EPA-600/2-76-050
March 1976
Environmental Protection Technology Series
                           ECONOMIC ASSESSMENT  OF
                 BACKFITTING  POWER  PLANTS WITH
                    CLOSED-CYCLE COOLING SYSTEMS

                                 Industrial Environmental Research Laboratory
                                      Office of Research and Development
                                      U.S. Environmental Protection Agency
                                Research Triangle Park, North Carolina 27711

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                RESEARCH REPORTING SERIES

 Research reports of the Office of Research and Development, U.S. Environmental
 Protection Agency, have been grouped into five series. These five broad
 categories were established to facilitate further development and application of
 environmental technology. Elimination of traditional grouping was consciously
 planned to foster technology transfer and a maximum interface in related fields.
 The five series are:
     1.    Environmental Health Effects Research
     2.    Environmental Protection Technology
     3.    Ecological Research
     4.    Environmental Monitoring
     5.    Socioeconomic Environmental Studies

 This report  has been assigned to the ENVIRONMENTAL PROTECTION
 TECHNOLOGY series. This series describes research performed to develop and
 demonstrate instrumentation, equipment, and methodology to repair or prevent
 environmental degradation from point and non-point sources of pollution. This
 work provides  the new or improved technology required for the control and
 treatment of pollution sources to meet environmental quality standards.
                     EPA REVIEW NOTICE

This report has been reviewed by the U.S. Environmental
Protection Agency,  and approved for publication.  Approval
does not signify that the contents necessarily reflect the
views  and policy of the Agency, nor does mention of trade
names or  commercial products constitute endorsement or
recommendation for use.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.

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                                 EPA-600/2-76-050
                                 March 1976
            ECONOMIC ASSESSMENT OF

           BACKFITTING POWER PLANTS

      WITH CLOSED-CYCLE COOLING SYSTEMS
                      by

A. R. G1aqu1nta, T.  E, Croley II,  V.  C.  Patel,
J. G. Melville, M.  S.  Cheng,  and A. S. Uzuner

              University of Iowa
     Iowa Institute of Hydraulic Research
            Iowa City, Iowa  52242
           Contract No,  68-03-0430
             ROAP No.  21AZU-019
          Program Element No.  1BB392
     EPA Project Officer:  James  P.  Chasse

 Industrial Environmental  Research  Laboratory
   Office of Energy, Minerals,  and  Industry
       Research Triangle Park,  NC  27711
                 Prepared for

     U.S. ENVIRONMENTAL PROTECTION AGENCY
      Office of Research and Development
            Washington, DC  20460

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                               CONTENTS
Section
	                                                          Page
   I  CONCLUSIONS                                                 1
  II  RECOMMENDATIONS                                             6
 III  INTRODUCTION                                                8
  IV  GENERAL CONSIDERATIONS AND ASSUMPTIONS                      12
      A.  Turbine characteristics                                 15
      B.  Geographical location and meteorological conditions     32
      C.  Economic considerations                                 39
      D.  Treatment of a variable loading pattern                 49
   V  MECHANICAL-DRAFT WET COOLING TOWERS                         51
      A.  Capital cost of towers (C  )  and auxiliary equipment    54
                                   cs
      B.  Reference length of cooling towers, L*                  67
      C.  Operation of a tower of given size (L, H)               71
      D.  Parametric studies                                      74
      E.  Operating costs with cooling towers                     85
      F.  Procedure for the economic evaluation of backfitting    104
      G.  The computer program                                    108
                                                  *
      H.  A hypothetical test case                                111
      J.  Example of a variable loading pattern                   116
  VI  NATURAL-DRAFT WET COOLING TOWERS                            120
      A.  Operation models for natural-draft, crossflow,
          wet cooling towers                                      124
      B.  Capital cost of towers and auxiliary equipment          128
                                 iii

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                         CONTENTS (continued)

