WATER QUALITY MANAGEMENT PLANNING
Addendum to
Simplified Mathematical
Modeling of Water Quality
THIS REPORT SUPPORTS MATERIAL PRESENTED IN THE MAIN TEXT,
"SIMPLIFIED MATHEMATICAL MODELING OF WATER QUALITY"
AS THIS ADDENDUM EXPLAINS IN DETAIL SOME OF THE SIMLIFYING
ASSUMPTIONS MADE IN THE MODEL DEVELOPMENT, IT IS STRONGLY
RECOMMENDED THAT USERS CAREFULLY REVIEW THIS DOCUMENT
BEFORE ATTEMPTING TO APPLY THE MODELS PRESENTED IN THE MAIN TEXT.
ENVIRONMENTAL PROTECTION AGENCY
Washington,D.C. 20460
MAY 1972
-------
INTRODUCTION
This Addendum was prepared in response to suggestions from EPA
regional personnel on topics needing additional comment or clarification
in connection with the handbook,, "Simplified Mathematical Modeling
of ¥ater Quality". Topics covered in this Addendum are:
Section Title Page No.
I Waste Treatment Efficiencies E-l
II Nitrification E-9
III Determination of 0 from Observed
Data E-15
IV Reaeration Over Dams E-25
V Temperature Coefficients (for K^, Ka) E-35
VI Evaluation of the Dispersion
Coefficient, E E-35
Sections I and II, which explain some of the simplifying assumptions
made during model development, indicate specific situations where
additional discretion and judgment may be required before using
the handbook. When lagoon treatment is being considered, Figure E-1A
from Section I replaces Figure B-l (Chart B) and Figure E-l (Chart E)
from the main text. If the possibility of high algal concentrations
in lagoon effluent exists, Section I recommends against the use of
this guide. All handbook users faced with possible water quality
problems related to nitrogenous oxgen demand should read Section II
which discusses the assumptions made in the main text concerning
nitrification. Sections III, V, and VI provide additional assistance
on the derivation and use of several model coefficients. Section IV
presents new material on modeling reaeration over dams; this topic
is not discussed in the main text.
An errata sheet for the main text is included at the end of this
Addendum.
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APPENDIX E
ADDENDUM
I. Waste Treatment Efficiencies
The purpose of this section is to further explain
the bases of Tables III-3 and III-4 of the main text (see
pages 53-54), which deal with the estimated efficiencies of
treatment levels. The basic assumptions used for these tables
were: (a) 125 gallons/capita-day; (b) 0.174 pounds five-day
carbonaceous BOD (CBODj.) /capita-day; (c) 0.044 pounds oxidiz-
able nitrogen (organic nitrogen and ammonia)/capita-day; and
(d) 0.025 pounds PO./capita-day. The ultimate to five-day
carbonaceous BOD ratio used was 1.43. This term results from
a BOD bottle decay coefficient of 0.24/day, which is repre-
sentative of municipal wastes. The ultimate nitrogenous oxy-
gen demand to nitrogen ratio used was 4.57. This term results
from the stoichiometric balance of the conversion of ammonia
to nitrate, which shall be discussed in Section II of this
addendum. Application of these ratios resulted in (a) 0.25
pounds ultimate carbonaceous BOD/capita-day and (b) 0.20
pounds ultimate nitrogenous BOD/capita-day.
E-l
-------
With respect to carbonaceous BOD, the column labeled
"% Removal" in Table III-3 is in terms of estimated CBOD5 re-
moval efficiencies. Since carbonaceous removal efficiencies
are usually reported in terms of CBOD,., the normal procedure
in a stream or estuary analysis is to calculate the pounds of
CBODj. inputed into the water body, and subsequently increase
this load by the ultimate to five-day carbonaceous BOD ratio.
In Table III-3, the calculations were initiated with the 0.25
pounds ultimate carbonaceous BOD/capita-day, and the CBODj-
efficiencies were applied to this value based on the assump-
tion that the ultimate to five-day carbonaceous BOD ratio does
not significantly change in the secondary effluent. Under
this assumption, both procedures result in the same value when
reduced to the ultimate carbonaceous demand inputed into the
water body. The ultimate to five-day carbonaceous BOD ratio
may increase with more advanced treatment. However, the value
used is appropriate for interim planning.
Figures B-l (Chart B) and E-l (Chart E) of the main
text are obtained directly from Table III-3. The following
illustrative example problem on treatment efficiencies is
presented:
E-2
-------
Illustrative Example
Existing Population - 25,500
Proposed Treatment - High Rate Biological Treatment
DO Standard - 4 mg/1
River - Intermediate Channel, depth 5-10 feet
2
Drainage Area at Discharge Location - 1,700 mi
2
Estimated Drought Flow Rate - .05 cfs/mi
Maximum Water Temperature - 30°C
1) From knowledge of Area - moderate to high growth
fl = 2.00 (Table III-l, p. 49)
Design Popultion: 25,000 x 2.00 = 51,000
2) Chart B - Enter Figure B-l
Design Popultion - 51,000 at High Rate Treat-
ment gives effluent load of 10,000 Ib/day
ultimate BOD.
