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                        CONTROL





                       PROCESS CHANGES





                    Increased Efficiencies



     The adage about prevention and cure applies as well  to waste



heat as to anything else.  Reduction of waste heat production is



desirable for two reasons:  1) less waste of expensive energy, and



2) fewer problems with or after disposal.  Upgrading the efficiency



of operations which produce heat as a by-product is, therefore, a



logical starting point when considering control of thermal  pollu-



tion.



     Efficiency gains in fossil-fueled, steam-electric stations



have reduced their waste heat discharge rate by approximately one-



half over the past 30 years (Table 3).  Such gains have been accom-



plished through a number of refinements in the plant itself and in



operating conditions.  Figure 2 presents a schematic diagram of the



basic components of a fossil-fueled steam-electric plant which may



be referred to for a better understanding of plant operation and



efficiency.



     The basic steam plant cycle is as follows:  the steam drum



furnace combination turns water into high-pressure steam, which



is carried to the turbines at a speed of about 200 miles per hour.



Within l/30th of a second the steam rushes through the turbines,

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                                                                 53
traveling through a series of stationary nozzles and revolving
buckets which spin the turbine rotor and connected generator shaft
at either 1800 or 3600 revolutions per minute.
     Drastic changes occur in the steam as it releases its energy
to the rotating buckets.  Steam may enter the turbines at tempera-
tures of over 1000°F and leave at less than 100°F.  It enters at a
pressure of 2000 or more psi, expands to a thousand times its en-
trance volume, and leaves at a pressure less than atmospheric.
     From the turbine exhaust the expanded, low-pressure steam goes
to the condenser, where it is cooled until it condenses to water.
The process reduces the volume of the steam by a factor of 27,000
in a near-perfect vacuum, thereby returning it to a state in which
it can be easily handled.  The water is returned to the boiler
through the feedwater heaters to be used over and over again as the
cycle continues endlessly.
     As the cycle repeats, it is necessary to continuously remove
from the condenser an amount of heat equal to that given up in
converting exhaust steam into water.  Plant and operational refine-
ments reduce the amount of heat entrained in exhaust steam which,
in effect, increases the overall plant thermal efficiency.  Reduc-
tion of exhaust heat is attained through several methods (44):
     1) Increasing steam pressure—Elevating the steam pressure at
the turbine entrance reduces exhaust heat by varying increments,
but in general a 100 psi pressure increase will reduce exhaust heat

-------
54




per unit of electricity by 0.4%.



     2) Superheating steam—Steam generated in the boiler is heat-



ed even more in a superheat section of the furnace.   Each 50°F ad-



ditional temperature rise reduces exhaust heat per unit of electri-



city by about 1.4%.



     3) Reheating steam--After the steam has passed  through the



high-pressure turbine section it  is returned to the  furnace reheat



section to absorb additional  heat energy.  Again,  each 50°F increase



here reduces exhaust heat per unit of electricity  by about 1.4%.



     4) Boiler feedwater heating--A portion of the steam is with-



drawn before it reaches the final turbine exhaust, thereby eliminat-



ing its passage through the condenser.  This steam is utilized to



increase the temperature of water entering the boiler.  Feedwater



heating can reduce exhaust heat up to 37% per unit of electricity,



depending on the number of heaters used.



     5) Reducing exhaust pressure—The pressure in the condenser is



transmitted to the turbine exhaust, i.e., turbine  backpressure.



This pressure influences heat rejection to the extent that each 1



psi reduction in pressure reduces exhaust heat per unit of electri-



city by 2.5%.



     Modern power plants are designed to make use  of these effi-



ciency refinements as much as possible.  Through such techniques,



new fossil-fueled plants attain efficiencies near  40%; nuclear-fueled



plants about 33%.

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                                                                 55
     Nuclear-fueled plants are inherently less efficient than
fossil-fueled plants even though they too utilize the basic steam
cycle to spin turbines and generate power.  The major factor in
the efficiency limitation is that imposed through reduced operat-
ing temperatures.  Technological difficulties make it impractical,
uneconomical, or unsafe to produce high-pressure, superheated steam
in a water-cooled reactor system.  Whereas modern fossil-fueled
plants utilize steam at temperatures near 1050 F and pressures over
3000 psi, nuclear-fueled reactors of the boiling water or pressur-
ized water types produce steam at about 600 F and about 1000 psi
or 2000 psi, respectively.
     Lower temperatures and pressures imply less energy content per
unit volume of steam.  Hence, nuclear-fueled plants, compared to
fossil-fueled plants, require larger turbines and condensers for a
given generating capacity in order to compensate for the lower
quality of steam used.
     The principal advantage of nuclear fuel is its tremendous energy
density.  One ton of uranium has the energy potential of three mil-
lion tons of coal.  Present-day reactors convert only about 0.5%
of this energy to usable heat, i.e., combustion efficiency is 0.5%.
Advanced reactor design, i.e., breeder types, will convert much
more energy into a useful form (66).  However, while advanced de-
signs will improve fuel consumption, they will not necessarily in-
crease the thermal efficiency to reduce waste heat in steam-electric

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56




plant operation.



     Reduction of waste heat output from nuclear plants will de-



pend on development of advanced converters which will allow higher



operating temperatures.  Such converters will employ a reactor



coolant other than water in the primary flow loop, which circulates



fluid through the reactor core for heat absorbtion.  The heat is



then transferred to steam through a heat exchange process in a steam



generator.  Systems of this type, still in developmental stages,



are using fluids such as helium, liquid sodium or liquid potassium



for coolants.  Reactor outlet temperatures of over 1000°F are pos-



sible.



     Because of the vast energy stores in nuclear fuel, its utili-



zation for power production is inevitable.  For the next 15 to 20



years, the number of plants in the 30% efficiency class will in-



crease rapidly, which indicates that more efficient systems will



surely lag behind our demands for power.  This being the case, our



immediate efforts must focus on waste heat utilization and dissi-



pation while technology is being developed for more efficient power



production methods.





                         N_ew_Methp_ds_






     Gas turbines offer a means of power production without cool-



ing water.  Air is taken from the atmosphere, compressed, and sub-



sequently burned with a liquid or gaseous fuel.  The resulting

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                                                                57



high-temperature, high-pressure gases expand through a power tur-



bine and then exit to the atmosphere.



     Today's gas turbine efficiencies of less than 25% are not



competitive for power production on a large scale, although some



relatively small turbines are being used for standby and peaking



operation.  Future development may achieve higher operating tem-



peratures and increased air flow, which in turn would increase



efficiency to a level near that of fossil-fueled steam plants.



     Heat exhausted from gas turbines might possibly be put to use



in a conventional steam-electric plant.  Such a combination would



reduce the waste heat discharge rate, although cooling water would



still be used.



     Other systems currently under development may offer promise



for future bulk power generation without the need for cooling water.



Two systems receiving much attention lately are fuel cells and



magnetohydrodynamics (MHD), which would convert heat energy directly



into electrical energy (38).



     Fuel cells are somewhat similar to conventional storage bat-



teries in that they consist of two electrodes separated by an



electrolyte.  The fuel  cell does not contain a store of energy; it



generates current as long as fuel and oxidant supply chemical energy



for conversion to electricity.



