondary*
unless applicable planL.-specific data indicate some other value.
These higher ratios resulting from greater levels of treatment are
also consistent with intuitive expectations. Site-specific or
transferable data should be collected whenever possible to help
support the selected value.
A-41

-------
All EPA Regions, the States, and others are strongly urged to
participate in a nationwide data gathering effort so that more
accurate ratios can be developed. Such an effort would not be very
resource intensive, and the results would be extremely useful. Care
should be taken to ensure that only the carbonaceous demand is
measured. This data collection effort should include information on
the type of treatment and type of influent, and the sampling should,
to the extent possible, only be performed on sanitary wastewaters that
are unchlorinated. This data should be submitted to EPA Headquarters
for compilation and analysis.
(7) Post-Aeration. Post-aeration of the effluent to a DO
concentration of 7 mg/1 should always be evaluated as an alternative
to higher levels of treatment, unless there is a site-specific
constraint that precludes the use of post-aeration equipment. This
technique can be particularly useful in cases where dilution is low
and reaeration rates are also low.
(8) Nonpoint Sources. In some cases, nonpoint sources may
preclude attainment of dissolved oxygen water quality objectives even
with stringent advanced treatment. For example, streams with
extensive wetlands may contribute low DO water in sufficient
quantities to cause standards violations, and agricultural or urban
runoff in the vicinity of a plant discharge may also nullify the
benefits of advanced treatment. In cases such as these, nonpoint
A-42

-------
C495A.5 (I)
source control tradeoffs must be considered before advanced treatment
is chosen. Site-specific evaluations should be made to identify
possible nonpoint source problems.
D. Sensitivity Analysis
The sensitivity of computed stream responses to changes in
estimated input variables must be determined before a final decision
of treatment levels is made. A sensitivity analysis combined with
judgement is essential to help establish greater confidence in the
results that are obtained.
The sensitivity of computed (predicted) instream responses to the
various input values should be determined by repeating the analyses
described above with changes (increases and decreases) in the input
variables. The following steps should be followed:
1) Initially, three sets of calculations should be made to reflect a
"worst," "best," and "average" case for each alternative treatment
level. This can be accomplished by using model input values that
represent, respectively, the "worst" and "best" ends of their
sensitivity ranges and the values actually selected for the model.
The outputs of these computations should be plotted as DO profiles.
If all three cases indicate a violation of the water quality
standard with the given level of treatment, then the next level of
treatment is needed, and no further justification is necessary. If
all three cases do not indicate a violation, then the next step
must be taken.
A-43

-------
C495A.5 (I)
2) Next, each input variable to each equation above should be
individually increased and decreased, so that the magnitude of the
cifferences in predicted instream responses can be assessed. Each
input variable (including rate coefficients, travel time, physical
characteristics, etc.) should be varied over a range of values that
reflects the uncertainty in the particular variable. If direct
measurements of certain input variables are made, then the uncer-
tainty in the variable would tend to be relatively small and,
therefore, the range to be used in the sensitivity analysis would
generally be relatively small. Very close scrutiny should be given
to those input variables which have no site-specific or transfer-
able data to support their having been selected. If rates (or rate
formulations) other than those suggested in the above analyses are
used, then the sensitivity analysis should be used as part of the
justification for the alternative rates (or formulations).
The results of these sensitivity analyses (in step 2) should be
reviewed within the context of the effluent quality expected for
various treatment levels. Therefore, if the effluent requirements
determined using the range of inputs for each variable fall within
the expected effluent quality from a single treatment level (e.g., AST
or AWT), then additional analyses would generally not be required for
that variable since the need for that level of treatment is obvious.
However, if the required treatment level is heavily sensitive to, and
dependent on, the selection of an input value(s) especially where
existing data are inadequate to characterize the variable(s), then a
A-44

-------
C495A.5 (I)
sufficient amount of additional data shall be obtained to more
accurately define that model variable(s) (thus increasing the
confidence in that variable) so that the selection of the treatment
alternative can be clarified. For even further confirmation of the
selected effluent limitations, the sensitivity analysis can also be
rerun for the individual input variables at a less stringent level of
treatment and the results analyzed to determine if the desired water
quality objectives could possibly be met at that lesser treatment
level within the range of individual inputs being utilized. It must
be emphasized that the use of sound professional judgment is
essential when evaluating the confidence in the model input variables
used and in the modeling results obtained.
To further assist in evaluating the results of the sensitivity
analyses, the incremental present worth cost (construction and O&M) of
the proposed improved treatment process may also be considered when
deciding the necessary level of treatment. For example, if oversizing
the clarifiers, providing additional aeration and clarifiers for
nitrification, or seasonal chemical addition could provide the level
of treatment in question, such treatment could be partly justified
based on best judgment due to the relatively low cost of such
additional treatment. On the other hand, filters (as an add-on to
nitrification), due to their high incremental cost, could be justified
by this Simplified Method only if the results of these sensitivity
analyses indicate sufficient confidence in the results. Otherwise,
additional data (including for calibrating and verifying the model)
would be required.
A-45