Calculation:
HR-BIO Treatment - Table III-3
85% removal of CBOD5
20% removal of oxidizable N
Q>25 C - OOP x ( _ > Ibs C - UOD
> >
cap-day cap-day
0.20 lbs N - UOD x (1 - .20) = .160 lbs N - UOD
cap-day cap-day
TOTAL = .197 lbS - UOD
cap-day
E-3
-------
.197 x 51,000 = 10,000 Ib UOD/day
197
Note: 25'+ 2Q (100) = 44% Remaining
56% Removal of UOD
Estimation of Municipal Loads
Ibs C - UOD lbs CBODc
0.25 lb ™V
cap-day ' *-~ "•"" cap-day
N - UOD 4>57 = lbs oxid. N
> >
cap-day cap-day
at 125 gallons/capita-day
.174 lbs CBOD ./cap-day 6
5 125 gal/cap-day 8.34 Ibs/gal
=167 mg/1
., .044 lbs Oxid.N/cap-day 106
uxia.N ^25x 8T3T
= 42 mg/1
3) Alternate Calculation:
Effluent CBOD5 reported in design as 25 mg/1
F, _ 51,000 x 125 gallons/cap-day
106 gal/MG
= 6.375 MGD
No nitrogen information.
Assume 20% removal of Oxid. N
42 mg/l-H x (1 - .20, x 4.57 *£
x 6.375 MGD x 8.34 = 8160 lbs N-UOD/day
E-4
-------
25 mg/1 CBOD5 x 1.43 ibs C "600° X 6'375 x 8-34
= 1900 Ibs C-UOD/day
Total - 10,000 Ibs UOD/day
4) See page 86 for solution
Allowable load - 4,000 Ibs UOD/day
5) Review of existing data indicates 20 mg/1
Oxid N in effluent
20 mg/l-N x 4.57 x 6.375 x 8.34 = 4860 Ibs N-UOD/day
1900 Ibs C-UOD/day
TOTAL = 6760 Ibs UOD/day
Additional Treatment still required to meet
DO standard in the future.
6) The planner may investigate when additional
treatment is required. At the present pop-
lation the load is 3380 Ibs UOD/day. Since
the allowable load is 4000 Ibs UOD/day, the
DO standard will be met under the proposed
treatment scheme for the present. There-
fore the planner could allow construction
of the HR-BIO system now with provisions
for the additional treatment needed as
growth occurs. A detailed planning study
would be required after construction.
Where sufficient land area is available lagoons have
been employed as a method of treatment. Lagoons may be class-
ified as four types:
E-5
-------
Type I - Aerobic Algae Ponds I „_,. , ., . . . „ ,
Type II - Facultative Ponds J "Stabilization" basins
Type III - Anaerobic Ponds )( or simPle
Type IV - Aerated lagoons - mechanical aeration
As a whole, lagoon treatment efficiencies average
about 80% CBOD5 removal, with a range of 50% to 90%. In the
colder climates, the lower efficiencies will be encountered
during the winter, due to the sensitivity of this type of
treatment to ambient temperatures. In mechanically aerated
lagoons, nitrogen (organic nitrogen and ammonia) removals may
range from 10% to 20%. However, for "stabilization" basins,
or simple lagoons which are not mechanically aerated, an over-
all average for nitrogen removals cannot be realistically de-
fined, due to the seasonal dependence of these forms of treat-
ment with the associated wide variation in nitrogen removals.
This situation is further complicated in that the effluents
from aerobic algae ponds and facultative ponds often have a
high content of organic nitrogen. This nitrogen is associated
with both living cells and detritus. The susceptability to
hydrolysis and the rate of oxidation will vary widely depend-
ing on the form of organic nitrogen in the effluent.
For the purposes of the report, when lagoon treat-
ment is considered, Figure E-1A replaces Figure B-l (Chart
E-6
-------
100,000
en
en
Z
X
o
UJ
10,000
1,000
1,000
10,000 100,000
DESIGN POPULATION
1,000,000
FIGURE E-IA
LAGOON TREATMENT EFFICIENCIES
-------
B), and Figure E-l (Chart E). The discharged loads shown in
Figure E-1A make use of the following table:
TABLE E-l
ESTIMATED EFFICIENCY OF LAGOON TREATMENT
ULTIMATE OXYGEN DEMAND
f4
Treatment % Removal #/capita/UOD remaining f .
Level * + * + traction
C N C N total remaining
Lagoon 80 15 .050 .170 .220 .49
*
C = carbonaceous BOD
N = oxidizable nitrogen
f. = residual fraction after treatment
The separation of algae and other suspended matter
from the effluents of aerobic algae ponds and facultative
ponds generally result in higher nitrogen removals than indi
cated in the foregoing table. However, higher nitrogen re-
movals should only be applied when justified on the basis of
consistent historical data of removal efficiencies of "sta-
bilization" basins in the specific geographical area under
investigation.
