EPA-R2-73-273
July 1973 Environmental Protection Technology Series
Predicting And Controlling
Residual Chlorine In
Cooling Tower Slowdown
National Environmental Research Center
Office Of Research And, Development
U.S. Environmental Protection Agency
Corvallis, Oregon 97330
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RESEARCH REPORTING SERIES
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EPA-R2-73-273
July 1973
PREDICTING AND CONTROLLING RESIDUAL
CHLORINE IN COOLING TOWER
SLOWDOWN
By
Guy R. Nelson
National Thermal Pollution Research Program
Pacific Northwest Environmental Research Laboratory
National Environmental Research Center
Corvallis, Oregon
Program Element 1B2392
NATIONAL ENVIRONMENTAL RESEARCH CENTER
OFFICE OF RESEARCH AND DEVELOPMENT
U. S. ENVIRONMENTAL PROTECTION AGENCY
CORVALLIS, OREGON 97330
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ABSTRACT
A mathematical model which predicts residual chlorine levels In cooling
tower blowdown streams at any time during the chlorination cycle
Is developed and analyzed In this paper. To quantify the absence
or presence of residual chlorine In the blowdown, the model Interprets
residual chlorine as negative chlorine demand.
The general model has eight variations applying to specific chlori nation
program characteristics. The program characteristics affecting the
general model are:
a. Split stream vs. no split stream chlori nation (the fraction
of the recirculating water chlorinated).
b. Residual data feedback vs. no residual data feedback
(the type of chlorine feed equipment used).
c. Positive vs. negative demand at the end of the chlorine
feed period. (The time length of the chlorine feed period.)
The variations to the model are useful not only 1n predicting residual
chlorine levels in the blowdown, but also in making alterations 1n
existing chlorination programs which minimize chlorine waste, provide
more disinfecting efficiency, and reduce residual chlorine levels
in the blowdown.
11
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CONTENTS
*
Page
Abstract 11
List of Figures 1v
Sections
I Conclusions 1
II Recommendations 3
III Introduction 4
IV Model Development 6
V Model Analysis 14
VI References 26
VII Glossary 27
VIII Appendices 34
111
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FIGURES
No. Page
1 Cooling Tower Sump Flows 6
2 Water Flows at the Top of the Tower 7
3 RATIO during TSA 17
4 Time Step B for the Mechanical Draft Program . . 19
5 Study One RATIO Values 20
6 Residual Data Feedback vs No Residual Data
Feedback 22
7 Split Stream vs No Split Stream Chlorination. . . 25
8 Time Steps of the Chlori nation Cycle 29
9 Cooling Tower System 32
10 Split Stream Chlorination 41
11 Residual Data Feedback Chlorination 44
12 Combination Split Stream/Residual Data
Feedback Chlorination 46
iv
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SECTION I
CONCLUSIONS
The models which are developed and analyzed 1n this paper predict
the value of RATIO during the chlorination cycle of a cooling tower
system. RATIO is defined as the ratio of the blowdown chlorine
demand value at any time during the chlorination cycle to its value
at the start of the chlorination cycle. A positive value of RATIO
Indicates that there is no residual chlorine present in the blowdown.
A negative value of RATIO indicates that residual chlorine is in
the blowdown. RATIO'S rate of decrease and increase during the
chlorination cycle, and its minimum value at the end of the chlorine
feed period are all a function of the cooling tower and chlorination
program characteristics of specific systems.
The analysis of the models shows potential methods of reducing or
eliminating residual chlorine levels in the blowdown by taking
advantage of some of the optional program characteristics. These
potential methods include one or more of the following alternatives:
a) Installing residual data feedback equipment into the chlorine
feed system.
b) Practicing split stream chlorination.
c) Reducing the chlorine feed period, if possible.
d) Reducing the initial residual chlorine level in the condenser
eff1uent.
e) Increasing the water volume of the cooling tower. This
alternative may not apply to existing cooling towers because it
involves the system design. The alternative can apply to systems
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on the engineering drawing boards. This alternative may have other
advantages—such as an extra supply of water for fire protection.
f) Cutting off the blowdown when residual chlorine appears in
the sump. The blowdown flow can resume after the residual is dissipated
by the flashing effect and the makeup water chlorine demand. The
length of time during which the blowdown can be eliminated is a
function of the system's upper limit on dissolved solids.
g) Mixing the blowdown with another stream which has a high
chlorine demand.
To date there is no accurate field verification of the mathematical
models described in this paper. For field verification it is necessary
to use the amperometric procedure to measure low levels of residual
chlorine (5). The amperometric procedure for determining residual
chlorine in aqueous solutions is not applicable to all cooling tower
waters. Some cooling tower waters contain copper* turbidity,
natural buffering, and water treatment chemicals. These constituents
may produce interferences in the analytical procedure which result in
erroneous residual chlorine readings. In cases where limited field
analyses have been performed on waters amenable to amperometric
testing, trends are identified which conform to model predictions.
Even without substantial field verification, the models have utility.
They can be used to modify existing and proposed chlorination
programs in cooling tower systems. The modifications can provide
increased chlorination efficiency and reduced residual chlorine levels
in the blowdown.