     Individual fuel cells produce very small quantities of power.



Hence, thousands of cells would have to be connected in groups

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58



to increase power output to a level which would permit large-



scale production.  Predicted eventual efficiencies of 50 to 85%



is a further attribute of the fuel cell system.  A prototype and



larger scale central station fuel cell plant are being developed



by Westinghouse under a contract from the Office of Coal Research,



Department of the Interior.  Target dates for construction of the



two plants are 1969 and 1973, respectively (38).



     MHD generators utilize the principle of passing a conductor



through a magnetic field to produce current.  In this system the



moving conductor is an ionized gas.  Very high temperatures and



gas velocities must be maintained, which at the present time pre-



sents some major technical difficulties.  In theory, the applica-



tion of a MHD generator can be visualized, possibly in combined



operation with a conventional steam plant, but major advances in



materials must be achieved before the future of MHD power generation



can be predicted (38).





                      ENERGY UTILIZATION





     The optimum solution to problems associated with waste heat



disposal would be the use of rejected heat for beneficial purposes.



When dealing with power plant discharges, however, one is con-



fronted with immense quantities of water which are of low quality



when considered as a heat source.  Utilization of waste heat in



this form  is therefore restricted to only a very few possible

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                                                                 59



applications.



     One potential for such utilization is aquiculture, the farm-



ing of plants or animals in fresh or salt water.  Aquiculture has



been successfully practiced in Japan and elsewhere.  Heated dis-



charges could be used to enhance the environment and increase pro-



duction of commercially valuable species such as pompano, catfish,



shrimp, oysters, and scallops.  Research, development, and pilot



studies are in progress to determine the feasibility of such cul-



tivation in American waters (50).



     Some nuclear plants could possibly be located to provide bene-



ficial use of heated discharges in keeping shipping lanes free from



ice for extended seasons.  A recent journal  article (5) contained



specific recommendations for such application to the St. Lawrence



Seaway, proposing extension of the shipping  season to the end of



December or even January.



     Heated discharges may have application  in irrigating and creat-



ing controlled environments for agricultural  crops.  In this manner,



growing seasons could be lengthened in certain areas for common



crops, and subtropical or tropical varieties  might be produced where



they are not normally adaptable.



     Cooling water may provide heat to warm  swimming areas.  Such



use should be guided by the National Technical Advisory Committee



on Water Quality Criteria (76) which recommends:  "In primary con-



tact recreation waters, except where caused  by natural conditions,

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60
maximum water temperature should not exceed 30°C (85°F)."
     Thermal discharges may also provide heat for desalination
or other processes, some of which might require higher temperature
water than that normally discharged from steam plants.  In such
cases, it may be possible to implement a "trade-off" whereby it
would be economical to alter the usual process for other benefits.
For example, steam from the final turbine exhaust may be 80°F and
0.5 psia.  If the steam were tapped off in front of the final tur-
bine stage it may be 250°F and at 10 psig, which might be worth more
for some use other than its final turbine passage.  Marketable
steam for use by other industries, for home heating, or for any
other purpose may warrant "trade-off" situations which would help
to reduce waste heat loads to streams and other water bodies.
     Creation and application of improved technology for electri-
cal energy conversion is an indirect, but effective, control mea-
sure.  The advent of the fluorescent light is a classic example of
getting more useful work from a watt of electricity.  Other fertile
areas are the heating, refrigeration, air-conditioning and motor
industries.

                       COOLING DEVICES

                            Types
     Waste heat rejection to the aquatic environment can be re-
duced through the  use of cooling ponds or cooling towers.  The most

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                                                                 61
popular devices now in use in this country are various types of
evaporative cooling towers.  In the future, large reservoirs used
as cooling ponds may find increased application in some areas.
     Any method that provides air-water contact for cooling removes
about 75% of the heat through evaporation and the remainder through
conduction-convection.  As water is vaporized, heat is consumed .at
the rate of about 1000 BTU per pound of water evaporated.   Almost
all of this heat is taken from the water that remains, thereby
lowering its temperature.

Cooling Ponds
     A cooling pond or reservoir is the simplest method of cooling
thermal discharges, although it is the least efficient in  terms of
air-water contact.   In a flow-through system, warm water is intro-
duced at one end of the pond, cooled through heat dissipation to
the atmosphere, and eventually withdrawn as cold water from the op-
posite end of the impoundment.  Since the natural cooling  process
is relatively slow without induced air and water movement, surface
area requirements may average about two acres per megawatt output,
depending on local  climatic conditions.
     Advantages of cooling ponds or reservoirs include:
     1.  Low construction cost.
     2.  Serves as  a large settling basin.
     3.  May be beneficial for other purposes, e.g., recreation.

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62




     Disadvantages are:



     1.  Low heat transfer rate, necessitating large land area.



     2.  Possible fogging, icing of nearby roads, etc.




     Cooling can be accelerated in a pond by introducing the warm



water through a spray system located 6 to 8 feet above  the water



surface.  Such a system may reduce the required pond surface area



by a factor of 20 through increased cooling efficiency.   This ad-



vantageous savings in land area may be negated through  spray system



cost, pumping costs, and increased water loss with its  associated



problems.





Cooling Towers



     There are many versions of cooling towers.  Terminology applied



to towers stems from basic differences in design or operation which



serve to categorize the types.



     A tower may be either "wet" or "dry," depending on whether



water is exposed directly to the air; "natural draft" or "mechani-



cal draft," depending on whether fans are employed for  air movement;



"cross-flow" or "counter-flow," depending on horizontal  or vertical



air flow through the heat transfer section of the tower.  In mechani-



cal draft towers, air flow can be either "forced," i.e., pushed



through by fan on bottom, or "induced," i.e., pulled through by fan



on top.  See Figures 3, 4, 5 and 6 for schematics (29,41) illustrat-



ing these types.

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                FIGURE 3

          NATURAL DRAFT TOWER
              DRIFT
 HOT WATER /ELIMINATOR
DISTRIBUTION
      COLD WATER
         BASIN
      WET (Evaporative) COUNTERFLOW

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               FIGURE 4

        NATURAL DRAFT  TOWER
HOT WATER
  BASIN
FILL   I
            DRIFT
         ELIMINATOR
                                SHROUD
                                      AIR
                                     INLET
        ^COLD WATER
           BASIN
      WET (Evaporative) CROSSFLOW

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                  FIGURE 5


         MECHANICAL DRAFT  TOWER
                   AIR OUT
 WATER IN
  \ ' /' ' ,

.'/ ','•', \'!/


!'.  0:/',^/V,
  VII, • Ml ' / "
  <•*,/ '"//
WATER OUT
                                   DRIFT

                                   ELIMINATOR
                                        AIR IN
                 FAN
     WET,(Evaporative) FORCED AIR FLOW

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                FIGURE 6
        MECHANICAL DRAFT TOWER
                        AIR OUT
          FAN
 WATER IN
WATER OUT
   AIR IN
                               -COOLER
                               SECTION
AIR IN
          DRY, INDUCED AIR FLOW

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                                                                 67


     Because it is important to understand the working "language


when discussing cooling towers, the following discussion of signi-


ficant terms is presented.