E-8
-------
When there is no separation, the algae in the ef-
fluents of aerobic algae ponds and facultative ponds may
cause significant diurnal variations in dissolved oxygen in
a stream. In such a situation, the modeling procedures pre-
sented in this guide are inadequate. In general, when the
possibility of high algal concentrations in an effluent exist,
the use of this guide is not recommended. In addition the
possible high solids content and color of such effluents may
be of concern.
II. Nitrification
In addition to the oxidation of carbonaceous ma-
terial in a water body, the oxidation of nitrogen by specific
bacteria also exerts an oxygen demand on the water body. In
long term biochemical oxygen demand tests, this is usually
observed as a second stage. This phenomenon is called nit-
rification. The important forms of nitrogen in this pheno-
menon are:
(a) organic nitrogen (amines, proteins)
(b) ammonia
(c) nitrite
(d) nitrate
E-9
-------
All forms may be discharged by municipal and indus-
trial waste sources. Organic and ammonia nitrogen, however,
are the more common forms discharged by municipal sources.
A series of reactions takes place in the nitrification phen-
omenon which essentially convert organic and ammonia nitrogen
into nitrate. In the process of this bacterial conversion or
oxidation, oxygen is drawn from available resources to allow
the reaction to proceed. Figure II-l of the main text (see
page 20), shows this process.
Organic nitrogen, when discharged into a water body,
undergoes an hydrolysis reaction with ammonia as one of the
end products. The ammonia formed from organic nitrogen, to-
gether with direct discharges of ammonia from waste sources,
is oxidized under aerobic conditions to nitrite by bacteria
of the genus Nitrosomonas, as, follows ' ' :
(NH4) + OH~ + 1.5 02 bacteria H+ + NO2~ + 2H20 +59.4 Kcal.
Note that oxygen is utilized in this biochemical reaction.
Stoichiometrically, the reaction requires 3.43 pounds of oxy-
gen for one pound of nitrogen oxidized to nitrite.
The nitrite formed is subsequently oxidized to nit-
rate by the Nitrobacter as follows :
E-10
-------
N02 + 0.5 O2 bacteria NC>3 + 18 Kcal,
This reaction requires 1.14 pounds of oxygen for one pound
of nitrite nitrogen oxidized to nitrate. The total oxygen
utilization in the entire forward nitrification process is
4.57 pounds of oxygen per pound of ammonia nitrogen. By con-
trast, carbonaceous BOD,- has an ultimate oxygen demand of
about 1.43. Thus, a pound of carbonaceous BOD5 requires about
1.43 pounds of oxygen, while a pound of organic nitrogen or
ammonia requires 4.57 pounds of oxygen. Nitrification reac-
tions are, therefore, a potential large source of oxygen de-
pletion in natural waters.
The forward sequential nitrification phenomenon is
illustrated in Figure E-2. If the sequence of reactions is
allowed to proceed uninterrupted, the ammonia decays almost
exponentially, nitrite builds up, but is quickly oxidized to
nitrate. Eventually, all of the original ammonia nitrogen is
converted bacteriologically to the nitrate form of nitrogen,
a bacterially stable end product. In natural waters subjected
to large discharges of nitrogenous waste materials, the re-
action generally proceeds in the direction indicated in Fig-
ure E-2. There are several factors which may modify the
sequence of the reactions. Under conditions of low dissolved
E-ll
-------
LJ
DISTANCE
FIGURE E-2
SEQUENTIAL REACTIONS IN NITRIFICATION
-------
oxygen, nitrification is inhibited, and at values approach-
ing zero, nitrification may be completely suppressed. This
has been experimentally verified by the British in the Thames
Estuary work , and earlier by Waksman . For all practical
purposes, nitrification may be assumed suppressed at dissolved
oxygen levels below 1.5 mg/1. However, as a water body re-
covers, nitrification may resume and cause a secondary dis-
solved oxygen sag further downstream. Since dissolved oxygen
concentrations of less than 1.5 mg/1 are intolerable in most
cases, the modeling of the secondary sag has not been included
in this guide. This may, however, cause some difficulty in
verification analyses, as shall be discussed in Section III of
the addendum.
At low water temperatures, less than 10°C, nitrifi-
cation is inhibited . In application of this guide, it may
be assumed that nitrification is suppressed at water temper-
atures below 10°C. The suppression of nitrification can be
simulated by eliminating the nitrogenous ultimate oxygen de-
mand portion of the waste input in the modeling analyses.
This concept is important in the evaluation of seasonal treat-
ment schemes.
If significant quantities of phytoplankton are pre-
sent, ammonia will be used as a nutrient source. As a result,
E-13
-------
the available ammonia for nitrification is depleted. In this
situation, the diurnal variation in dissolved oxygen caused
by the phytoplankton may create problems of low dissolved oxy-
gen at times.