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SECTION II
RECOMMENDATIONS
The predictive models in this paper require substantial field
verification on a broad range of cooling towers and makeup water
qualities. Input from field verification can provide adjustments
to the models on such factors as:
1. Incomplete mixing in the system.
2. Time dependence of chlorine demand.
3. Nonequilibrium chlorine demand.
In addition to field verification of the model, an effort is needed
to improve the amperometric procedure for determining residual chlorine
in problem waters. Some cooling tower waters contain varying amounts
of chloramines, copper, and color which can produce interferences
in the amperometric testing procedure (11). These interferences need
to be averted for accurate chlorine measurement.
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SECTION III
INTRODUCTION
Many cooling tower systems use chlorine or hypochlorites to
control bacteria and slime growth In the condenser tubes carrying
cooling water In the plant process. The biological growth, 1f left
uncontrolled, causes excessive tube blockages, poor heat transfer,
and accelerated system corrosion—all of which reduce plant efficiency.
For any cooling tower system the length of time of the chlorine feed
period and the number of chlorine feed periods per day, week, or month
change as the biological growth problem changes. In most cooling
tower systems, the chlorine is added at or near the condenser inlet
in enough quantity to produce a free residual chlorine level of
0.1-0.6 mg/1 in the water leaving the condenser. The amount of
chlorine added to maintain the free residual chlorine depends upon
the amount of chlorine demand agents and ammonia in the water.
Chlorine and ammonia react to form chloramines. These chloramines
constitute the combined residual chlorine of the water. This combined
residual chlorine is less efficient and slower in providing biological
control than free residual chlorine (1, 2, 3, 4).
Although chlorlnation is effective for slime control in the
condenser tubes of cooling tower systems, its application may result
in residual chlorine in the blowdown discharged to the receiving
water. The effects of residual chlorine on aquatic life are of
great concern (1, 5, 6, 7). Data on the toxicity of residual chlorine
to aquatic organisms is available. W. A. Brungs1 publication,
"Effects of Residual Chlorine on Aquatic Life: Literature Review",
-------
recommends criteria for maximum residual chlorine concentrations in
receiving waters (5). For the intermittent presence of residual
chlorine, not to exceed two hours per day, the criteria indicate a
maximum tolerable concentration of 0.2 mg/1. For the continuous
presence of residual chlorine, the maximum tolerable concentration
is 0.01 mg/1. These concentrations would not protect trout, salmon,
and some important food organisms and are potentially lethal to
sensitive life stages of sensitive fish species. Brungs recommends
a lower criteria to protect trout and salmon. These lower criteria are
0.04 mg/1 for the intermittent presence (2 hrs/day) of residual chlorine
and 0.002 mg/1 for the continuous presence of residual chlorine.
The potential effects of residual chlorine on aquatic organisms
require the measurement, prediction, and control of residual chlorine
in effluent discharges to the aquatic environment. The purpose of
this paper is to develop and analyze a model which predicts levels
of residual chlorine in the recirculation systems and blowdown streams
of cooling towers. The model can be used to improve chlorination
programs resulting in less chlorine waste, more disinfecting efficiency
and reduced environmental impact. Although the paper is directed
toward the application of chlorine in condenser cooling systems of
thermal electric power plants, the model presented can be used in
other industrial chlorination programs where the conditions are
similar.
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SECTION IV
MODEL DEVELOPMENT
Mass balance equations of the cooling tower system are the bases
for the model development In this section. The vocabulary, concepts,
and notations herein are defined 1n the Glossary Section. Figure 1 is
a schematic of the water flows to and from the cooling tower sump.
Figure 1
Cooling Tower Sump Flows
I
QBCB
From Figure 1, the chlorine demand mass balance arouno the cooling
tower is,
Equation (1) assumes that good mixing within the system causes the
chlorine demand in Q, and QB to be the same as the chlorine demand
in the sump.
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Figure 2 is a schematic of the water flows to and from the top of
the cooling tower.
Figure 2
Water Flows at the Top of the Tower
QECE
V
7
From Figure 2, the chlorine demand mass balance is,
QR CR = Q£ CE + Qs Cs
or
(2)
CR - QE CE = % cs
A mass balance around the entire cooling tower system is,
(3)
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Just prior to the start of the chlorine feed period (Q, = 0). the
chlorine demand mass balance is,
CM = % CBO + QE CEO
Where CEQ is the chlorine demand in the evaporated water.
The model assumes that positive chlorine demand is not evaporated
or flashed from the tower.
Just prior to the chlorine feed period, the chlorine demand in the
system is positive and CEQ = 0; therefore,
QM CM ' QB CBO
A mass balance around the condenser section during chl or 1 nation
1s,
Q! + QL = QR (4A)
The model assumes that QL (the flow rate of chlorine) 1s negligible
compared with Q* and QR; thus,
Qj = QR («)
By the substitution of Equations (2), (4), and (4B) back Into the
sump mass balance, Equation (1) becomes
= QB CBO + QR CR - QE CE - ^R CB - % CB
8
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Equation (5) is the general model. It is the base for determining
the alternate models which apply to specific chlori nation programs.
MODEL NNN
One alternate model is model NNN. This model applies to a chlorination
program which: (1) does not practice split stream chlorination,
(2) does not have residual feed back, and (3) has a negative demand
(residual chlorine) in the blowdown at the end of the chlorine feed
period.