     Dry-Bulb Temperature:  (  F,  C)  Temperature of air read on


     an ordinary thermometer.

                             O   ""I
     Wet-Bulb Temperature:  (  F,  C)  Obtained by covering the


     bulb of an ordinary thermometer with wetted gauze and reading


     in moving air.  It depends on the dryness and initial tempera-


     ture of the air, but is lower than dry-bulb temperature because


     some water evaporates from the gauze, removing heat.   The wet-


     bulb temperature is the theoretical  limit to which water can


     be cooled through evaporation.


     Relative Humidity:  (%)  The ratio of the amount of water vapor


     actually present in the air to the greatest amount it could


     hold if saturated at that temperature and pressure.  When rela-


     tive humidity is 100%, wet-bulb temperature equals dry-bulb


     temperature; therefore, the lower the relative humidity, the


     greater the difference between wet-bulb and dry-bulb tempera-


     tures .


     Evaporation Rate:  The rate, e.g., gallons per minute, at which


     water is being evaporated to cool the circulating water.  It


     depends on the area of air-water surface contact, length of


     time of contact, and difference between wet-bulb temperature

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68




     of the air and water temperature.



     Cooling Range:  (  F,  C)   The temperature  difference  between



     hot water entering a tower and cold water  leaving.



     Approach:  (°F,  C)  The  temperature difference between cold



     water leaving a tower and wet-bulb temperature of the surround-



     ing air.



     Heat Load:  (BTU/hr, BTU/min)  The amount  of heat dissipated



     in a cooling  tower per unit time.   It equals water  circulation



     rate multiplied by cooling range,  i.e.,




                                             )  -  BTU/mln
     Drift,  Carry-Over,  or Windage Loss:   Water  carried  out  of a



     tower in mist or small  droplet form.   It is usually expressed



     as a percentage of  the circulating  water rate.   Caused  by high



     air velocities, it  can be almost entirely eliminated through



     good design and operation.



     t3as_i_n_:   The depressed bottom portion  of a tower used for col-



     lecting and storing cold water.



     Slowdown :   The continuous or intermittent discharge to  waste



     of a small  portion  of circulating water from the tower  basin.



     It is usually expressed as  a percentage of  the  circulating



     water rate.  It prevents build-up of  dissolved  solids left



     behind  during evaporation.



     Makeup:  (gpm,cfs)   Water required to replace normal system



     losses  from evaporation, drift,  blowdown, and small leaks.

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                                                                 69
     Packing or Fill:   Material  placed in a tower over which water
     flows.  It increases the air-water surface area and time of
     contact and maintains uniform air and water flow distribution.
     Packing design dictates the type of flow.   Counter-flow towers
     usually use film-type packing; cross-flow towers usually use
     splash- or droplet-type packing.
     Water Distribution System:   A network of pipes (usually-) which
     spreads incoming  hot water  uniformly over the packing in a
     tower.
     Drift Eliminators:  Baffles located above the water distribu-
     tion system in a  tower.  As air flows through the baffles in
     a curved path, water particles are thrown from the airstream
     by centrifugal force.

     Natural Draft Towers.--The  cooling tower finding frequent ap-
plication to large power plant discharges at the present time is
the wet, natural draft, hyperbolic type.  Over 20 of these towers
are now in various stages of operation or construction in this
country.
     Hyperbolic towers derive their name from the hyperbolic profile
of the reinforced concrete shell.   The largest are almost 450 feet
high and over 300 feet in diameter at the base.  The function of
the shell is that of a stack or  chimney in providing an enclosure
for air flowing through the packing which is located near the ground

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70




either inside or outside of the shell.   Air flow through a tower



is created by the difference in density between the internal  and



external  air.  Warm water passing through the packing heats the



air and saturates it with water vapor during evaporative heat trans-



fer.  Both processes decrease the air density and cause it to rise



up the tower.  More air is drawn in, resulting in the establishment



of a continuous air flow through the tower.  External winds moving



across the top of the tower also contribute somewhat to the air



flow by reducing the internal pressure, thereby creating a drawing



effect.  However, tower operation is not dependent on external  wind-



induced air movement.



     Internal packing is located in the bottom 10 to 20 feet of the



tower shell.  Warm water distributed above the packing flows down-



ward through it in thin layers, contacting air rising vertically



through the tower.  Such opposed flow denotes the counter-flow clas-



sification.  (See Figure 3)



     Packing may also be located on the outside periphery of a shell.



In this system the water is broken up into droplets by splash-type



packing and allowed to fall downward.  Incoming air flows horizon-



tally through the falling water and then travels upward through



the empty tower shell.  This case describes the cross-flow classi-



fication.  (See Figure 4)  Water loading over the packing is from



2 to 4 gpm per square foot of horizontal area (29).

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                                                                 71



     Advantages of the evaporative, natural  draft type of tower



are (48):



     1.  Does not have mechanical  or electrical  components, yet



         for a given load it has the same cooling capability as



         the mechanical draft type.



     2.  Low maintenance cost, ijoth in time  and  money.



     3.  Independent of wind velocity.



     4.  Large water loading capacity.



     5.  For counter-flow design,  air and water  flows are opposite



         in direction, with the driest air meeting the colder



         water first, ensuring maximum efficiency.



     Disadvantages are (48):



     1.  Internal resistance to air flow must be kept minimal.



     2.  Great shell heights are required to produce a draft.



     3.  Inlet hot water temperature must be hotter than air dry-



         bulb temperature to induce air movement.



     4.  Exact control of outlet water temperature is difficult



         to achieve.



     Evaporative loss of water through the system amounts to about



1.5% of the flow circulated.  Slowdown may require an additional



2 or 3%, depending on the quality  of the circulating and makeup



water.   Drift is negligible in a well designed tower, not exceed-



ing 0.2% of the circulating flow (41).

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72

     A fossil-fueled power plant in the 600 MW class or a nuclear-

fueled plant of about 400 MW would discharge about 2500 X 106 BTU's

per hour.  Typical design conditions for a hyperbolic, evaporative

tower to handle this heat load may be as follows (41):


         Waterflow	  450 cfs
         Hot Water Temperature	  115°F
         Cold Water Temperature	   90 F
         Design Wet-Bulb Temperature	   72°F
         Design Relative Humidity	   50%

Such conditions would require a tower about 400 feet high and 285

feet in diameter for counter-flow design, or about 370 feet high

and 380 feet in diameter for cross-flow design (41).

     Care must be exercised when comparing natural draft evaporative

tower requirements at different sites.  Each design is necessarily

based on specific conditions—temperature, humidity, etc.--for a

given geographical location.  Hence, the size and performance cited

for a tower at one plant site may not apply to another, even though

the plants to be served are quite similar.

     Other kinds of natural draft towers depend on air movement

without the use of a chimney or shell.