Sawyer indicates that the optimum pH range for
nitrification is 8.0 to 8.5. An optimum pH range of 7.0 to
(8)
9.0 was reported by Engle and Alexander . Nitrification
studies performed by Hydroscience, Inc., indicate that opti-
mum nitrification is not significantly affected within a pH
range of 7.0 to 8.5. Since most natural waters are within
these ranges, pH should normally not hinder nitrification.
Nitrifying bacteria use free carbon dioxide or bi-
(4)
carbonate ions as the primary sources of carbon for the
growth of new cells. Generally, in natural waters, the con-
centration of inorganic carbon available in the above forms
is greatly in excess of requirements and nitrification pro-
ceeds.
Under conditions of high organic carbon concentra-
tions, the heterotrophic bacteria (organic carbon oxidizers)
may predominate over the autotrophic bacteria (nitrogen oxi-
dizers) which would result in a delay in nitrification. This
is usually exemplified in the standard biochemical oxygen de-
mand test by the occurence of two stages. With untreated and
E-14
-------
heavily polluted water, the two stages are usually distinct.
The first stage, which reflects the aerobic oxidation of the
organic material, is usually substantially completed before
the second stage, which reflects the oxidation of ammonia
through nitrite to nitrate, is significantly underway. In
treated effluents and less polluted waters, the lag between
the two stages may be reduced. As the first stage is reduced
with nitrifying organisms present, the two stages may occur
simultaneously. Since this guide will be applied to effluents
which have at least secondary treatment, nitrification has
been assumed to occur simultaneously with the oxidation of
carbonaceous material in the modeling procedures.
III. Determination of $ from Observed Data
The deoxygenation coefficient, K,, and the reaeration
coefficient, K , can be estimated from field data. With both
a.
stream area and flow as constants (an underlying assumption
used in the guide), Equation (IV-2) of the main text (see page
69), yields:
_ V
L = LQe U (E-l)
E-15
-------
where:
L = BOD concentration (mg/1)
L = BOD concentration at x = 0 (mg/1)
U = velocity (miles/day)
K-, = deoxygenation coefficient (I/day)
x = distance (miles)
The field estimate at K, can be obtained from semi-logarithmic
plots of observed long term ultimate BOD stream data (five
day BOD stream data may also be used) as a function of dis-
tance downstream. Thus, in natural logs, Equation (E-l) is
written as:
K,x
In L = |j- + In LQ (E-la)
A semi-log plot of field data usually results in a straight
line, the slope of which is defined by:
K,
Slope = J (E-lb)
This procedure provides a first estimate of the deoxygenation
coefficient. An example of this procedure is shown in Figure
E-3 where a straight line has been fitted by eye to the Mohawk
E-16
-------
in
Q
O
CD
O
10.0
9.0
8-0
7.0
6.0
5.0
4.0
3.0
2.0
U = 4. MILES/DAY
Kd= -SLOPE x U
= 2.3 (°-°17
MILES
Kd= 0.16/DAY
/4MILESx
\ DAY I
I
0
I
16 24
DISTANCE (MILES)
32
36
INPUT
FIGURE E-3
ILLUSTRATION OF COMPUTATION OF Kd
FROM BOD STREAM DATA
-------
River data. Note that care must be taken to include the con-
version from base 10 logarithms as given in semi-log plots
to base e logarithms as required by Equation (E-l) .
The reaeration coefficient, K , may be estimated from
a
depth and velocity data by the following formula developed
(9)
by O'Connor from field studies:
(DO)17'
L 3/2
H
(E-2)
o
where DT is the oxygen diffusivity at 20°C (0.000081 ft /hour)
j-i
U is the average stream velocity, and H is the average depth.
A more convenient from of this equation is:
1 9 QIT '
Ka -
ti
where:
K = reaeration coefficient (I/day)
cl
U = velocity (fps)
H = depth (feet)
The reaeration coefficient is a surface controlled
phenomenon and for all practical purposes, is independent of
E-18
-------
water quality. In view of this, K, is usually the more var-
iable unknown coefficient in the term , it is necessary that the K and K, terms be in-
a ci
vestigated separately as indicated.
The estimation of the reaction coefficients K, and
K from which is obtained along with the estimation of the
a
loading conditions from observed data is the first step in a
verification analysis. The general procedure for a verifica-
tion analysis is presented in Section II-F of the main text
(see page 22). Some typical dissolved oxygen verifications
accomplished by Hydroscience, Inc. ' are shown in Fig-
ures E-4 and E-5.
There are, however, possible difficulties or "pit-
falls" that may be encountered in the verification analysis
using the basic assumptions applied in this guide.