TIME STEP A
During the chlorine feed period, residual chlorine (negative demand)
is in the condenser effluent. The chlorine demand relationship at
the condenser with the start of chlorination is
CBO + QL CL ' QR CRO
and at any time during the feed period it is,
«R CB + «L CL = «R CR
Subtracting Equation (7) from Equation (6) results in
QR CBO - QR CB = + QR CRO - QR CR
or
r = r - r + r
LR LRO LBO UB
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The model expresses residual chlorine as negative chlorine demand.
Negative demand enters the condenser section via Q, . The term CR
thus Is treated as a negative demand Input In the model equation.
A portion of this negative demand (residual chlorine) flashes off or
otherwise degrades in the tower.
The flashed portion is expressed in the model as QE C£. Equation (9)
expresses the QE C£ term as a fraction of the negative demand returning
to the tower.
or FQR CR = QE CE
During Time Step A of model NNN, the general model expression is
revised to,
QB CBO + «R CR - F «R CR> - "R CB - % CB
or
• QB CBO - QB CB - QR CB + QR V-V
' QB CBO * QR (1'F) (CRO ' CBO> - (QB + % F) CB
This Is a first order differential equation with the solution,
= _B s x M . e } ) +e ] (11)
LBO '
10
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Where
and
QB/QR+F
i' V/QR
Equation (11) expresses the value of RATIO during the chlorine feed
period of model NNN. In the model, the ratio starts at unity and
decreases as TSA continues. At the end of TSA, RATIO is negative.
This indicates the presence of residual chlorine in the blowdown.
The concentration of residual chlorine (mg/1) in the blowdown is
found by multiplying RATIO by CDQ.
RATIO • CBQ = Residual Chlorine.
The time symbol, (t), in Equation (11) represents the time during
TSA (i.e. at the start of TSA, t=0).
TIME STEP B
Time step B (TSB) defines the length of time which RATIO remains
negative after the end of TSA. The model expression for TSB, therefore,
requires a negative value of RATIO at the start of TSB. The symbol,
(Cg/CgQ)g, represents the value. During TSB, no chlorine Is added,
thus, CR = Cg.
11
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Since there is still residual chlorine in the water returning to the
tower, the flashing term still applies in the mass balance.
The general model expression during TSB is
dC0
v-atT = QB CBO - % CB - OR CR + 'R ^ CB
or
dC
R
= QB CBO - % CB - QR F CB
This is a first order differential equation with the solution,
CR ^ -Y2t -Y2t
RATIO =^-^2 0-e Z ) + (CB/CBO)B e Z (12)
BO
t = 0 at the start of TSB
VQR + F
Where X9= p *
2 VQR
Qn/0« + F
V/QR
and PB/CBO)B= The value of RATIO at the start of TSB.
Equation (12) is the mathematical expression for TSB of models NNN,
NRN, SNN, and SRN. By definition models NNP, NRP, SNP, and SRP do
not have TSB in the chlorination cycle.
12
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TIME STEP C
During TSC there Is no negative chlorine demand (residual chlorine)
entering the cooling tower sump. The chlorine demand mass balance
around the sump 1s therefore,
= QB CBO - QB CB
This 1s a first order differential equation with the solution:
_QBt
RATIO = !-[!- (CB/CBQ)] e ~T' (13)
Where t = 0 at the start of TSC and (CB/CBO)C is the value of ratio
at the start of TSC. Equation (13) 1s the mathematical expression for
TSC of all the models.
For models NNN, NRN, SNN, and SRN, (CB/CBQ)C is zero so Equation (13)
1s reduced to,
_
RATIO = 1 - e V (14)
Equation (14) 1s the mathematical expression covering TSC of models
NNN, NRN, SNN, and SRN.
Appendix A contains the mathematical expressions for all of the
time steps Of the eight models.
Appendix B contains the derivations of the expressions for TSA of
models NRN, NRP, SRN, SRP, SNN, and SNP.
13
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SECTION V
MODEL ANALYSIS
The purpose of this section Is to analyze and discuss the models
developed in the previous section. The purpose is accomplished by
detailing three chlori nation program studies on two cooling tower
systems. One program is for a mechanical draft cooling tower
system; the other is for a natural draft cooling tower system.
Six cooling tower characteristics affect the value of RATIO during
the chlori nation cycle in both cooling tower systems.
a) The cooling system volume (V)
b) The recirculation rate (QR)
d) The initial chlorine demand in the blowdown (CBQ)
e) The flashing rate of residual chlorine to the atmosphere (F)
f) The initial residual chlorine level in the condenser
effluent
g) The blowdown flow rate
These characteristics manifest themselves in the predictive models
through the terms discussed below.
The V/Qo term (expressed 1n minutes) 1s the ratio of the water volume
of the entire cooling system to the recirculatlng water flow rate.
This term, indicates the length of time for a given water parcel to
make one pass through the system. With conventional system design,
this value is 10-15 minutes for mechanical draft towers and 20-22 minutes
for natural draft towers.
14
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The dimension less term, QB/QRis tne ratl'° of tne blowdown water flow
rate to the recirculating water flow rate. Its value, along with
the V/QR term, expresses the length of time that-a conservative
chemical remains in the system.