Section                                                          Page
      C.  Reference size of cooling towers, S*                    133
      D.  Operation of a tower of given size (S,  H)                136
      E.  Parametric studies                                      136
      P.  Procedure for the economic evaluation of backfitting    143
      G.  The computer program                                    184
      H.  A hypothetical test case                                186
 VII  COOLING PONDS                                               192
      A.  Operation model for the fully-mixed pond                193
      B.  Capital costs of cooling ponds                       '   197
      C.  Reference area of cooling pond, A*                      199
      D.  Parametric studies                                      199
      E.  Procedure for the economic evaluation of backfitting    222
      F.  The computer program                                    223
      G.  A hypothetical test case                                224
VIII  SPRAY CANALS AND PONDS                                      229
      A.  Operation models of spray cooling                 ,      231
      B.  Capital costs of spray canals                           239
      C.  Reference size of spray canals, N*                      241
      D.  Parametric studies                                      242
      E.  Procedure for the economic evaluation of backfitting    265
      F.  The computer program                                    266
      G.  A hypothetical test case                                267
  IX  REFERENCES •                                                 273
   X  GLOSSARY OF SYMBOLS                                         278
  XI  APPENDICES                                                  284
                                  IV

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                                FIGURES
Number                     Title
  1     Typical turbine heat rate correction curves               16
  2     Typical turbine heat rejection rate characteristics       19
  3     Typical variation of plant efficiency with
           turbine back pressure                                  21
  4     Heat rate characteristics of turbine A                    27
  5     Heat rate characteristics of turbine B                    28
  6     Heat rate characteristics of turbine C                    29
  7     Variation of the fixed charge rate with remaining life
           of plant or unit                                       47
  8     Overall view of typical mechanical-draft tower            53
  9     Mechanical-draft crossflow tower                          53
  10    Typical rating factor charts for mechanical-draft
           crossflow towers                                       55
  11    Relation between tower units and physical
           dimensions of the tower                                58
  12    Range, approach and water flow rate as
           functions of tower size
        (a)  T ,_  = 60°F (15.56°C)                                60
              wb,
        (b)  T ,_  = 70°F (21.11°C)                                61
              wb,
        (c)  T    = 80°F (26.67°C)                                62
              wb,
                d
  13    Capital cost of pump and pipe system                      63
  14    Required surface area of new condensers                   64
  15    Construction for the definition of reference
           tower length, L*                                       69
                                  v.

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                          FIGURES  (continued)
Number                      Title                                Page
«"•"""•""•*•••H-ABM-----^^                      ^^VBMHB^W^^M_                                 , -?*	
  16    Reference length of towers                                70
  17    Variation of capacity loss with tower size and
           plant capacity                                         75
  18    Variation of energy loss with tower size and
           plant capacity                                         76
  19    Variation of excess"fuel consumption with tower
           size and plant capacity                                77
  20    Variation of evaporation with tower size and
           plant capacity                                         78
  21    Normalized capacity loss                    "              81
  22    Normalized energy loss                                    82
  23    Normalized excess fuel consumption                        83
  24    Normalized evaporation                                    84
  25    Normalized capacity loss
        (a)  Chicago                                              86
        (b)  Los Angeles                                          87
        (c)  Miami                                                88
        (d)  St. Louis                                            89
  26    Normalized energy loss
        (a)  Chicago                                              90
        (b)  Los Angeles                                          91
        (c)  Miami                                                92
        (d)  St. Louis                                            93
  27    Normalized excess fuel consumption
        (a)  Chicago                                              94
        (b)  Los Angeles                                          95
        (c)  Miami                                                96
        (d)  St. Louis                                            97
  28    Normalized evaporation
        (a)  Chicago                                              98
                                 VI

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Number
                          FIGURES (continued)
                            Title
        (b)  Los Angeles               -                           99
        (c)  Miami                                                100
        (d)  St. Louis                                            101
  29    Hyperbolic natural-draft crossflow, wet
           cooling tower                                          122
  30    Pile characteristics curve and air flow rate
           calculations                                           125
  31    Typical cost-performance curves for budget
           estimates for the natural-draft crossflow
           cooling tower (1970 dollars)                           129
  32    Capital cost estimates for the natural-draft
           crossflow, wet cooling tower                           131
  33    Determination of reference shell height                   135
  34    Normalized capacity loss                                  137
  35    Normalized energy loss                                    138
  36    Normalized excess fuel consumption                        139
  37    Normalized evaporation                                    140
  38    Variation of normalized capacity loss with shell
           height and plant capacity, 36% turbine efficiency      144
  39    Variation of normalized energy loss with shell
           height and plant capacity, 36% turbine efficiency      145
  40    Variation of normalized excess fuel consumption
           with shell height and plant capacity, 36% turbine
           efficiency                                             146
  41    Variation of normalized evaporation with shell height
           and plant capacity, 36% turbine efficiency             147
  42    Variation of normalized capacity loss with shell
           height and plant capacity, 28% turbine efficiency      148
  43    Variation of normalized energy loss with shell height
           and plant capacity, 28% turbine efficiency             149
                                 Vll