For example, assume that a verification is to be
attempted in a stream into which a raw municipal effluent is
presently inputed. Such an effluent probably has highly
settleable solids. As a result, in the vicinity of the out-
fall, the removal of ultimate oxygen demand is accomplished
by the physical settling and the oxidation of the organic
matter, simultaneously. Oxidation of the ultimate oxygen
E-19
-------
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demand requires dissolved oxygen, while removal of the ulti-
mate oxygen demand (organic matter) by settling does not di-
rectly use dissolved oxygen. As one proceeds downstream, the
physical removal is completed and only oxidative removal re-
mains. In such a situation, a semilog plot similar to Figure
E-3 would probably yield two straight lines as shown in Figure
E-6. The slopes of these lines are defined by:
Zone I: slope = -K /U
Zone II: slope = -K,/U (E-3)
where :
K = BOD removal coefficient (I/day)
K, = deoxygentaiton coefficient (I/day)
In this guide, a constant deoxygenation coefficient
has been assumed down the length of the water body. This
assumption is considered valid, since the guide was meant to
be applied to municipal effluents with at least secondary
treatment. As a result, verification with the modeling pro-
cedures presented in this guide for the hypothetical problem
presented above, may only be approximate.
A constant background dissolved oxygen deficit of
1.0 mg/1 has been recommended in the guidelines. However, if
E-22
-------
Q
O
CD
UJ
CL
h-
C/)
SETTLING 8
'OXIDATION
OXIDATION
ZONE I
STREAM
LENGTH
WASTE
DISCHARGE
FIGURE E-6
ILLUSTRATION OF SPATIALLY VARYING BOD REMOVAL RATE
-------
a verification analysis is being attempted where raw munici-
pal effluents are involved, a background level of 1.5 to 2.0
is recommended due to the probable high organic content of
the bottom due to settling.
It has been pointed out that nitrification is sup-
pressed at low dissolved oxygen levels (<1.5 mg/1). This re-
sults in a delay in nitrification and a secondary dissolved
oxygen sag is usually detected downstream. The guide proce-
dures do not incorporate the calculation of such a secondary
sag. However, if the primary dissolved oxygen sag is approx-
imately verified, the coefficientts used may be considered
valid.
High phytoplankton populations or extensive growths
of rooted aquatic plants, will have a significant diurnal
effect on the variation of dissolved oxygen. The modeling
procedures do not incorporate this phenomenon.
Toxic substances (copper, arsenic, zinc, mercury,
lead) will inhibit bacterial populations. Therefore, high
concentrations of these toxicants will affect dissolved oxy-
gen in the water body.
E-24
-------
The inclusion of the above phenomena is of the
(12)
realm of a detailed planning effort. Thomann presents
more sophisticated modeling procedures, which incorporate
the modeling of these phenomena.
In summary, the constituents of the term may be
evaluated from observed data. In situations where only dis-
solved oxygen data is available, a first approximation at
verification should begin with the appropriate average values
of K and K,, or $ as presented in Figures A-2, A-3, and A-4
cl Ci
of Appendix A, respectively. These figures were developed on
the basis of detailed planning efforts by Hydroscience and
others. Final verification of observed data should be accom-
plished with coefficients within the ranges presented in these
figures. If other phenomena above the assumptions used in
this guide are present, good engineering judgment will deter-
mine the degree of validity of the coefficients obtained.
IV. Reaeration Over Dams
The reaeration occurring at dams is similar to the
natural reaeration phenomenon occurring in a stream, and al-
ways drives the dissolved oxygen concentration of the water
toward saturation.
E-25
-------
Based on experimental data ' and later verified
(14 )
with field data ', the British developed the following
equation for reaeration over dams:
r = 1 + 0.11 ab(l + 0.046T)H (E-4 )
where :
C - C D
r = deficit ratio = ~ - ~ = =^
s " Lb Db
C = dissolved oxygen concentration above
dam (mg/1)
C, = dissolved oxygen concentration below
dam (mg/1)
C = dissolved oxygen saturation (mg/1)
o
D = dissolved oxygen deficit above dam
D, = dissolved oxygen deficit below dam
(mg/1)
T = temperature (°C)
H = height (feet) through which the water
falls
a = 1.25 in clear to slightly polluted
water: 1.00 in polluted water: 0.80
in sewage effluents
b = 1.00 for weir with free fall: 1.3
for step weirs or cascades
E-26
-------
Rearrangement of the above equation to the appropriate form
to be used in this manual is as follows:
Da - Db = f1 - 1 + 0.11 abU + 0.046T)H J Da (E~4a)
An alternate equation developed by Mastropietro
from field data on the Mohawk River and Barge Canal in New
York State is as follows:
C. C
-£ = (1 - 0.037H) ^ + 0.037H (E-5)
s s
Rearrangement to the appropriate dissolved oxygen deficit
formulation is:
D - D,= 0.037H D (E-5a)
a jj a
A plot of this formula which calculates the decrease in dis-
solved oxygen deficit over a dam, is presented in Figure E-7.