The dimensionless term, CRO/CBO, is the ratio of the initial residual
chlorine level in the ^circulating water (CRQ) to the initial chlorine
demand in the blowdown (CDn).
oU
The dimensionless term, F, is the fraction of the residual chlorine
which flashes or decomposes as it passes through the cooling tower
fill. The theoretical range of the value of F can be 0.0-1.0.
Probably F is related in some yet unquantified way to tower inlet
temperature and to cooling range and/or the water to air ratio;
the chemical form of the chlorine residual may also be a factor.
No field verified value of F is available; however, its existence
1s documented (1,3,9). In the draft Environmental Impact
Statement for the Davis Besse steam electric generating plant, Oraley
suggests an F value of 0.5 for combined residual chlorine in the
natural draft tower system (9).
Table 1 lists the values of cooling tower and chlorination program
characteristics found in typical cooling tower systems. The table
also lists the values which will be applied to the two hypothetical
cooling tower programs.
15
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TABLE 1
Cooling Tower and Chiorination Program Characteristics
(Ref. 1, 2, 3, 4, 8, 9, 10)
Characteristic
Typical Values
Values Applied
To Program Studies
A. Chiorination Program:
Chiorination cycle
Chlorine feed period
Split stream Cl2
Residual Feedback
B. Cooling Tower:
[:RO
CBO/C
CRO/CBO
Min
Max
8 hrs 7 days
10 min 30 min
Optional
Optional
0.008
0.3
0.1
0.5
0.1
0.015
0.6
-1.0
3.0
-1.2
24 hr
15 min
Program Study 3
Program Study 2
0.01
0.4
-0.4
0.667
-0.6
V/Q
C. Model Constant
(calculated from
B. above):
Xl
Y*
Y»**
X2
* Mechanical draft
** Natural draft
10
20
15
22
10
20
-2.32
0.041 min
0.0205 m1n
0.0244
-1
-1
16
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PROGRAM STUDY ONE
In this first study, the ch 1 or i nation program characteristics do not
contain residual data feedback or split stream chlorination. From
Appendix A, the expression for TSA of models NNN and NNP is
RATIO = X
]
-Y t -Y t
(1-e ] ) + e ]
Figure 3 is a graphical representation of the model during TSA for
both programs. In the natural draft program, RATIO remains positive
throughout the chlorine feed period. This indicates that there is
no residual chlorine in the blowdown.
1.01
RATIO
Figure 3
RATIO During TSA
NATURAL DRAFT TOWER
TIME (MIN.)
MECHANICAL DRAFT TOWER
In the mechanical draft program, RATIO becomes negative during TSA.
The boundary condition, t = 15 min., determines Its value at the
end of TSA.
RATIO * -2.32
'°'041
-0.523
17
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The chlorine residual in the blowdown at the end of ISA is,
C12 residual =0.523 (0.667 mg/1)
=0.349 mg/1
The first appearance of residual chlorine in the blowdown occurs when
there is zero chlorine demand in the sump, or RATIO = 0. The time
during the chlorine feed period when this occurs is,
RATIO = 0 = e-°'041t-2.32 (l-e'0'0414)
t = 24.4 [In (1.432)] minutes
= 8.75 min
From the above calculations, residual chlorine is present in the
blowdown for 6.25 minutes during TSA.
A residual first appears at 8.75 minutes after the start of the
chlorine feed period. This residual increases in value until the end
of the feed period^ at which time it is at its maximum value. Since
the model defines residual chlorine as negative chlorine demand,
RATIO is at its minimum value at this time.
TIME STEP B
The TSB expression does not apply to the natural draft program,
because its terminal demand value is not negative. The TSB expression
for the mechanical draft program is,
18
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-v
RATIO = X2 (1-s 2 ) + (CB/CBO)B e
Figure 41s a graphical representation of TSB. The value of RATIO
at the start of TSB Is,
RATIO = (CB/CBO)B = -0.523
RATIO Increases through TSB until It reaches the value of zero.
Figure 4
Time Step B for the Mechanical Draft Program
RATIO
TIME (MIN)
The boundary condition, RATIO = 0, at the end of TSB quantifies the
time of TSB:
0 = 0.0244 (l-e-°-041t) - (0.523)
t = 24.4 In (22.4) min
76 min
19
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The mechanical draft program In this study causes residual chlorine
in the blowdown to occur for nearly 83 minutes (76 + 6.25) during
the chlorination cycle.
Figure 5 illustrates the value of RATIO through the complete chlorination
cycle for both programs under program study one.
Figure 5
Study One RATIO Values
1.0-
RATIO
-10-
NATURAL DRAFT TOWER K
TIME (MINI
MECHANICAL DRAFT TOWER
CHLORINATION CYCLE *
In order to minimize repetition, the following two program studies
will concentrate on alterations to the mechanical draft program.
The concepts in program studies two and three are applicable to natural
draft programs.
PROGRAM STUDY TWO
This program study analyzes the effect of residual feedback on the
value of RATIO for the mechanical cooling tower draft. Either model
NRN or NRP applies in this case—depending on the value of RATIO at
the end of TSA.