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                         FIGURES  (continued)
Number                     Title

  44    Variation of normalized excess fuel consumption
           with shell height and plant capacity, 28%
           turbine efficiency                                     150
  45    Variation of normalized evaporation with shell
           height and plant capacity, 28% turbine efficiency      151
  46    Normalized capacity loss, 36% turbine efficiency
         (a)  Chicago                                              152
         (b)  Los Angeles                                          153
         (c)  Miami                                                154
         (d)  St. Louis                                            155
  47    Normalized energy loss, 36% turbine efficiency
         (a)  Chicago                                              156
         (b)  Los Angeles                                          157
         (c)  Miami                                                158
         (d)  St. Louis                                            159
  48    Normalized excess fuel consumption, 36% turbine
           efficiency
         (a)  Chicago                                              160
         (b)  Los Angeles                                          161
         (c)  Miami                                                162
         (d)  St. Louis                                            163
  49    Normalized evaporation, 36% turbine efficiency
         (a)  Chicago                                              164
         (b)  Los Angeles                                          165
         (c)  Miami                                                166
         (d)  St. Louis                                            167
  50    Normalized capacity loss, 28% turbine efficiency
         (a)  Chicago                                              168
         (b)  Los Angeles                                          169
         (c)  Miami                                                170
                                  viii

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                         FIGURES  (continued)
Number                     Title                                 Page

        (d)  St. Louis                                            171
  51    Normalized energy loss, 28% turbine efficiency
        (a)  Chicago                                              172
        (b)  Los Angeles                                          173
        (c)  Miami                                                174
        (d)  St. Louis                                            175
  52    Normalized excess fuel consumption, 28% turbine
           efficiency
        (a)  Chicago                                              176
        (b)  Los Angeles                                          177
        (c)  Miami                                                178
        (d)  St. Louis                                            179
  53    Normalized evaporation, 28% turbine efficiency
        (a)  Chicago                                              180
        (b)  Los Angeles                                          181
        (c)  Miami                                                182
        (d)  St. Louis                                            183
  54    Reference area of cooling ponds                           200
  55    Normalized capacity loss                                  202
  56    Normalized energy loss                                    203
  57    Normalized excess fuel consumption                        204
  58    Normalized evaporation                                    205
  59    Normalized capacity loss
        (a)  Chicago                                              206
        (b)  Los Angeles                                          207
        (c)  Miami                                                208
        (d)  St. Louis                                            209
  60    Normalized energy loss
        (a)  Chicago                                              210
        (b)  Los Angeles                                          211
                                  IX

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                         FIGURES  (continued)
Number                     Title

         (c)  Miami                                                212
         (d)  St. Louis                                            213
  61    Normalized excess fuel consumption
         (a)  Chicago                                              214
         (b)  Los Angeles                                          215
         (c)  Miami                                                216
         (d)  St. Louis                                            217
  62    Normalized evaporation
         (a)  Chicago                                              218
         (b)  Los Angeles                                          219
         (c)  Miami                                                220
         (d)  St. Louis                                            221
  63    Reference size of spray canals                            243
  64    Normalized capacity loss                                  245
  65    Normalized energy loss                                    246
  66    Normalized excess fuel consumption                        247.
  67    Normalized evaporation                                    248
  68    Normalized capacity loss
         (a)  Chicago                                              249
         (b)  Los Angeles                                          250
         (c)  Miami                                                251
         (d)  St. Louis                                            252
  69    Normalized energy loss
         (a)  Chicago                                              253
        (b)  Los Angeles                                          254
        (c)  Miami                                                255
        (d)  St. Louis                                            256
  70    Normalized excess fuel consumption
        (a)  Chicago                                              257
        (b)  Los Angeles                                          258