-------
C495A.5 (I)
Generally, the variables to be analyzed in the sensitivity
anlaysis should include those listed below, and should generally be
-rarled by sensitivity ranges in the order of those which are suggested
below (especially if little or no data is available to support the
variable's selection):
	CBOD rate - vary by about +50 to 100Z (and appropriate
increments in between), depending on the uncertainty in the
estimated value.
	NBOD rate - vary by about +25 to 75X or more (and
appropriate increments in between), depending on the
uncertainty in the estimated value.
	Reaeration rate - vary by about + 25Z to +1002 or more
(depending on the uncertainty in the estimated value), and
by intermediate increments. An appropriate sensitivity
analysis should also be performed on the variables used in
the respective reaeration equations (i.e., velocity, and
slope or depth).
	Benthic demand - generally should use the suggested ranges
presented in Section 111(C)(4)(d).
	Temperature, pH - use ranges appropriate for the
situation. -
E. Results
1) Permit Conditions. After determining the final effluent
limitations necessary for the maintenance of water quality standards,
these limitations should be entered into the NPDES permit. Municipal
effluent limitations are often specified as 30-day and 7-day average
values for BOD^ ammonia-N, and suspended solids. For streams with
zero flow at the critical conditions, the results of the DO analysis
shall be used as 7-day average effluent limits rather than 30-day
averages, since these small streams are often very reactive to
variable waste inputs. For streams with nonzero flow at the critical
A-46

-------
C495A.5 (I)
conditions, the currently adopted and applicable State or EPA Regional
procedures for applying modeling results to POTW discharge permit
effluent limitations shall be used.***
The CBOD and NBOD outputs from the DO analysis should be
converted to BOD^ and ammonia-N NPDES permit limitations using the
following relationships (established earlier):
(a)	BOD5  CBOD/r
(where r = the UCBOD:BODj ratio, for the appropriate level
of treatment, selected in section 111(C)(6).)
(b)	NH3	NBOD/4.57
2) Seasonal Effluent Limitations. The effects of variations
in temperature and flow should be evaluated to determine whether or
not operating costs can be reduced through seasonal relaxation of
effluent limitations. For example, it is conceivable that in winter,
higher flows and lower temperatures would allow for a relaxation of
BOD and ammonia limitations from a toxicity and DO standpoint.
EXAMPLE PROBLEM
(An example'problem will be prepared and provided to the users of
this Method in the near future.)
***-NOTE: This issue is currently being analyzed and will be
addressed in the forthcoming regulation on wasteload allocations/total
maximum daily loads. The Agency is presently leaning towards using
modeling results as 7-day averages. Comments are welcomed on this
issue.
A-47

-------
C495A.A CI)
APPENDIX A1
METHOD FOR DETERMINING EXPECTED DOWNSTREAM pH
Calculating the pH of the stream after mixing of upstream flow
with wastewater discharge is straightforward - provided there is some
minimal water quality information available on each.
It can be done with information on different combinations of
alkalinity, acidity and pH. The most direct method, and simplest to
present for a simplified methodology, requires information on pH and
alkalinity. If no pH or alkalinity data is presently available for
the POTW and/or for upstream, then a short-term program of collecting
the needed pH and/or alkalinity data should be initiated. Assuming
generally average conditions exist at the POTV and upstream during the
data collection program, then a fairly accurate determination of their
average pH and alkalinity conditions can be made in several days or a
few weeks. The tests for pH and alkalinity are easy and inexpensive:
	fiE - is easily (and commonly) measured by pH meter.
	Alkalinitv - is also commonly measured. Standard
Methods specifies titration with strong acid (0.02 N
^SO^) - in which case alkalinity is reported as
mg/1 as Ca C0^.
The ionic forms comprising alkalinity (HCO^**, COj"
and OH" be calculated from the relative amounts of acid
A-49