20
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From Appendix A, the expression for models NRN and NRP during ISA 1s,
V% + (1'F) CRO/CBO 'V "V
RA™ = B QD/QD * 1 - BLJ*L (1'e > + e
B R
Where Y -
5- V/QR
From the values of Table 1, this reduces to,
RATIO = -0.346 (l-e'0'101*) + e'0*1011
The value of RATIO at the end of the chlorine feed period is
RATIO = -0.346 (1-e"1'515) + e"1'515
= -0.27 + 0.22
= -0.05
The negative value of RATIO indicates the presence of residual chlorine.
Its value is
Residual chlorine = 0.05 (0.667) mg/1
= 0.033 mg/1
The time during TSA in which a residual appeared is
RATIO = 0 = -0.346 (l-e'0-1014) + e'°'}OH
t = 9.9 In 3.89 min
= 13.45 m1n
21
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Since the value of RATIO is negative, TSB of model NRN for this
case is
RATIO = 0.0244 (l-e'°'101t) -0.05 a'
The time required for RATIO to recover to zero is,
t = 9.9 In (3.05) min
= 13.4 min
In this case residual chlorine is in the blowdown for about 15 min.
Its highest value during this time is 0.033 mg/1.
Figure 6 compares the ch 1 or 1 nation cycle in this study to the cycle
for the mechanical draft program which did not have residual data
feedback.
Figure 6
Residual Data Feedback vs. No Residual Data Feedback
-1.0-
FEEDBACK
CHLORINATION CYCLE
TIME
-H
22
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The comparison of the two studies shows a marked reduction 1n the
concentration of residual chlorine In the blowdown of the cooling
tower In study two. The use of residual data feedback in the mechanical
draft program not only reduces the concentration of residual chlorine
in the blowdown, but also reduces the length of time during the
chlori nation cycle in which the blowdown contains residual chlorine.
PROGRAM STUDY THREE
In this program study, the chlori nation program for the mechanical
draft tower Includes split stream chlori nation and excludes residual
data feedback. In this case, either SNN or SNP applies— depending
on the value of RATIO at the end of TSA.
The TSA expression in both models is (from Appendix A),
Substep 1
1 ) - V - V
RATIO = [ 3 0-e 6 ) + e 6
Substep 2
+ -F s ^-l)
](Ve
Where S is the fraction of the redrculating water chlorinated and
1s the Initial residual of the split stream.
23
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There are two substeps to ISA in models SNN, SNP, SRN, and SRP- The
first substep applies until there is residual chlorine in the
recirculating water after the split stream is remixed with the remaining
streams. The flashing term (F) does not appear in the substep 1
expression because the chlorine demand is positive (no residual
chlorine). Negative demand appears in the recirculating water when
RATIO = S (1 - CTQ/CBO). Once the condition 1s reached, then the
substep 2 expression applies for the rest of TSA.
If the chlorination program calls for the chlorination of 50 percent
of the recirculating water at an initial residual chlorine level of
0.4 mg/1, the substeps for this study are:
Substep 1
RATIO = (-79) (l-e-°-001t) + e'0'0'0011
Substep 2
RATIO = -1.15 (l-e-°-041t) + 0.8 e-°-041t
To determine the time length of substep 1, RATIO is set equal to
the boundary condition, -S (CTQ/CBQ -1). = 0.8 and the expression Is
solved for t.
0.8 = -79 (l-e-°-001t) + e-°-001t
t = 1000 In (1.0025) m1n
= 2.5 min
24
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The length of substep 2 Is
15 -2.5 = 12.5 min
The value of RATIO at the end of TSA is
RATIO = -1.15 (l-e-°-041 <12'5>) + 0.8 e'0'041 <12'5>
= + 0.02
The positive demand value at the end of TSA indicates that there
is no residual chlorine in the blowdown. TSB does not apply; therefore,
RATIO regenerates back to the value of positive unity before the
start of the next chlorine feed period. Figure 7 compares the
chlorination cycle of this study to the cycle of the mechanical
draft program of study one which does not contain split stream chlorination,
Figure 7
Split Stream vs. No Split Stream Chlorination
SPLIT STREAM
NO SPLIT STREAM
CHLORINATION CYCLE
TIME
Study three shows the value of split stream chlorination in minimizing
or eliminating residual chlorine in the blowdown.
25
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SECTION VI
REFERENCES
1. Draley, J. E., The Treatment of Cooling Waters with Chlorine,
Argonne National Laboratories, February, 1972.
2. Cooling Towers, pp. 79-80, American Institute of Chemical
Engineers, 1972.
3. White, George, Handbook of Chiorination, Van Nostrand Reinhold
Company, 1972.
4. Personal Communication with Paul Puckorius, Zimmite Corp., West
Lake, Ohio.
5. Brungs, W., Effects of Residual Chlorine on Aquatic Life: Literature
Review, EPA publication, 1973.
6. Hamilton, Flemer, Keefe, and Mihursky. "Primary Production,"
Science, July 10, 1970, 169, 197-8.
7. Brook, A., and Baker, A., "Chiorination at Power Plants: Impact
on Phytoplankton Activity," Science, June 30, 1972, 176, 1414-5.
8. Cooling Water Treatment Manual. TPC Publication II, p. 19, National
Association of Corrosion Engineers, 1971.