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                         FIGURES  (continued)
Number                     Title

        (c)  Miami                                                259
        (d)  St. Louis                                            260
  71    Normalized evaporation
        (a)  Chicago                                              261
        (b)  Los Angeles                                          262
        (c)  Miami                                                263
        (d)  St. Louis                                            264

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                                TABLES

Table
  1   Reference conditions for turbines A, B and C
      for example calculations                                     31
  2   Annual summary of weather data at Miami                      34
  3   Frequency of occurrence of T , , T,_  at Miami                 37
                                  wb   db
  4   Temperatures equalled or exceeded less than 10 hrs/yr        38
  5   "Design" temperatures for cooling towers                     38
  6   Capital cost of replacement capacity and fuel
      (1980 estimates)                                             43
  7   Variable loading pattern for mechanical-draft wet
      cooling tower example                                        117
  8   Comparison of selected results from the mechanical-
      draft wet cooling tower examples for different
      loading patterns                                             118
                                  Xll

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                           ACKNOWLEDGEMENTS

This study was sponsored by the Environmental Protection Agency under
Contract No. 68-03-0430.  Special acknowledgement is due to Mr. James
P. Chasse, the EPA Project Officer, for making constructive suggestions
and for providing useful information and literature, not readily
accessible elsewhere, at several stages of the study.  Acknowledgement
is also due to the many individuals and companies who responded to
our plea for realistic design, performance and cost data for various
types of cooling systems.  In particular, we are grateful to the staff
of the Marley Company (Mission, Kansas), for their assistance with the
analysis of cooling towers, and to the Ashbrook Corporation (Houston,
Texas), Cherne Industrial, Inc. (Edina, Minnesota), and Richards of
Rockford, Inc. (Rockford, Illinois) for the information which they
supplied related to spray cooling.
                                  xiii

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                               SECTION I
                              CONCLUSIONS

The general methodology for the economic evaluation of backfitting
power plants with closed-cycle cooling systems has been presented.
The following major conclusions can be drawn from the study.

1.  The computer programs developed here can be used to assess the
    total differential cost of backfitting power plants with  any of
    the following closed-cycle systems:
         Mechanical-draft crossflow wet cooling towers,
         Natural-draft crossflow wet cooling towers,
         Cooling ponds, and
         Spray canals.
    The programs accept as input data turbine size and characteristics,
    size of cooling system, fluctuations in power demand,  variations
    in site meteorological conditions, and economic parameters.   The
    thermodynamic and performance models used to evaluate  the operating
    consequences such as capacity and energy losses, excess fuel
    consumption and water requirements are representative  of  those in
    current use.  The overall accuracy of the economic predictions
    therefore depends largely on accurate projection of the capital
    cost of the cooling system and on the unit costs associated
    with capacity replacement, make-up energy and fuel. While an
    effort has been made to incorporate the most recent estimates for
    capital costs of cooling systems, it is also recognized that these
    costs vary over a wide margin, particularly in the cases  of cool-
    ing ponds and spray canals, due to unforeseen problems associated

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    with construction at particular sites.

2.  The overall complexity of the backfit analysis is such tha
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    simple graphical form.

4.  The present study indicates that the total cost of backfitting,  in
    milLs/kW-hr of energy delivered, depends mainly on the capital
    cost of the cooling system, the capital cost associated with the
    replacement of lost capacity, the operating costs of peaking
    plants built to replace the energy losses, and the excess fuel
    consumption of the affected units due to higher back-pressure
    operation resulting from the backfit.  Under the assumption of
    full-throttle power demand, however, the excess fuel consumption
    is much smaller than.would actually result from a variable power
    demand, but there is a corresponding increase in the energy losses.
    Comparison between the detailed calculations using the computer
    programs with realistic power demand variations and those performed
    using the graphical results with full-throttle power suggest
    that the total costs calculated by the two methods may differ only
    by a few percent.  This small difference gives added confidence
    in the use of the results presented graphically.

5.  The  sensitivity of the total cost of backfitting to the
    factors listed above suggests that great care must be taken in
    estimating the following for each application:
         Capital cost of the cooling system/
         Unit cost of replacement capacity,
         Unit cost of replacement energy,
         Unit cost of fuel, and
         Fixed charge rate.