This formulation was developed specifically for the Mohawk
River and Barge Canal, and is valid for dams up to fifteen
feet high and critical temperatures in the range of 20° to
25°C. Successful application of this formula was accomplished
in a detailed planning study
E-27
-------
o
U-
LU
Q
UJ
C/)
<
LJ
o:
O
UJ
Q
Q
I
a
Q
I 2345678
Da : DEFICIT ABOVE DAM (MG/L)
10
FIGURE E-7
REAERATION OVER DAMS
-------
Under the same conditions, Equation (E-5a) predicts
less reaeration than the British formulation and is, there-
fore, more conservative. In view of this and successful veri-
fication analyses in a detailed planning effort , it is
recommended that Equation (E-5a) be used if conditions are
within the stated dam height and temperature constraints.
To evaluate the effect of a dam, it is necessary to
obtain the entire deficit profile even if there is only one
waste source. The usual procedure in a stream analysis is to
reevaluate the problem at the location of the dam. Reference
is made to Equation (IV-5) of the main text (see page 72) , re-
peated here as :
V V
K,L U U
D = _K [e - e ] (E-6)
a d
This equation defines the deficit profile until the dam is
reached. At this location, X = X , , the ultimate oxygen de-
mand not oxidized, L1 is calculated from Equation (IV-2) of
the main text (see page 69), repeated here as:
K,x
d
U~
L = LQe (E-7)
E-29
-------
The remaining ultimate oxygen demand is analogous to a waste
input at the dam. The deficit above the dam, D , calculated
a
from Equation (E-6) at X = X^ is applied to Equation (E-5a) ,
which results in an estimate of the deficit, D, , after dam
reaeration. With these parameters, the deficit profile after
the dam is defined by:
K, K K
KdL' ~ -U(x ~ V - ~!J(X ~ V " ~l(x ~ xd)
D = d [e U d - e U d ] + D,e U d (E-8)
Ka " Kd b
Due to the fact that these equations are linear, manipulation
of Equation (E-8) results in the following equation:
a
KqL — — r: — — — p: — — fr(X — X.,)
a d
- V
Note that the first part of this equation is the same as if
there were no dam in the river . Therefore , the procedures
outlined for multiple waste sources (Section IV-D. , pp. 87),
can be applied as originally presented. The analyst need
only subtract the second term of Equation (E-9) from the
total dissolved oxygen deficit response (Table IV- 2, Column
8, pp.91) calculated.
E-30
-------
Chart F shows the technique for computing the nega-
tive term of Equation (E-9). Figure F-l is entered with mile
point beginning at X = 0, at the dam location. With knowledge
of K /U, this distance is converted to the dimensionless ratio
a
of the negative deficit at the milepoint to the decrease in
deficit at the dam. Since K,, (j>, and U have already been es-
timated, K /U is readily obtained.
a
Figure F-2 requires the decrease in deficit at the
dam, D - D,, due to dam reaeration. This value is obtained
a D
from Figure E-7, which is entered with the deficit previously
calculated above the dam, and the height of the dam. The
deficit values obtained from Figure F-2 are subtracted from
column (8) of Table IV-2 at the appropriate milepoints, and
the calculation of columns (9), (10), (11), and (12) proceed
as before.
If one wishes to use the British formulation, the
decrease in deficit at the dam can be directly calculated from
Equation E-4a, and the same procedure as outlined above will
be followed, except for use of Figure E-7.
Illustrative Example
The same problem as presented in Section IV-D-l-a
(see page 95), will be reevaluated with a ten foot dam at
E-31
-------
Q
"3
t 8
< (/>
5 5
-------
mile point 30. Table E-2, which is a continuation of Table
IV-4 of the main text (see page 97), indicates the numerical
analysis of the estimated dissolved oxygen profile due to the
four waste sources with the dam included. Note that column
(8) is the same as that of Table IV-4, except that it is re-
labeled Subtotal DO, etc. At milepoint 30, the Subtotal dis-
solved oxygen deficit response is 4.8 mg/1. From Figure E-7,
with a dam height of 10 feet, the decrease in deficit at the
dam is 1.8 mg/1. Column (8A) was obtained from Chart F using
a K /U of 0.12/miles. Column (8B) was obtained from the sub-
a
traction of column (8A) from column (8), and represents the
total dissolved oxygen deficit response. The remaining columns
are obtained as previously outlined. Column (10) shows the
estimated dissolved oxygen profile and indicates a new spatial
minimum of 3.2. This may be compared to the spatial minimum
of 2.6 previously calculated without the dam. As indicated,
the standards are still violated from about mile 25 to mile
60.
E-33
-------
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-------
V. Temperature Coefficients
The deoxygenation (K,) and reaeration (K ) coeffi-
cients presented throughout this manual are for water temper-
atures of 20°C. Conversion to other temperatures can be made
by applying the following formula:
= K20(6)T 2°
where KT is the reaction coefficient at temperature, T (°C),
K~n is the reaction coefficient at 20°C, and 0 is a constant.
^ u
(12) (12)
The term Q is equal to 1.047V ' and 1.0241 ' for the deoxy-
genation and reaeration coefficients, respectively. Nitrifi-
cation is assumed to occur simultaneously, and at the same
rate as carbonaceous oxidation. The 6 value for nitrification
is also assumed as 1.047. However, at low temperatures (<10°C)
nitrification may be assumed suppressed.
