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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                                                 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",

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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

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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

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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

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(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

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(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

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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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