    As indicated earlier,  the first of these quantities can be
    found readily from the data presented in this report, but an on-
    going check must be maintained in order to ascertain the impact
    of inflation within the industry.  Needless to say, the most
    reliable and up-to-date information can best be obtained
    directly from the manufacturers and construction engineers.

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    A considerable amount of variation in these costs can be
    expected from site to site, but for cooling towers the estimates
    presented here appear to be reliable within about 15 percent for
    applications up to 1980.  The remaining factors listed above
    depend upon the particular utility situation.  However, if
    capacity and energy losses are to be made up by means of gas-
    turbine peaking units, the unit costs will be of the order of
    $100/kW for capacity replacement and 10 mills/kW-hr for energy
    replacement based upon 1975 estimates.

6.  In the hypothetical examples analyzed in detail in the text,
    where the power plant characteristics as well as the site meteor-
    logical conditions were approximately the same for all four
    closed-cycle cooling systems, the total excess unit costs of
    backfitting  (in mills/kW-hr) were found to be
         Mechanical-draft crossflow wet codling towers:   0.582
         Natural-draft crossflow wet cooling towers   :   0.916
         Cooling ponds                                :   0.666
         Spray canals                                 :   0.694
    These costs can not, of course, be compared on an absolute scale
    since the size of each cooling system was chosen arbitrarily, and
    no attempt was made to verify an "optimum" size.  Nevertheless,
    since each size is realistic and since the same values of the unit
    costs of replacement capacity, replacement energy, fuel, water, and
    fixed charge rate have been used, the total costs listed above
    give a good general indication for each type of cooling system.

7.  The computer programs as well as the graphical results of the
    present study can be used to make an independent assessment of
    the cost of backfitting a given power plant or unit at a known
    site with a range of sizes of the four different types of closed-
    cycle cooling systems.

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8.  Finally, the assessment of backfitting costs can best be made for
    any particular situation by using the computer models given in the
    appendices.  No interpolation error will be involved, and inclusion
    of the actual design power loading for the specific situation may
    be made  (instead of the assumed "full-throttle" design loading
    implicit in the figures of this report).  The programs are de-
    signed to accomodate a design loading composed of two power levels
    (one of which is the maximum) and can be easily extended to more.

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                              SECTION II
                            RECOMMENDATIONS

Four major recommendations are made on the basis of the present study:

1.  As far as possible, the computer programs presented in this report
    should be used to independently assess the economic consequences
    of backfitting power plants with closed-cycle cooling systems
    and to compare the estimated total costs with those evaluated by
    other methods.  Rapid estimates of backfitting costs can also
    be made by using the representative set of graphical results,
    which will, however, involve a certain amount of approximation.

2.  The utilization of the computer programs allows the economic
    analysis of backfitting to be based upon the actual design power
    loading instead of the full-throttle loading assumed in the
    graphical results.  Design power loadings with more than two,
    defined levels of power output can be analyzed with slight mod-
    ifications of the program.  The actual performance of the affected
    unit during open-cycle operation can also be modeled by incorpor-
    ating expected variations in the water-body temperature in the
    program.

3.  The validity of any economic analysis of cooling systems will
    depend upon the proper selection of Individual cost factors and
    constraints.  Among the more important site-specific considera-
    tions is  the requirement for land and its availability.  While
    the example problems for cooling towers in this report have land

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    requirements based on noise attenuation, other criteria such as
    construction area and plume recirculation may be more applicable.

4.  An on-going survey should be maintained to determine the prevailing
    and expected costs of cooling systems, unit costs of replacement
    capacity, replacement energy, fuel, and water, as well as the
    fixed charge rate, so that the general methodology developed for
    this study can be updated periodically.