     Atmospheric spray-filled towers, which are really more like

narrow spray ponds, have nozzles located from 6 to 15 feet high

surrounded by a louvered fence which permits air passage but inhi-

bits water loss.  Air circulation is dependent mainly on wind velo-

city.  Such cooling systems are suited for small refrigeration and

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                                                                 73



engine-water jacket installations, where variations in a relative-



ly small cooling range will  not seriously hamper operations.   Where



locations permit prevailing  winds to flow unobstructed, the system



works fairly well with a minimum of maintenance.  Water loading



capacity may be up to 1.5 gpm per sq ft of active horizontal  area



with wind blowing at 5 mph (29).  Disadvantages may include clog-



ging nozzles, nigh pumping pressures required to atomize water, and



high windage losses.



     Atmospheric packed towers are similar to the spray-filled type



except that they are usually larger and contain packing for water



breakup and additional wetted surface exposure.  Such systems are



rarely built any more because of their high capital and pumping



costs, and of their dependence on wind for air circulation.  Small



mechanical draft towers which handle comparable loads at similar



costs are now preferred.



     A final consideration in the natural draft category is the



hyperbolic dry tower.  This  type also employs a shell for the draft



effect, but utilizes indirect heat transfer instead of evaporation



for cooling.  Completely closed cooler sections give up heat through



conduction-convection, hence there is no evaporative loss of heat



or water.  The indirect transfer of heat is much less efficient than



the evaporative process so that much larger volumes of air must be



circulated than in a wet tower.  Therefore, the shell size must be



larger, which adds to capital cost.

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74




     Dry towers are also at a disadvantage compared to wet types



because of the lower limit to which water may be cooled.  The theo-



retical lower limit in a dry process is the dry-bulb air tempera-



ture; the corresponding limit in a wet process is the wet-bulb



temperature, which is usually appreciably lower (64).



     Natural draft dry towers have not been generally used for



large-scale cooling because the capital cost is estimated to be



about three times as much as its wet counterpart (64).  However,



the elimination of water loss through the use of such systems may



prove to be a deciding factor in their acceptance in some loca-



tions in the future.



     Mechanical, Draft Towers.--Until 1963 when the first hyperbolic,



natural draft evaporative tower was built at the Big Sandy power



plant at Louisa, Kentucky, only mechanical draft towers had been



used in the United States.



     Advantages of evaporative, mechanical draft cooling towers



are (48):



     1.  Close control of cold water temperature.



     2.  Generally low pumping head.



     3.  Location is not critical.



     4.  More packing per unit volume of tower.



     5.  A smaller approach and greater cooling range are possible.



     6.  Small land area requirements.



     7.  Capital cost is less than for a natural draft chimney.

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                                                                 75



     Disadvantages include the following (48):



     1.   High operating costs, including power.



     2.   High maintenance costs,  both in time and money.



     3.   Subject to recirculation of hot,  humid  exhaust into



         the air intakes.



     4.   Climatic variation can affect performance because fans



         move a fixed volume of air regardless  of its density and



         related heat transfer properties.   Also, efficiency de-



         creases as wind speed increases,  up to  a critical  velocity;



         at velocities above the critical  value  the opposite is



         true because of less recirculation.



     Mechanical draft towers are used over a broad range of heat



loadings because they can be designed specifically for almost any



capacity.  Maximum fan sizes limit the capacity  of any single cell,



but additional cells may be built to form  a bank or unit capable



of meeting the total requirement.



     The two air flow designs commonly used in mechanical  draft



towers,  forced draft or induced draft, were referred to previously



and depicted schematically in Figures 5 and 6.



     Forced draft towers, with one or more fans  located in the air



intake,  are slightly more efficient than induced draft types because



some of  the pressure of air velocity is converted to static pres-



sure in  the tower and recovered in the form of  useful work.  Fan

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76




location close to solid foundation lessens vibration.  Also, locat-



ing fans at the air inlets reduces the possibility of moisture con-



densation on the equipment since most of the air moved is dry.



     Recirculation of hot air is common in forced draft towers be-



cause of the proximity of the exhaust to the low-pressure air-intake



region.  Hence, efficiency may vary and winter operation often causes



frost and ice formation on equipment or nearby buildings due to the



presence of moisture-laden air near ground level.



     Forced draft type fan diameters are limited to 12 feet or less,



compared to nearly 60 feet for the induced draft type, which neces-



sitates more cells for a given capacity (29).



     While forced draft towers employ only counter-flow air movement



through the packing, induced draft towers may use either counter-



flow or cross-flow design.  The basic differences in packing design



and arrangement, as described previously, apply here also.  For



either type of flow, recirculation is generally not a problem because



the top-mounted fan discharges heated air upward, directly away from



the air intake below.  Because hot, humid exhaust air moves through



the fan, corrosion of mechanical parts is more pronounced than in a



forced draft system.



     Operational pros and cons of cross-flow design versus counter-



flow design are fairly well balanced for operational characteristics.



Physically, cross-flow types can be built lower and provide easier



access to the water distribution system.

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                                                                 77



     Mechanical draft systems also may provide air movement in dry



towers, thereby fulfilling the purpose of the hyperbolic shell as



previously discussed.  As noted before, large volumes of air are



required because of less efficient heat transfer through conduction



and convection than through the wet evaporative process (64).



Therefore, large fans are required which continuously demand an



appreciable amount of power—about 3% of total electric power pro-



duction (6).   Economics related to mechanical draft dry systems



discourage large-scale application at this time.





                        Side Effects



     Concern  over possible side effects from cooling devices has



risen along with the projected use of such systems.  Primary con-



cern is with  potential fogging conditions caused by cooling towers



(14,62), but  other possible adverse side effects should be considered.



     Because  of the large amount of water vapor expelled from eva-



porative towers, extreme climatic conditions may cause condensation,



resulting in  ground level fog or drizzle.  However, such conditions



are not often encountered in practice (48).   A recent investigation



of fogging problems from natural and mechanical draft towers pres-



ently operating in the eastern U.S. supports this conclusion (11).



Reports indicate that natural draft towers did not produce ground-



level fog or  drizzle under any weather conditions.  Plumes rarely



dropped below the top of the tower for an extended distance, and

-------
78




 generally  dissipated within a few hundred feet of a tower.  Mechani-



 cal,  induced draft  towers reportedly produced substantial amounts



 of  ground  level  fog, especially during the winter.  The area affect-



 ed  by the  fog was very  small, however, extending a maximum of about



 one-fourth mile  from the towers.  Carry-over of some water droplets



 was also noted from the mechanical draft type.  Resulting precipita-



 tion  occurred in the immediate vicinity of the towers, causing some



 minor icing problems up to 300 feet away.



      In general, undesirable meteorologic effects from towers can



 be  prevented or  controlled to a large degree through modern design--



 effective  drift  eliminators, air-flow control, etc.  In situations



 where problems arise, the area affected is limited to that immediate



 to  the tower installation (16).



      Water circulating  through a condenser-cooling tower system may



 be  treated chemically to prevent corrosion and inhibit biological



 growth (21).  hence, water extracted for blowdown purposes may con-



 tain  constituents which would be detrimental to aquatic life in



 receiving  waters.   Such effects may be prevented by treating blow-



 down  waste separately or, more efficiently, by integrating blowdown



 disposal with other plant waste disposal facilities.