9. Draley, J. E., Davis Besse Nuclear Power Station Draft Environmental
Impact Statement. Appendix B. U.S. Atomic ! '' * "' "~
1972. (Final statement issued March 1973)
Impact Statement. Appendix B, U.S. Atomic Energy Commission, November,
" . (Final
10. Personal review of proposed chlorination practices in cooling towers
from draft environmental impact statements.
!!• Standard Methods, American Public Health Association, Inc., 12th
Edition, 1965, p. 104.
26
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SECTION VII
GLOSSARY
VOCABULARY
Free residual chlorine Is that portion of the total residual chlorine
which will react chemically and biologically as hypochlorus acid
or hypochlorite 1on.
Combined residual chlorine 1s that portion of the total residual
chlorine which will react chemically and biologically as chloramines.
Total residual chlorine is the sum of the free and combined residuals.
Unless otherwise specified, throughout this paper residual chlorine
refers to the total residual chlorine.
Chlorine demand 1s the amount of chlorine (mg/1) required to be
added to a water (sample) before any stable residual chlorine 1s
formed. Organics and reducing agents in the water cause this demand.
These materials have varying reaction rates with chlorine. The
reaction rates cause the chlorine demand value to be time dependent.
For the purpose of this paper, the chlorine demand 1s that demand
which reacts with chlorine within five minutes of exposure.
The chlorination program describes the manner 1n which chlorine 1s
fed and controlled in the cooling tower system.
27
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The chlorination cycle is the length of time between the start
of two sequential chlorine feed periods.
Split Stream chlorination is an alternate method of chlorine
addition. It is the practice of splitting the total recirculation
flow through the condenser into a number of separate streams. One
of these streams is chlorinated at a time. The chlorinated stream
is then mixed with the remaining streams. The presence or absence of
split stream chlorination is a chlorination program characteristic.
Residual feedback describes a function performed by chlorine feed
equipment. If the control system in the equipment is capable of
adjusting the flow of chlorine to produce a constant residual in
the recirculation water out of the condenser, the system has residual
feedback. The presence or absence of residual feedback is a
chlorination program characteristic.
CONCEPTS
Residual chlorine vs. chlorine demand - The model expresses the
change in the chlorine demand of the blowdown during the chlorination
cycle. To quantify the absence or presence of residual chlorine in
the blowdown, the model interprets residual chlorine as negative
chlorine demand. By conceptual definition, residual chlorine is
not present in the blowdown unless the chlorine demand is satisfied.
CB - In the model development, the term CB represents the chlorine
demand in the blowdown at any time during the chlorination cycle.
CDA - The term CDn represents the chlorine demand in the blowdown
DU DU
at the beginning of the chlorination cycle.
28
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RATIO - The term RATIO represents the ratio of the chlorine demand
1n the blowdown at any time during the ch1or1 nation cycle to Its
Initial value at the beginning of the cycle (I.e., RATIO = CB/CBQ).
Time Steps - In order to predict the chlorination cycle* the model
breaks down the cycle Into time steps. Figure 8 Illustrates the time
step concept.
Figure 8
Time Steps of the Chlorination Cycle
CHLORINATION CYCLE
RATIO
-10-
.TSA
TIME (MIN.)
TSC
Time Step A (TSA) - TSA is the length of time during which chlorine
1s added to the system (the chlorine feed period).
Time Step B (TSB) - TSB is the length of time after TSA 1n which the
value of RATIO 1s negative.
29
-------
Time Step C (TSC) - TSC is the length of time after ISA of a chlorination
cycle in which the value of RATIO is zero or positive. TSC ends at
the start of the next chlorination cycle.
Although equations can be (and have been) written for Time Step C the
numerical output is rather spurious and of no practical value
in either environmental protection or chlorination program design. This
is true primarly because the length of Time Step C is dictated
by the biocidal requirements of the cooling system rather than
any level or function of chlorine demand or residual obtainable
from the equations. Also, extraneous factors such as dust washout
or changes in makeup water characteristics are not accounted for.
Finally, optimal use of the models for environmental protection and
chlorine conservation require chlorine demand data at start of
the cycle (CBO).
Terminal Demand Value (TDV) - TDV is the value of RATIO at the end
of TSA. It is the lowest value of RATIO during the chlorination
cycle.
Positive vs. Negative TDV - TDV can be either positive or negative
at the end of TSA. If TDV is negative as shown in Figure 1, then
the cycle contains three time steps (TSA, TSB, and TSC). If TDV is
positive or zero, then the cycle contains only two time steps (TSA
and TSC). The positive vs. negative TDV is a chlorination program
characteristic.
MODEL NOTATION
There are eight specific models based upon the general model discussed
in this paper. Each specific model applies to a set of chlorination
program characteristics. Table 2 is a-matrix which defines the
30
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shorthand notation used to describe each model. For easy reference,
the first letter in the shorthand notation refers to sidestream
filtration or no sidestream filtration (S or N). The second letter
refers to residual feedback (R or N). The third letter refers to
positive TDV or negative TDV (P or N).
TABLE 2
Model Notation
Residual Feedback No Residual Feedback
(-) TDV (+) TDV (-) TDV (+) TDV
Split Stream Chiorination SRN SRP SNN SNP
No Split Stream NRN NRP NNN NNP
Chi ori nation
For example, model NNN applies to a chlorination program which
a) does not have split stream chlorination, b) does not have residual
feedback, and c) has a negative chlorine demand at the end of the
chlorine feed period. Model SRP applies to a program which a) has
split stream chlorination, b) has residual feedback, and c) has a
positive chlorine demand at the end of the chlorine feed period.