-------
C495A.A (I)
required to reach the two end points (Fhenolphthaleln
at pH 8.3* and Methyl Orange at about pH 4.5). For
natural waters between pH 4.5 and 8.3 (essentially all
we need be concerned with for this exercise)* there
will be no phenolphthalein end point  and all of
the alkalinity will be present as bicarbonate ion
(hco3~).
Note that the procedure presented, and the chart used, will apply
for any situation. The instructions for its use are much simpler to
present if it is assumed that the only waters being dealt with will be
in the pH 4.5 to 8.3 range (which will usually be the case).
There are a number of techniques, methods* etc., for calculating
pH. The one presented here seems to be best suited for these
purposes. The chart is taken from **Aquatic Chemistry** by Stumm &
Morgan (Viley Interscience, 1970), and the approach is a portion of
the overall approach they describe - which for simplicity is limited
to the usual case which was selected.
The calculation is illustrated by the following example:
 In a natural water system (or wastewater) with a pH in the
range of 4.5 to 8.3, the alkalinity measured is all
bicarbonate ion (HCOj") reported as mg/1 as CaCO^. The
Total Inorganic Carbon (CT) win consist of both HCO-j"
and soluble C0^ which coexist in water in this pH range.
(ROTE: The Standard Methods test for acidity would measure
soluble C02.)
A-50

-------
C495A.A (I)
	The chart requires that alkalinity be reported in terms of
milliequivalents/liter (meq/1). The conversion is as
follows:
Alkalinity-mg/1 as CaCOj X 1/50 = Alk.-meq/1
	Total Inorganic Carbon (C^,) must be in terms of
millimoles/liter (mM/1). However, if we are working with pH
and alkalinity, we need not worry about this conversion,
nor about determining the acidity or CO^ concentration.
	In a situation like the one being addressed, both alkalinity
and are conservative (pH is not). Thus, when two
waters with different concentrations of alkalinity and
are mixed - the final concentration in the blend can be
determined by simple mass balance.
	The steps are:
1.	From alkalinity and pH, determine for stream
and waste.
2.	Calculate concentration of alkalinity and C-. in'
blend.
3.	Determine pH of blend from blend alkalinity and
CT*
	An example problem and a calculation sheet are given in
Exhibit 5. A blank calculation sheet, with chart, is also
attached (Exhibit 6).
A-51

-------
EXHIBIT 5. EXAMPLE CALCULATION.
1. GIVEN
Flow 
pH -
ALK -
POTW Discharge
6 MGD - 3.86 CFS
7.2
150 mg/8  3.0 mg/f
as CaCo,
Upstream Flow
3.0 CFS
7.5
s
50 mg/B -1.0 mg/C
as CaCo-
2. DETERMINE C^. FROM CHART
POTW Discharge
ALK - 3.01
I CT - 3.55
pH - 7.21 T
Upstream Flow
ALK = 1.01
pH
7.5
cT = 1.1
3. CALCULATE BLENDED ALK AND CT
B - Blend S - Stream D = Discharge
TS	CT0
C_ or ALK - IALW"ALIVQOl
VD>
(1.0- 3.0)+ (3.0- 3.86) 14.58
ALK.
(3.0 + 3.86)	6.86
(1.1  3.0)+(3.55-3.86) 17.00
B
(3.0 + 3.86)
6.86
2.12
2.48
4. DETERMINE pH OF BLEND FROM CHART
ALK - 2.12 J
2.48
pH - 7.2
3
>
e
t
*3
>
'5
%
c
To
Blend
POTW
B end
Stream
CT (Total carbonate carbon; millimoles/liter)
Note: Doubled scales apply II pH line through origin.

-------
cXHIBIT 6. BLANK CALCULATION SHEET.
>
i
U1
01
POTW Discharge
Upstream Flow
1. GIVEN
Flow ='
pH 
ALK -
2. DETERMINE FROM CHART
POTW Discharge	Upstream Flow
ALK "
ALK
pH
T
pH
3. CALCULATE BLENDED ALK AND CT
B  Blend S - Stream D = Discharge