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                                                                 79
                            Cqst^s
     An article (41) discussing natural draft, evaporative cool-
ing towers states the following in regard to tower costs:
     "Single towers, regardless of design, will cost in the area
of $2.5 to $3.5 million each for the size of towers which have been
utilized to date in the United States.
     "The physical size and cost of a tower installation for a
given size generating unit, however, can vary widely with location,
fuel costs, load factors, and with individual practices regarding
capability penalties and capitalization rates.  It is possible that
the optimum cooling tower installations for two plants with identi-
cal rated outputs could differ in cost by a factor of two.  For this
reason, it is difficult and, indeed, dangerous to generalize when
discussing tower reouirements and costs.'1
     The following outlines cooling tower costs as related to each
other, to total plant or production costs, and to consumer costs.
     Natural draft evaporative tower capital costs in the eastern
U.S. have been at least 5% of the total capital cost of a power
plant.   For a given plant heat load, mechanical draft, evaporative
towers cost approximately two-thirds as much as natural draft;
either natural draft or mechanical draft dry types would probably
cost three to four times more than their wet counterparts.
     The indicated savings in initial cost for the mechanical draft,
wet tower is somewhat negated because of power costs for fans, which

-------
80




consume about 0.8% of the power generated by the unit served (44).



For the proposed 540 MW nuclear plant at Vernon, Vermont, the an-



nual cost for production of power to operate fans is estimated to



be about $130,000--about 2% of the initial capital tower cost of



$6 million.  Other maintenance costs for the mechanical draft tower



installation are estimated at $60,000 annually--l% of initial tower



costs.  For this plant, the initial cost for mechanical draft



towers amounts to 5.1% of the total plant cost of $118 million (19).



     In a detailed study for siting 1000 MW nuclear power plants in



the Pacific Northwest (55), natural draft cooling towers were recom-



mended at a number of locations.  At all sites the estimated initial



cost of such towers and related appurtenances was about $7.5 mil-



lion, or approximately 5.5% of a total plant capital cost of about



$140 million.  Induced draft towers were recommended in one case,



also at a capital cost of about 5.5% of the total plant cost.  The



cost of a 2600-acre pond at a location conducive to that type of



cooling system would be about 2.3% of the total plant cost.  It



should be noted, however, that the pond location was in an area of



relatively low land value.



     These examples indicate that evaporative cooling systems will



increase the capital cost of a power plant by about 5%.  An assess-



ment of all fixed and variable costs indicates that power produc-



tion costs are also increased by about 5% (19).   It should be noted,



however, that such increases are not carried over to consumer costs

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                                                                 81



in the same proportion because of intermediate fixed costs in-



curred through transmission and administration.   According to



Converse (19), production cost is only about one-fifth of consu-



mer cost.  In that case, the cost of electricity to the consumer,



because of the use of evaporative cooling towers, would increase



approximately 1%.





             TRANSPORT AND BEHAVIOR MANIPULATION





             Dispersion and Dilution Techniques



      The design of discharge outfalls is, at the present time,



more art than science.  Hydraulic model  studies, along with other



empirical information, are new the basis for design because theo-



retical equations of fluid motion have not yet reached the stage



of engineering aoplication.  Future developments in the area of



mathematical  models, hopefully, will place the design of outfall



structures more on a theoretical, rather than empirical, basis.



      The physical and hydraulic characteristics of the effluent



and receiving water largely determine the rate of dispersion and



areal  extent  of dilution.  Rate of dispersion is a function of the



existing turbulence of the receiving water, turbulence induced by



the kinetic energy of the effluent, and  the density gradient be-



tween  the effluent and receiving water.   The areal extent of dilu-



tion is a function of the dispersion rate plus the number and

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82




orientation of ports in the discharge manifold.   Outfalls should



be designed to accomplish specific objectives.



      If the objective is to minimize temperature gradients within



the water body, a diffuser designed to maximize  induced turbulence



and to distribute the discharge over a broad area is recommended.



The diffuser pipe could be placed in any of the  three spacial  dimen-



sions of the water body, but common practice is  to use a horizontal



diffuser pipe placed across the stream.



      A discharge technique which is quite common with TVA is  the



use of a discharge channel which floats  the warm water on the  sur-



face of the receiving stream or reservoir.  The  objective of this



method is to maximize dissipation of heat to the atmosphere and



minimize the water areas and volume affected by  the effluent;  mix-



ing is not desired.  By forming a warm water wedge over the cool



receiving water, rapid heat loss to the  atmosphere is encouraged



by increasing the energy transfer due to evaporation, convection,



and back radiation.  Thus, the warm water wedge  acts in much the



same manner as a cooling pond.  However, this technique results in



sharp temperature gradients near the surface and serious problems



can occur if temperature sensitive organisms are subjected to  such



gradients.  For example, this technique would not be desirable on



a stream inhabited by a cold-water fishery.



      A third alternative discharge technique is to develop a



thermal plume.  A single-point discharge below the surface of  the

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                                                                 83
receiving water will result in a plume extending in the direction



of the water flow and vertical density gradient.  Mixing is oro-



tnoted by both the energy of the receiving water's current and by



the kinetic energy of the discharge.  In some streams where plumes



originate near the bed, vertical mixing is rather rapid, but



lateral mixing is slower.  For example, plumes from AEC's nuclear



reactors at Hanford, Washington, on the Columbia River exhibit



such characteristics.



      A term which has recently been appearing in the literature



regarding thermal pollution is "thermal block."  A thermal block



occurs when a warm water mass interferes with fish migration (76,



p. 31).  Outfalls should be designed to prevent such a block from



occurring.



      A final point must be made concerning the control of heated



discharges by dispersion and dilution.  Such techniques cannot be



expected to solve the problems associated with the discharge of



large heat loads into moderate volumes of receiving water.  Any



heated discharge which will promote excessive temperature rises



will require the use of cooling devices.





                  Hater Quality Management





Temperature Prediction



      Mathematical  and physical  models of varying degrees of com-



plexity have been developed to determine the fate and persistence

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84



of heat in quiescent waters, flowing streams, estuaries,  and the



ocean.  The ability to predict water temperatures accurately is



necessary in order to determine the thermal  impact of:



     1.  Proposed waste heat discharges.



     2.  Changes in the hydraulic characteristics of a  water



         body or stream—for example, due to the construction



         of a dam with its resulting flow regulation.



     3.  Releases of water from stratified reservoirs with



         multilevel outlets.



     4.  Unusual meteorological conditions.



     The following discussion presents the basic approach which



is used to solve temperature prediction problems.  However, the



mathematical formulation of the physical  heat transfer  processes



which occur is not a simple matter.  The  scope of this  guide pre-



vents a presentation of the mathematical  derivations leading to



temperature prediction models for all situations.  However, a



simplified case is presented in the example problem of  the next



section.  For information on more sophisticated models, the reader



is urged to consult the technical literature.  An excellent basic



reference is the Edison Electric Institute's Publication  No. 65-902,



Heat Exchange in the Environment, by J. E. Ldinger and  J. C. Geyer,



Department of Sanitary Engineering and Water Resources, The Johns



Hopkins University, June 1, 1965 (27).