31
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Cooling System Notation
Figure 9 is a schematic flow diagram of a typical cooling tower
system;
Figure 9
Cooling Tower System
.QcC
Where
QRCR
r i
\ QICB
\
^
"E
"s
BO
QBCB
= Blowdown flow rate in m /min (gpm)
o
= Water flow rate into the condenser in m /min (gpm)
= Chlorine flow rate into the condenser in m /min (gpm)
= Water flow rate returning to tower from the condenser
2
in m /min (gpm)
= Water evaporation rate leaving tower stack in m /min
(gpm)
o
= Water flow rate to the sump 1n m /min (gpm)
= Makeup water flow rate Into the tower sump in m /m1n
(gpm)
= Cooling tower system volume in m (gallons)
= Chlorine demand in the blowdown, (mg/1)
= Chlorine demand in the blowdown at the start of the
chlorine feed period (mg/1)
= Chlorine demand in the chlorine feed stream (mg/1)
32
-------
CR = Chlorine demand in water returning to the tower
from the condenser (mg/1)
CRO = Chlorine demand in the water returning to the tower
from the condenser at the start of the chlorine feed
period (mg/1)
CE = Chlorine demand In the evaporated water leaving the
tower (mg/1)
Cs = Chlorine demand In the reclrculatlng water entering
the sump (mg/1)
CM = Chlorine demand 1n the makeup water entering the
sump
33
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SECTION VIII
APPENDICES
Page
A. Alternative Model Expressions for Specific 35
Chlorination Programs
B. Derivations 40
34
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APPENDIX A
Alternate Model Expressions For Specific Chiorination Programs
TABLE 2
Models
Programs without
Split Stream Chiorination
Programs with
Split Stream Chiorination
Model Equations Model
TSA TSB TSC
NNN 1A 2A 4A SNN
NNP 1A 3A SNP
NRN 5A 2A 4A SRN
NRP 5A 3A SRP
Equations referred to in Table A-l
(1A) CR -Y,t -Y,t
4- xi°-° v-
Op BO
where X, - -~ x
o; + F
Equations
TSA TSB TSC
Sub Sub
1 2
6A 7A 2A 4A
6A 7A 3A
8A 9A 2A 4A
8A 9A 3A
-------
(2A) C. -Y2t CB -Y2t
^1-- >*#••
R
where X K
?
2 V
B - RATIO'S value at the start of TSB
BO B
(3A) CR C
e
BO BO
where
Q
B
CB
(7^- )r = RATIO'S value at the start of TSC
CBOL
**********
(4A) CB -Y4t
QD
where Y- =
36
-------
(5A) C -y t -Yt
where Xc =
5
(1-F)
'5
Q
R
(6A) CB -Yfit -Yfit
£ = X(l-e 6 ) + e 6
QB
I
where X, =
'e - r
r
TO = Chlorine demand in chlorinated condenser effluent at
the start of TSA
S = Chlorinated fraction of total recirculating water flow
37
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(7A)
where X7
CTn * chlorine demand in chlorinated condenser effluent at the
10 start of ISA
S = Chlorinated fraction of total recirculating water flow
**********
(8A) C -Yt
7-
LBO
fl
= X(l-e 8 ) + e
QB
where XQ
o
.
Q~ C —
_E. 4.
«R
iQ - chlorine demand in chlorinated condenser effluent at the
start of ISA
S = Chlorinated fraction of total recirculating water flow
38
-------
(9A) CB -y t s CTO -YQt
C5- • Xg(l-e 9 ) + (frrMr^ e 9
BO BO
where X = R B0
V s
T9
~ + S+F-FS
7T- + S + F - FS
WD
CTn = chlorine demand in chlorinated condenser effluent at the
IU start of ISA
S = Chlorinated fraction of total recirculating water flow
39
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APPENDIX B
Derivations
MODELS SNN AND SNP
Time Step A
TSA in these models has two substeps. Substep 1 covers the time during
TSA when the QR stream has a positive demand. This condition occurs
during the time when the residual chlorine in the chlorinated split
stream does not satisfy the chlorine demand of the remaining portion
of the recirculating water. The boundary conditions are:
at t = 0, RATIO = 1
CTO
at t = t, , RATIO = -S (TT^- - 1 )
1 LBO
S = fraction of the total recirculating water flow which
is chlorinated,
and
initial residual chlorine level in the split stream out
of the condenser.
Substep 2 covers the time during TSA when the chlorine demand in the
QR stream is negative (residual chlorine present).
40
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Substep 1
Figure 10 is a schematic of the condenser system with split stream
chlorination.
Figure 10
Split Stream Chlorination
SQRCT QRCR
QI.CL.