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                              SECTION III

                             INTRODUCTION
                              I

Following the recent enactment of "environmental"  legislation  (The
Federal Water Pollution Control Act Amendments  of  1972), the Environ-
mental Protection Agency has been charged with  the task of developing
guidelines and standards of performance for steam  electric power
plants.  Originally, the EPA's proposed §304 guidelines and  §306
standards [1,2,3,4] suggested that, except for  the power plants re-
ceiving exemption under §316(a), all plants operating  with open-cycle
cooling systems should be backfitted with closed-cycle systems by the
year 1983.  However, these guidelines soon met  with much opposition,
and in ensuing adversary hearings, a set of revised guidelines were
constructed [5],  In accordance with these new  EPA guidelines, the
thermal discharges are to be limited according  to  the  following
schedule [6:§423.13 £(1)-(6),m]:
   A.   There shall be no discharge of heat from the main condensers
   except
       (1)  "Heat may be discharged in blowdown  from recirculated
       cooling water systems provided the temperature  at which the
       blowdown is discharged does not exceed at any time  the low-
       est temperature of recirculating cooling water  prior  to the
       addition of the make-up water.
       (2)  "Heat may be discharged in blowdown  from recirculated
       cooling water systems which have been designed  to discharge
       blowdown water at a temperature above the lowest temperature
       of recirculated cooling water prior to the addition of make-
       up water providing such recirculating cooling  systems have
       been placed in operation or are under construction  prior to
       the  effective date of this regulation (July 1,  1981).
       (3)  "Heat may be discharged where the owner or  operator of
       a  unit  otherwise subject to this limitation can demonstrate

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       that a cooling pond or cooling lake is used or is under
       construction as of the effective date of this regulation
       to cool recirculated cooling water before  it is recircu-
       lated.  to  the main condensers.
       (4) "Heat may be discharged where the owner or operator
       of a unit otherwise subject to this limitation can dem-
       onstrate that sufficient land for the construction and
       operation of mechanical draft evaporative  cooling towers
       is not available  (after consideration of alternate land
       use assignments) on the premises or on adjoining property
       under the ownership or control of the owner or operator as
       of March 4, 1974, and that no alternate recirculating
       cooling system is practicable.
       (5) "Heat may be discharged where the owner or operator of
       a unit otherwise  subject to this limitation can demonstrate
       that the total dissolved solids concentration in blowdown
       exceeds 30,000 mg/1 and land not owned or  controlled by the
       owner or operator as of March 4, 1974, is  located within
       150 meters  (500 feet) in the prevailing downwind direction
       of every practicable location for mechanical draft cooling
       towers and  that no alternate recirculating cooling system
       is practicable.
       (6) "Heat may be discharged where the owner or operator of
       a unit otherwise  subject to this limitation can demonstrate
       to the regional administrator or State, if the State has
       NPDES permit issuing authority, that the plume which must
       necessarily emit  from a cooling tower would cause a sub-
       stantial hazard to commercial aviation and that no alter-
       nate recirculated cooling water system is  practicable.  In
       making such demonstration to the regional  administrator or
       State the owner or operator of such unit must include a
       finding by  the Federal Aviation Administration that the
       visible plume emitted from a well-operated cooling tower
       would in fact cause a substantial hazard to commercial
       aviation in the vicinity of a major commercial airport.
       (m) "The limitation of paragraph (1) of this section shall
       become effective on July 1, 1981.

   B.  These new guidelines shall have both the exclusions implicit

   in the above paragraphs and the additional exclusions outlined here:

       units on line before January 1, 1970, are  excluded;
       units of 500MW or less on line before January 1, 1974,
          are excluded;
       units of less than 25MW are excluded; and
       units in a  system of 150MW or less are excluded.

The above guidelines are to be effective July 1,  1981, as indicated in

paragraph (m)  above; however, there are provisions of deferral of

compliance until July 1, 1983, if system reliability would be seriously

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affected.

The present study is concerned with the development of a detailed
methodology for the evaluation of the cost of backfitting a plant or
unit currently operating on open-cycle with a closed-cycle cooling
system.  Four different closed-cycle systems are considered:
      Mechanical-Draft Crossflow Wet Cooling Towers,
      Natural-Draft Crossflow Wet Cooling Towers,
      Cooling Ponds, and
      Spray Canals.
It is recognized that a large number of conflicting factors enter into
the estimation of the cost of backfitting.  Since many of these are
highly site-dependent, it is not possible to arrive at general con-
clusions applicable to all utility situations.  However, the purpose
here has been to develop a method which is flexible enough to take
these factors into consideration so that when they are prescribed or
determined the cost can be estimated.