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                                                                 85



      It is necessary to consider heat transfer mechanisms in



water and between water and the atmosphere in order to describe



temperature regimes mathematically.  For localized problems,



e.g., outfalls or plumes, the mechanisms acting in the water



are most important; analysis of conditions throughout larger



systems (rivers, reservoirs, etc.) requires emphasis on the air-



water heat transfer mechanisms as well as those in water.   In



either case, specific predictions are desirable so that effec-



tive control or management techniques can be applied.



      There are two heat transport mechanisms which occur in



water--advection and dispersion or turbulent mixing.  Advection



is the transport of heat by the motion of a mass of water and is



accomplished through ordinary streamflow, utilization of a dis-



charge stream's kinetic energy, or water movement due to density



gradients.  Mathematical terms for advection express the rate of



heat energy transfer in terms of the water mass temperature and



velocity along longitudinal, lateral, and vertical axes.



      Turbulent mixing or dispersion cause heat interchange through



eddy diffusion or molecular diffusion.  Eddy diffusion occurs under



turbulent flow, which depends on fluid velocity and channel



characteristics.  Mixing results from the action of small  fluid



masses known as eddies, which are random both in size and orienta-



tion.  Molecular diffusion is that resulting from random motion



of molecules.   Its influence is much less than that from turbulent

-------
86
mixing.  Diffusion effects are combined in mathematical expres-
sions, and may be defined along longitudinal, lateral, and
vertical axes.
      Heat exchange which takes place between the water surface
and the atmosphere is made up of seven mechanisms.
      The mechanisms which are independent of water temperature
are (27):
      Qs = Incoming short-wave solar radiation (400 to 2800
           BTU/ft2/day).
      Q, = Incoming long-wave atmospheric radiation (2400 to
       a
           3200 BTU/ft2/day).
      Qsr  Qar = Portions of both short-wave and long-wave
                 radiation which are reflected or scattered by
                 the water surface (40 to 200 and 70 to 120
                 BTU/ft2/day, respectively).
      The mechanisms of heat transfer which are dependent on the
surface water temperature include the following (27):
      Qbr = Long-wave back radiation from the water to the
            atmosphere  (2400 to 3600 BTU/ft2/day).  It is pro-
            portional to the fourth power of the absolute water
            surface temperature (AT$), i.e., 0.^ <* (ATS)  .
      Qc  = Heat exchange due to conduction-convection (-300 to
            +400 BTU/ft2/day), which is proportional to the wind
            speed  (W) and the difference between water temperature

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                                                                87
            (T_) and air temoerature (T J, i.e., (1  cc W(TC-T ).
              b                        a          c      b  a
            A positive Qc indicates an energy loss.
      Qe  = Heat loss due to evaporation (2000 to 8000 BTU/ft2/
            day), which is proportional to the product of wind
            speed (W) and the difference between the water vapor
            pressure in saturated air at the water temperature
            (es) and the water vapor pressure in the overlying
            air (ea), i.e., Qe <* W(es - ea).  If ea > es, conden-
            sation takes place and the water body gains energy.
      The algebraic sum of these surface heat exchange parameters
is equal to the net rate of surface heat exchange.  Equilibrium
temperature is reached when this sum is zero.
      Micro Models.--In temperature prediction terminology, a micro
model is one which describes or predicts the distribution of heat
in the immediate vicinity of a thermal  discharge.  The micro models
available at the present time are based on many simplifying assump-
tions which render them less than totally adequate for predicting
local temperature distributions.  However, they are useful for
approximating heated discharge dilution rates by receiving waters.
Theoretical work is  progressing in areas such as mixing and dis-
persion and will aid in development of generalized micro models
for jets and plumes.
      Another factor which adds to difficulties with micro models
is the  unique character of many situations.   For example,  the nature

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88




of a stream channel at any location will influence mixing charac-



teristics.  Curvature or depth variation may direct discharges into



certain portions of a channel, thereby nullifying the theoretical



description of the length or degree of mixing.   Each situation will



therefore require careful description in terms  of discharge pumping



rate, river flow, and channel characteristics.



      Until generalized micro models can accurately predict local



temperature distributions under various hydraulic conditions, esti-



mates based on simplified models and past experience will be required.



      Macro Models.--Macro models are those which describe or pre-



dict temperature regimes in a complete river or river system, lake



or reservoir, estuary, or coastal area.  Such models combine heat



transfer mechanisms and water movement on a continual basis with



respect to time.  With the current state of the art, technology for



macro-prediction is more reliable than for micro-prediction.  This



is possible because of the compensating and averaging effects of



spacial differences in environmental variables.



      A macro model maintains an energy budget for the water body



under consideration, i.e., it maintains a heat balance of both the



internal heat exchange and the heat transfer at the water surface.



This heat budget may be expressed as follows:



       (Rate of Heat In) - (Rate of Heat Out) + (Rate of Heat



      Storage) + (Rate of Heat Exchange at Water Surface) - 0



The rate at which heat flows into and out of the water body is

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                                                                 89
determined from the flow rates and temperatures of inflowing and
outflowing water.  These rates require evaluation of the heat
transfer mechanisms in water to define the motion of heat entrained
water masses.  The rate of heat storage is determined from the
temperature and volume of the water body in consecutive time
periods.  The rate of heat exchange at the water surface is the
algebraic sum of all the water-atmosphere heat exchange rates.
      Macro models evaluate terms in the heat budget over specific
time periods, e.g., hourly, daily, weekly, etc.  The rate-time
evaluation results in quantitative values for each portion of the
heat budget for each period through the study time span.  By super-
imposing flow rates on the time scale, the location of a specific
water mass may be determined at any desired time.  For temperature
prediction, a model routes hypothetical masses of water along a de-
scribed course in order to simulate their movement and changes in
thermal properties; temperatures are thereby predicted at specific
locations and points in time.

Thermal Regulation
      The need to manage our environment has only recently been rec-
ognized, but we now realize that in order to continue the effective
use of our natural resources, environmental management is a neces-
sity.  In terms of thermal pollution control, we can perform water
temperature management through plant siting, coupled with effective
use of regulated river systems.  Effective water temperature predic-

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90
tion models will enable water resources managers to predict tempera-
tures which will result from combined dam releases and thermal in-
puts to a system.  Conditions can then be selected to minimize un-
desirable thermal effects.  Such temperature-discharge requirements
can be met through the use of multilevel dam outlets which permit
waters of various temperatures to be selectively released from
stratified reservoirs.

                       EXAMPLE PROBLEM
      This section presents a problem concerning temperature predic-
tion on a well-mixed stream and the sizing of flow-through cooling
ponds.  A complete explanation of the methodology is beyond the scope
of this guide, and the reader is urged to consult the literature for
an in-depth review of the many available computational techniques.
The problem solution uses basic methods, all of which can be found in
the publication by Edinger and Geyer (27).  As an aid in analyzing the
problem, references to appropriate pages in this reference are given.