The chlorine demand relationship at the chlorinated condenser is:
S QR CB + QL CL = S QR CT
At the start of the feed period it is:
S QR CBO * QL CL = S QR CTO
(1)
(2)
41
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Subtracting (1) from (2) results 1n:
5 OR CB - s «R CBO ' s «R CT - s OR CTO
and
CT ' + SCB
or
CR • CB + s "TO - CBO)
Substep 1 holds for all positive values of CR. It terminates when:
t = t, CR - 0 = CB + S (On, - CBQ)
42
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or
CB = ' S (CTO ' CBO}
and
RATIO = - S (- 1)
LBO
During substep 1 the mass balance around the sump Is:
vdT = % CBO - QB CB - OR CB + % tcB + s (CTO - CBO)] (6)
The solution of (6) 1s:
CTO
CR QD/QP + S (f^-- 1) -Y-t -Yfit
4 B RCR" -6 6
Equation (7) Is the expression of RATIO during substep 1.
Substep 2
During substep 2 the value of CR Is negative, thus, the mass balance
1s:
* QB CBO - QB CB - % CB * OR ^-p) tS ^CTO ' CBO^ + CB^
43
-------
With the solution:
RATIO
BO
n /n * F
VQR F
r
Cl"6
BO
Equation (8) is the expression of RATIO during substep 2.
TSB and TSC for the models are derived in the main body of
the paper.
MODELS NRN AND NRP
Figure 11 is a schematic of the condenser system with residual data
feedback. Residual data feedback holds a constant residual chlorine
level in the recirculating water out of the condenser.
Figure 11
Residual Data Feedback Chlorination
CONDENSER
44
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The chlorine demand relationship at the condenser during TSA Is
CB + \ CL = OR CRO
Since the residual chlorine level out of the condenser remains
constant during TSA; the expression for CR is:
CR = CRO
and the mass balance around the sump 1s:
QB CBO - "B CB - «R CB + % <'-F> CRO
The solution for Equation (9) is:
con
W (1'F) Cm "V 'V flO)
RATIO = * T + n yn B 0'« ) + e
Equation (10) is the expression for models NRN and NRP during TSA.
MODELS SRN AND SRP
These two models require two substeps during TSA. Figure 12 1s
a schematic of the condenser flows during TSA.
45
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Figure 12
Combination Split Stream/Residual Data Feedback Chlorination
SQRCTO
SQRCB
(I-S)
The residual feedback mechanism holds the residual chlorine level
constant in the chlorinated split stream.
Substep 1
During substep 1, the chlorine demand in the recirculating water after
the split streams are rejoined is positive. The relationship at the
point of juncture is:
d-s) QR CB + s QR CTO = QR CR
or
CB - SCB + SCTO = CR
CR = (1-S) CB + SCTO
46
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and the mass balance around the sump Is:
dCD
V j»P g QC -QC-QC+Q ((1-S) C + S C )
dt BBOBBRBR B B
* % CBO ' QB CB ' QR s CB + <>R scro
• QB CBO * QR SCTO * (QB + QR S> CB
The solution to this equation Is:
-e^WV „„
Equation (11) Is the expression for RATIO during substep 1 of TSA.
The boundary conditions for substep 1 are:
at t = 0, RATIO » 1
-SCTO
at t = tj, RATIO = (^V c
Substep 2
During substep 2, the mass balance around the sump 1s:
-QC -QC-QC+Q (1-F) [SC * (1-S) C ]
B BO B B R B R TO B
47
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or
CBO + QR <]-F> SCTO - % CB ' % CB
= % CBO + QR (1'F) SCTO - QB CB - QR (S+F-FS> CB
The solution to this equation Is:
QB/QR + d-F) s ,. -Ygt scTO -Y9t
RATIO = / * -' tl-e 9 ] - e 9 (12)
Equation 12 1s the expression for RATIO during substep 2 of TSA.
48
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SELECTED WATER
RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
EPA-R2-73-2;
Accession Nc.
w
4. Ti'f/e
Predicting and Controlling Residual Chlorine In Cooling
Tower Slowdown
G. R. Nelson
a. organization National inermaT Pollution Research Program
Pacific Northwest Environmental Research Laboratory
National Environmental Research Center - Corvail 1s
Environmental Protection Agency
10. Project No.
11. Contract/ Grant No.
Inhouse
1.5. Supplementary ATorfes
Environmental Protection Agency report number,
EPA-R2-73-273. July 1973. •
16. Abstract
A mathematical model which predicts and controls residual chlorine levels 1n
cooling tower blowdown 1s developed and analyzed. The model has eight variations
to allow for a) the fraction of the redrculatlng water chlorinated, b) the type of
chlorine feed equipment used, and c) the time length of the chlorine feed period.
The variations to the model are useful not only In predicting residual chlorine
levels 1n the blowdown, but also 1n making alterations 1n existing chlorlnatlon
programs which minimize chlorine waste, provide more disinfecting efficiency, and
reduce residual chlorine levels In the blowdown.
17a. Descriptors
Chlorlnatlon*, Chlorine*, Biological control, Water treatment, Water reclrculatlon,
Chemical control
17b. Identifiers
Control, monitoring, blowdown control*, cooling towers*, residual chlorine,
splitstream chlorlnatlon
17c. COWRR Field & Group 05A, 05F
18. Availability
Send To:
WATER RESOURCES SCIENTIFIC INFORMATION CENTER
U.S. DEPARTMENT OF THE INTERIOR
WASHINGTON, O. C. 2OI4O
Abstractor
G. R. Nelson
Institution EPA
WRSIC 102 (REV JUNE 1971)
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