-------
C495A.A (I)
APPENDIX A2
The results of new data supplied by EPA EMSL-Cincinnatl show that
BOD^ levels in nitrification system effluents range from BOD^ 5-8 mg/1.
Tests run on typical nitrified effluents using the Standard Methods
BODj test consistently exhibited higher than actual carbonaceous BOD^ due
to nitrification occurring, during the CBOD test. The reason for the high
BOD^ result is that aqueous solutions containing ammonium salts are used
 in the standard BOD^ test. These ammonium salts in the presence of nitri-
fying organisms in the nitrified effluent create an additional apparent
BODj demand in the effluent. For this reason, data from plants with
nitrification cannot be used to predict treatment capabilities unless
nitrification inhibitors are used.
The Agency has proposed (December 3, 1979 Federal Rp^iatgr)
an inhibitory BOD^ test for nitrified effluents. Early work at the
Washington, D.C.~~Pilot Plant used allyl thiourea as the inhibitory
chemical. These tests show that the BOD^ measured for uninhibited
nitrified effluents is two to three times greater than for inhibited
effluents (See Exhibit 7).
It is advised that all treatment plants with nitrification use
the inhibiting chemical and report the BOD^ values that are
determined from this method to expand the data base of plant
operational capabilities.
A-57

-------
C495A.5R (II)
REFERENCES
1.	Tetra Tech Inc. 1977. Water Quality Assessment; A Screening
Method for Nondesignated 208 Areas, EPA Publication No.
EPA-600/9-77-023, August.
2.	Thomann, R.V. 1972= Systems Analysis and Water Quality
Management. McGraw Hill Book Co., pp 65-122.
3.	Streeter, H.W. and E.B. Phelps. "A Study of the Pollution and
Natural Purification of the Ohio River, III, Factors
Concerned in the Phenomena of Oxidation and Reaeration",
U.S. ;Public Health Service, Public Health Bulletin No. 146.
4.	Covar, A.P. 1976. "Selecting the Proper Reaeration Coefficient
for use in Water Quality Models", presented at the EPA
Conference on Environmental Modeling and Simulation, April.
5.	Bennett, J.P. and R.E. Rathbun. 1972. "Reaeration in Open-
Channel Flow, Geological Survey Professional Paper 737".
6.	Rathbun, R.E. 1977. "Reaeration Coefficients of Streams,
Statei-of-the-Art", Journal of the Hydraulics Division, ASCE,
Vol. 103 No. HY4, April.
7.	Tsivoglou, E.C. and J.R. Wallace. 1972. "Characterization of
Stream Reaeration Capacity", U.S. Environmental Protection
Agency,- Report No. EPA-R3-72-Q12, October.
8< Grant, R.S. and Skavroneck. , 1980. Comparison of Tracer Methods
and Predictive" Equations for Determination of Stream
Reaeration Coefficients on Three Small Streams in Wisconsin.
U.S. Geological Survey, Water Resources investigation 80-19,
March.
9. Personal Communication with Dr. Ernest Tsivoglou, March 26, 1980.
10. Personal Communication with Maan Osman, Upper Oletangy Water
Quality Survey, Ohio EPA, September 1979.
11- ?heiffer, T.H., L.J. Clark, and N.L. Lovelace. 1976. "Patuxent
River Basin Model, Rates Study", Presented at EPA Conference
on Environmental Modeling and Simulations, April.
A-58

-------
C495A.5R (II)
12.	Personal Communication with Dr. ,T;P. Chang. 1979. West Fork of
Blue River Water Quality Survey, Indiana State Board of
Health, September.
13.	Hydroscience Inc. 1971. Simplified Mathematical Modeling of
Water Quality. EPA, March.
14.	Raytheon Co. 1974. Oceanographic and Environmental Services,
Expanded Development of BEBAM-A Mathematical Model, of- Water.
Quality for the Beaver, River Basin. EPA Contract No.
68-01-1836, May.
15.	Tetra Tech Inc. 1978. Rates, Constants, and Kinetic Formulations
in Surface Water Quality Modeling. EPA Publication No.
EPA-600/3-78-105, December.
16.	EPA, Region V, Eastern District Office, Dischargers Files.
17.	Personal Communication with Mark Tusler, Water Quality Evaluation
Section, Wisconsin Department of Natural Resources, October
17, 1979.
18.	Upper Mississippi River 208 Grant Water Quality Modeling Study.
Hydroscience Inc., January 1979.
19.	Personal Communication between E.D. Driscoll and R-7. .Thppjaan,
August 1980.
20.	Tsivoglou, E.C. and L.A. Heal. 1976. "Tracer Measurements of
Reaeration: III. Predicting the Reaerat ion Capacicy of
Inland Streams". Journal WPCF. December.
21.	Wright, R.M. and A.J. McDonnell. 1.979." "In-Stream JJeoxygenation
Rate Prediction", ASCE Journal of the ^Environmental
Engineering Division, April.
22.	Personal Communication with R.F. McGhee, EPA Region IV,
August 1980.
A-59

-------