VI. Evaluation of the Dispersion Coefficient, E
The dispersion coefficient, E, for an estuary or
tidal river may be evaluated for a particular net advective
flow from the observed steady-state concentration profile of
salinity or chlorides, provided that vertical stratification
E-35
-------
of these constituents is not pronounced. The underlying equa-
tion that may be utilized is Equation III-3 in the main text
(refer to page 38), repeated here as:
C = C egx X < 0
(E-ll)
C = C e^x X > 0
Considering salinity or chlorides as conservative, and begin-
ning the model at the furthest point downstream (location of
maximum concentration), Equation (E-ll) becomes:
UX
E
C = CQ e X _< 0 (E-12a)
C = CQ X :> 0 (E-12b)
where:
C = salinity or chloride concentration (mg/1)
C = maximum concentration at X = 0 (mg/1)
U = net advective velocity (miles/day)
E = dispersion coefficient (miles2/day)
X = distance upstream (miles) - negative
(usually, X = 0 at mouth of estuary)
Taking the natural log of Equation (E-12a) yields:
E-36
-------
In C = . x + In C (E-13)
EI O
Therefore, a semi-logarithmic plot of log salinity or log
chlorides versus distance upstream should yield a straight
line, the slope of which is U/E. The dispersion coefficient,
E, may then be calculated directly from the net advective
velocity, which may be estimated from the freshwater inflow,
and cross-sectional area of the estuary. Figure E-8 illus-
trates the computation for data collected by U.S. Geological
Survey for a reach of the Hudson River Estuary. Note
that care must be taken to include the conversion from base
10 logarithms as given in semi-log plots to base e logarithms,
as required by Equation (12a).
If vertical stratification of salinity or chlorides
is encountered, it is suggested that the average over the
depth be used, which will result in a first cut evaluation of
the dispersion coefficient.
Dye data may also be used to obtain an estimate of
dispersion coefficients. Reference is made to O'Connor
(18)
and Diachishin , for the appropriate procedures which are
based on a more complicated analysis.
E-37
-------
10,000
9,000
8,000
7,000
6,000
5,000
4,000
3,000
2,000
c/)
LU
Q
cr
3 1,000
g 900
° 800
700
600
500
400
300
2001—
0
20
HUDSON ESTUARY (7)
SEPTEMBER 10,1962
Q
A
U
E
5,000 CFS
200,000 SQ.FT.
0.41 MILES/DAY
u Q.4I
SLOPE * 2.3(.02I4)
= 8.3 MILES/DAY
-5 -10 -15 -20 -25 -30 -35 MODEL MILES
25 30 35 40 45 50 55 RIVER MILES FROM BATTERY
FIGURE E-8
ILLUSTRATION OF COMPUTATION OF E
FROM CHLORIDE DATA
-------
REFERENCES
( ' Thomann, R.V., O'Connor, D.J., Di Toro, D.M., "Effect of
Nitrification on the Dissolved Oxygen of Streams and Es-
tuaries" Manhattan College, New York, N.Y., 1970.
(2)
Sawyer, C.N., Chemistry for Sanitary Engineers, McGraw-
Hill Book Company, New York, N.Y., 196TH
Hutchinson, G.E., A Treatise cm Limnology, Volume 1^ J.
Wiley and Sons, Inc. , New York~7 N.Y., 1957.
Effects of Polluting Discharges on the Thames Estuary,
Water Pollution Research Technical Paper No.11, Department
of Scientific and Industrial Research, Her Majesty's Sta-
tionary Office, 1964.
^ ' Waksman, Principles of Soil Microbiology, First Edition,
London, 1964.
Camp, T.R., Water and Its Impurities, Reinhold Publishing
Corporation, New York, 1963.
' ' Sawyer, C.N., Wild, H.E., and McMahon, T.C., "Factors
Affecting Nitrification Kinetics", presented at the 43rd
Annual Conference of the Water Pollution Control Federa-
tion, Boston, Massachusetts, October, 1970.
(8)
v ' Engle, M.S., and Alexander, M., "Growth and Autotrophic
Metabolism of Nitrosomonas Europaea", J. Bact., 76, 1958.
(9\
v ' O'Connor, D.J. and Dobbins, W.E., "Mechanisms of Reaera-
tion in Natural Streams, Trans.A.S.C.E., Vol. 123, 1958.
* "Water Qaulity Analysis for the Markland Pool of the Ohio
River", Malcolm Pirnie Engineers, Hydroscience, Inc.,
October, 1969.
-------
REFERENCES
(continued)
^ '"Water Quality Analysis of the Mohawk River-Barge Canal"
New York State Department of Health. O'Connor, D.J., and
Hydroscience, Inc., July, T9~68.
(12)
v Thomann, R.B., Systems Analysis and Water Quality Manage-
ment, Environmental Research and Applications, In~c., New
York, 1972.