                        The Situation
      A 1000 MW electrical output nuclear power plant of 33% effi-
ciency is to be located on a medium-sized river in the temperate
region of the nation.  Using applicable hydrologic and meteorologic
data, we wish to compute:
      A.  Downstream temperature, assuming once-through cooling
          and complete mixing in the river.
      B.  The area of a flow-through cooling pond necessary to
          prevent violation of water temperature standards.

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                                                                 91



Part A



     Compute the heat energy entering the cooling water as des-



     cribed in the "Plant Evaluation" section.
     1.  For 33% thermal  efficiency (r\.}:
                     •541-3

         Heat Rate = °  . 1An -  -    = 10,340 BTU/KWH
                     r).  v i uu    .00




     2.  Assuming a 5% in-plant heat loss:



         Heat to cooling water - (0.95 x Heat Rate - 3413)  BTU/KWH



         Heat to cooling water - [0.95(10,340) - 3413]  BTU/KWH



         Heat to cooling water = 6410 BTU/KWH



         Total heat to cooling water for the 1000 MW (106 KW)  plant



           106 KW x 6410 BTU/KWH = 6.41  x IP9 BTU/hr
     Compute the temperature rise in the stream, assuming once



     through cooling and complete mixing.




     Given a design flow in the stream of  3500 cfs,  which in terms



     of Ib/hr is:



          Q = (3500 cfs) (62.4 lb/ft3)  (3600 sec/hr)



          Q =  7.86 x 108 Ib/hr




     Since 1 BTU will raise the temperature of 1 Ib  of water 1°F,




          AT  = AT in river = <6'41  x 10'  BTU/h^	

            r                 (7.86  x 10B  Ib/hr) (1  BTU/lb °F)



          AT  = 8.2°F
            i

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92
     Equation for computing downstream temperatures.
     Downstream temperatures are computed by assuming exponential
     temperature decay.  This concept is presented mathematically
     as:

           ^= -K(T - E)                             (27, p. 43)

     where -rr = net rate of water surface heat exchange  (BTU ft   day   )

            K = energy exchange coefficient (BTU ft   day'  °F   )
            T = water surface temperature (°F)
            E = equilibrium temperature (°F)

     For a well-mixed stream, this equation can be written as:

         pCpyu|I = -K(Tx - E)                       (27, p. 129)
                                         _3
     where  p = water density (62.4 Ib ft  )
           C  = specific heat of water  (1 BTU Ib"1 °F"1)

            y = mean stream depth (ft)
            U = mean stream velocity (ft day  )

           TT~ = longitudinal temperature gradient  (°F ft" )

            x = downstream distance (ft)
     Define T  = temperature at x = o; then
                           -Kx  )
                          Pcpyu
            Tx = (T  - E)e
             /\     \J
                       Kx
     By defining a =  ^  y  ; then

            T  = (T  - E)ea + E
             x   v o

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                                                             93

Meteorologic Data

The following data are used in determining K and E:


Time Period
(6 hr intervals)
Midnight - 6 am
6 am - Noon
Noon - 6 pm
6 pm - Midnight
DAILY AVERAGE
For K
1 1
Wind ,u.
Speed w
(mph)
4.0
12.0
12.0
6.0
8.5

1
Net Radiation ,u ,
Input (tV
(BTU ft-* hr-1)
120
290
320
130
215
For E

Air (T ,
Temp 1V
(°F)
65
75
85
70
74


Relative
Humidity
{%}
40
30
20
35
--

Water Vapor '
Pressure of (e )
Ambient Air
(mm Hg)
6.3
6.7
6.2
6.6
6.5
Determination of K

The energy exchange coefficient is computed using a

variation of the equation given on page 48 (27):

     K = [15.7 + (0.26 + 3)(bW)]

where W = wind speed (mph)

      b = experimental evaporation coefficient  (a value of

          15 is used in this example)

      (3 = proportionality coefficient [See following table]

            Range of E              g
               (OF)(mm Hg op-I)

             50 to 60              0.405
             60 to 70              0.555
             70 to 80              0.744
             80 to 90              0.990

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94
     Thus, for an average daily value of K, using W = 8.5 mph:

          K = (15.7 + [0.26 + 3]  [(15) (8.5)])

     Using appropriate values of 3 for two ranges of E:


            i (°F)        K(BTU ft"2 day"1 °F"])

         60 to 70         120
         70 to 80         144

     Determination of E

     The equilibrium temperature is reached when the rate of change

     of energy at the water surface equals zero.  Edinger and Geyer

     (27) present a method for computing E (pp. 55-59). The method

     involves assuming a likely 10°F temperature range for E and by

     using the appropriate value for K and the given meteorological

     data, computing a value for E.  If the computed value of E falls

     within the assumed range, the process is complete. However, if

     the computed value of E falls outside the assumed range,

     another range must be assumed and the process repeated until E

     falls within the proper limits.  Thus, E is computed by a trial

     and error method.


     For the stated meteorological conditions and computed values

     of K, we can determine a daily average E by the following seven

     steps (27):

     Step 1.  Assumed range of E = 70 to 80°F

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                                                                95
Step 2.  Compute F(K) for use in step 6:
            K - 15.7
     F(K) =
               K
As computed for an E range of 70 to 80°F, K = 144 BTU ft"2 day"1 °F
     .'. F(K) -  ^ 144  - = °-891
Step 3.  Compute E-, for use in step 6:
          HD - 1801
     E  =
     -1       K
                                                        7    1
     From the meteorologic data table, HR =  215 BTU ft   hr

     or in terms of days, HR = 5160 BTU ft"2 day"1

      •     -  5160 - 1801  _
Step 4.  Compute E? for use in step 6:
          (0.26) (Ta)
     E2 ~ "(0.26 + 3)
     From the meteorologic data table, T  = 74°F, and from
                                        a
     the table of E range vs. 6, 3 = 0.744

      .  F  _ (0.26) (74)    _ ,q
     '  '  L2   (0.26 + 0.7447   Iy^
Step 5.  Compute E~ for use in step 6:
          e, - C(3)
           a
      3   (0.26 + 3)
     From the meteorologic data table, e  = 6.5 mm Hg.  C(3)
                                        a
     is related to ranges of E as follows:
           Range of E             C(3)
              (OF)   "            "(mm Hg)
            50 to 60              -11.22
            60 to 70              -20.15
            70 to 80              -33.30
            80 to 90              -53.33

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96
           Thus  for  an  E  range of  70 to  80°F, C(6) =  -33.3

           .   E   _ 6.5  - 1-33.3)   _ -q fi
          '  '  3   (0.26  +  0.744)   Jy'D

     Step  6.   Compute M for use in step  7:

          M =  E1  +  F(K) (E2 + E3)


          M =  23.3 + (0.891)  (19.2 + 39.6) = 75.7

     Step  7.   Compute E using the  following relationship:

          M=E+0.051E2
                     K

          Inserting M and  K and setting  up a quadratic equation  gives:


           2  °°

                       E - 75.7 - 0
          .'. 0.000354E2 +  E  - 75.7 - 0

          Solving  this equation using the quadratic formula gives:


          F  = -1 ± [1 -  (4)  (0.000354)  (-75.7)]1/2
          t        ~    2  (0.000354)


          F  = -1 ± (1.10719)172 =  -1 ±  (1.05223)
                   0.000708          0.000708
          Rejecting  the negative  value gives:

            =  n'nnrwna =  73.8°F   (This value  is  acceptable  because  it
                         	   falls within
                                 70  to 80°F.)
falls within the assumed range of
     Compute  Average  Stream  Velocity

          Q = 3500  cfs

     Given an average cross  section 800  feet wide  and  5  feet  deep:
          U  =             S  ft)  =  °'875  ft/sec = ZS^OO  ft/day

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                                                               97



Evaluation of a



          -Kx
     a =
         pCpyU
     For x'  in miles:  a = (      (1) (5) (75,600)
     a = -0.0322x'
Solve for T ,  for x1  = 10,  20,	50 miles
           X



     Assume unheated  river  temperature = 74 F



     .-.  TQ =  74°F +  ATR =  74°F + 8.2°F = 82.2°F




     TX,  = (TO - E)e-°-0322x'  + E



     For  x'  =  10 miles



     T ,  = (82.2-73.8)e-(°-0322>(10)+73.8
      X



     Tx,  = (8.4)e'°-322 + 73.8




     T ,  = (8.4) (0.725) +  73.8 = 79.9°F
      x
     For x'  =20 miles




     Use same value of a and replace T  by T ,  for x'  =  10  miles:
                                      0     X



     T ,  = (79.9 - 73.8) (0.725)  + 73.8 =  78.2°F
      A




     fojlA'  = 3°» 40'  50 miles



     Following  the same procedure:




     30 miles, T ,  - (78.2  - 73.8) (0.725) + 73.8 - 77.0°F
                X



     40 miles, T ,  - 76.1°F
                A



     50 miles, T ,  = 75.5°F
                X

-------
98

     These values represent the exponential temperature decay

which is graphically shown on the following plot:
Q  70
              Plant
  10         20        30
Distance Downstream from Plant
            (miles)
50
     This graph presents an idealized picture of the downstream

temperatures, since the computations were based on average daily

conditions, and thus no diurnal effect is evident.  It also assumes

that the weather data on which K and E are based are indicative

of conditions along the 50-mile stretch of the river.  In addition,

no tributary inflows or heated discharges are accounted for in the

50 miles.

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                                                                99



     The diurnal effect may be evaluated by using the six-hour



average meteorologic conditions given previously.  Following the



methods described, values of K and E were computed as:
Time Period
(6 hr intervals)
Midnight to 6 am
6 am to Noon
Noon to 6 pm
6 pm to Midnight
K
(BTU ft"2 day"1)
56
196
241
76
E
(°F)
53.8
79.2
84.0
58.1
0
(°F)
71
72
78
76
     The values of water temperature (T ) just upstream from the



plant reflect natural diurnal fluctuations.



     Using the exponential temperature decay relationship presented



previously and assuming slug flow in the stream, i.e., no longitudi-



nal mixing, the variation in temperature was computed for a parcel



of water which left the plant location at 6 pm.  The following



graph demonstrates the effect of diurnal variations in meteorological



conditions on the temperature of the water parcel for a distance of



50 miles downstream.  Note that the initial temperature of the



parcel is equal to the natural stream temperature (T ) plus the



temperature increase of 8.2°F caused by the plant discharge.

-------
100
                 TEMPERATURE OF A WATER PARCEL
    85
 Q)

 3

 O
 v_
 Q)
 a


 I


 E
 o
 «
 +-
 to
80
    75
             I
I
I
             10         2O         30        40

                Miles Downstream from  Plant
                                                          50
                          Time (Military)
0
o
00

o
o
^j-
CM
O
O
(Q
O
O
O
CM

O
O
5j-
CVI
O
O
CM
"™ *
O
o
^-
CM
6 '
o
CM

O
O

CM

-------
                                                           101
Part B
     Assuming a maximum allowable daily average stream temperature

of 80°F, what flow-through cooling pond area would be required at

the site?  The following sketch  describes the plant-river-pond lay-

out:
Q! = 1500 cfs

I, = 74° F
  RIVER
                             Q3 = 1500 cfs

                             T3 = 93°F
          COOLING
            POND
Q0=3500cfs^)
T0=74°F    '
,02= 2000 cfs
1T2 = 74°F
/Q4= 1500 cfs
 T4=   ?
   ;= 3500 cfs

-------
102



     Temperature Rise Through Plant



     Heat to cooling water = 6.41  x 109 BTU/hr



     Condenser flow = 1500 cfs = 3.37 x 108 Ib/hr
     AT  = AT through condenser =                   - = 19.QoF

       C                          (3.37 x 10b lb/hr)(l  BTU/lb °F)




       . T  = 74°F + 19°F = 93F
     Temperature Drop Through Pond



          A flow-through cooling pond is  assumed to be well  mixed



     in each cross section, but as in a stream,  there is a longitu-



     dinal temperature decay.  Thus,  the  equation for predicting the



     temperature drop through the pond is equivalent to the  exponen-



     tial  temperature decay equation  used on we'll -mixed streams.



          Using the temperature subscripts given on the sketch, the



     temperature from the pond can be computed by:




     T4 =  (T3 - E)e'a' + E                              (27, p. 113)




      ,      ,     KA
     where a  = ~r~nr~

                pCPQ3


                                  3    -1
          Q3 = plant discharge (ft  day  )


                            2

           A = pond area (ft )



          Using an experimental evaporation coefficient (b)  of 12, K =



     118 and E = 76.9 F.  These values are used  in the subsequent



     cooling pond calculations.

-------
                                                           103
Case I - Pond area required for discharge from pond =  80°F.




     .'.  T  = 80°F
     Solving the prediction equation for a'



     80 = (93 - 76.9)e"a'  + 76.9
     e~a= (80 - 76.9) / (93 - 76.9)
     e"a= 0.193
     .-. a'  - 1.65



     Solving the a'  equation for A:
     a< = T6274T7lTTi500jT24 hr/dayj73600 sec/hrj
     a1 = (1.46 x 10~°)A - 1.65




     .'.A = (1.65)7(1.46 x 10~8)  - 11.3 x 107 ft2
     In  acres: A =
                    (4.36 x 1(T ftVacre)
Ca,se__n_ - Pond area required for mixed river temperature  =  80  F.



     If a mixing zone is allowed in the stream such  that  the



mixed river temperature below this zone is equal  to  or less



than 80°F, a much smaller pond could be used.

-------
104

     Referring to the sketch:
     Solving for T. :


     T    T5Q5 - T2Q2 = (80)  (3500) - (74) (2000)
      4       Q4                  1500


     . M  = 88.0°F
     By using the same computational  techniques as for Case I

     a1 = 0.373

     .'.  A = (0.373)/(1.46 x 10"8) =  2.55 x 107 ft2


     in acres:  A = ^55 x 10' ft*> - = 585 acres
                   (4.36 x 10^ ft /acre)    -

-------
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