* 'Gameson, A.L., Vandyke, K.G., and Ogden, C.G., "The Effect
of Temperature on Aeration at Wiers", Water and Water En-
gineering, London, November, 1958.
(14)
Barrett, M.J., Gameson, A.L., and Ogden, C.G., "Aeration
Studies of Four Wier Systems", Water and Water Engineering,
London, September, 1960.
Mastropietro, M.A., "Effects of Dam Reaeration on Waste
Assimilation Capacities of the Mohawk River", Proceedings
of the 23rd Industrial Waste Conference, Purdue University
May, 1968.
* 'Giese, G.L., and Barr, J.W., The Hudson River Estuary - A
Preliminary Investigation of Flow and Water Quality Char-
acteristics, U.S.G.S., Bulletin 61, State of New York,
Conservation Department, Water Resources Commission, 1967.
^ 'Analysis of the Dye Diffusion Data in the Delaware River
Estuary - Evaluation of Diffusion Coefficients, Regional
Office, U.S. Public Health Service, Philadelphia, O'Connor
D.J., August, 1962.
* 'Diachishin, A.N., "Dye Dispersion Studies" Journal of
Sanitary Engineering Division, A.S.C.E., Volume 89, No.
SA1, January, 1963.
-------
ADDITIONAL REFERENCES
"Nitrification in the Delaware Estuary", Delaware River Basin
Commission, Trenton, New Jersey, Hydroscience, Inc., June,
1969.
"Nitrification in the Activated Sludge Process - City of Flint,
Michigan", Consoer, Townsend, and Associates, Hydroscience, Inc.,
July, 1971.
"Advanced Treatmnet Methods for the Roxbury, New Jersey, Treat-
ment Plant", Lee T. Purcell Associates, Hydroscience, Inc.,
December, 1971.
"Advanced Waste Treatment for Nitrogen and Phosphorus Removal"
Baldwin and Cornelius, Freeport, New York, Hydroscience, Inc.,
March, 1971.
"Studies to develop Solutions to Waste Treatment Problems",
Armour and Company, Pharmaceutical Division &_ Edible Oils
Division, Hydroscience, Inc., December, 19651
"Biological Waste Treatment", Hanmer Division Plant, American
Tobacco Company, Chester, Virginia, Hydroscience, Inc., April
1968.
"Comparison of Nutrient Nitrogen Sources on Anaerobic Lagoon
Performance", Allied Chemical Company, Hopewell, Virginia,
Hydroscience, Inc., March, 1966.
"Biological Treatment Studies - Treatment of Wastes from Tan-
nery Operations", Armour Leather Company, Bolivar, Tennessee,
Hydroscience, Inc., July,1970.
"Biological Waste Treament - Amcelle Plant", Celanese Corpor-
ation of_ America, Maryland, Virginia, Hydroscience, Inc.,
December, 1967.
"Lagoon Treatment for Fiber Wastes", Celanese Corporation of_
America, Houston, Texas, Hydroscience, Inc., November, 1966.
"Design Criteria for the Treatment of Organic Wastes in an
Aerated Lagoon", E.I. DuPont de_ Nemours and Company, Hydro-
science, Inc., November, 1963.
-------
ADDITIONAL REFERENCES
(continued)
"Treatment of Organic Wastes in Aerated Lagoons", Water Poll-
ution Control Board, New York State Department of_ Health,
W.W. Eckenfelder, Jr., and D.J. O'Connor, Sponsored by N.Y.S.
Department of Health, Water Pollution Control Board, Project
#C-12516, June, 1960.
"Preliminary Report on the Theory and Application of Lagoon-
ing to the Treatment of Organic Wastes", Bethlehem Steel Com-
pany, Bethlehem, Pennsylvania, W.W. Eckenfelder and D.J.
0'Connor, Hydroscience, Inc., February, 1960.
"Lagoon Treatment for Fiber Wastes", Celanese Corporation of
America, Houston, Texas, Hydroscience, Inc., November, T9~6F7
"Waste Treattment Alternatives for Swift de La Plata Slaugh-
terhouse and Packing Plant", Deltec International Limited,
Hydroscience, Inc., June, 1970.
And others cited in main text.
-------
ERRATA FOR SIMPLIFIED MATHEMATICAL MODELING OF WATER QUALITY
Hydroscience, Inc.
Page
52
53
Line
Correction
54
87
99
113
124
125
Last line
Table III-3 Last
Column
Treatment Level 4
Treatment Level 5
Table III-4 Last
Column
Treatment Level 1
Treatment Level 2
Treatment Level 3
Line 7
Line 3
Line 5
Last Line
Line 7
e) .044 pounds nitrogen.
.05
.01
.040
.035
.035
30°C, 5.9 mg/1...
...minimum of about 2.6 mg/1
(V-5)
(V-6_)
...(by Equation V-6)...
f, V S GOVERNMENT PRINTING OFFICE 1972—484-486/291
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