The evaluation of the additional costs against the power generated is
important to the utility since it provides a basis for determining the
necessary rate increases.  Of major concern in the backfitting op-
eration is the fact that the capacity of the unit will be reduced by
the amount of power consumed within the closed-cycle system and by
penalties that may be incurred by requiring adjustments in the oper-
ating characteristics of the unit, the main factor being the increase
in the turbine exhaust pressure.  This lost capacity must be replaced
either by adding new capacity at the same site or elsewhere, or by
operating other units at higher levels.

The major factors to be considered in the economic assessment of back-
fitting an existing unit are:
      1.   The cost of installing the closed-cycle system, including
          materials, labor, site acquisition and preparation;
      2.   The plant downtime for hook-up and testing;
      3.   The provision of additional generating capacity to replace
          the lost capacity;
                                  10

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     4.  Operation and maintenance costs of the cooling system;
     5.  Operation and maintenance costs of replacement capacity;
         and
     6.  Additional cost of power generation due to decrease in
         plant efficiency or limitations occasioned by the use of the
         closed-cycle system.
It will be clear that the first three of these are capital costs in-
curred at the time of backfitting while the last three are costs re-
curring over the remaining period of plant life.  When these factors
have been determined and the cost of borrowing the required capital
expenditure are known, it is a simple matter to find the total cost,
in mills per kilowatt-hour, to be charged against the actual power
delivered after the backfit operation.  The work described herein is
concerned primarily with the evaluation of the various factors listed
above.  It is of course possible to design a closed-cycle cooling systeitv
regardless of whether it is a cooling tower, pond, or spray canal, which
is sufficiently large to reproduce, very nearly, the performance of the
once-through system being used at present.  Such a system will obviously
be expensive, at least from a first-cost point of view, and the various
factors enumerated above will undoubtedly intervene and dictate a some-
what smaller closed-cycle system, requiring less operating and mainten-
ance expenses.  If the cost of backfitting is to be assessed in a
realistic manner, it is then obvious that a range of sizes must be
considered.
                                   11

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                              SECTION IV
                                                             ;
                GENERAL CONSIDERATIONS AND ASSUMPTIONS

Perhaps the most important question that needs to be considered
immediately is:  What are the characteristics of the power  plant or
unit which should be known before a backfitting study can be under-
taken?  Most of these are obvious:  the nameplate capacity  of the
affected unit, in megawatts; the type of unit i.e.,  fossil  or nuclear;
the thermodynamic characteristics of the existing turbine and condenser
system; the variations in the stream or water-body temperatures  in
open-cycle operation; the power demand history; and the general  economic
situation of the particular utility operating the unit.  Since the in-
tent here is to develop a general approach, it is necessary to make
certain simplifications and assumptions concerning some of  these vari-
ables and, at the same time, incorporate some flexibility which  allows
adjustments to be made in order to consider particular units. The
following restrictions are therefore made throughout this work:
                          1 <•  *
     (1)   It is assumed that the power plant or unit operates at full
          throttle,  when possible, throughout the year, to  satisfy a
                         f
          constant demand for nameplate capacity, except during
          scheduled or unscheduled outages.  (Although this loading
                               i
          pattern is rarely realized in practice, it is used herein in
          lieu of consideration of all possible loading patterns,
          which is impractical.   Consequences of this assumed loading
          pattern are examined in qualitative terms throughout this
          report).
     (2)   With the existing open-cycle cooling system, the  plant or
          unit is considered to operate with an "equivalent" constant,

                                  12

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          relatively low, turbine back pressure and that the corres-
          ponding heat rejection rate is known.
      (3)  The existing condensers may be retained without modification
          or new condensers  (compatible with the new cooling system)
          may be installed, but their performance is similar to
          currently available equipment.
      (4)  The detailed thermodynamic characteristics of the affected
          turbine-generator units are known.
      (5)  The net power available for sale must be the nameplate capac-
          'ity both before and after backfitting; any losses will have
          to made-up in some manner.

The first assumption implies that a base-loaded unit is being considered
The actual fluctuations in the power demand, which vary widely from
utility to utility, are therefore neglected in the first instance.  It
would be difficult to correct results, obtained under the full-throttle
assumption, to represent output demand loadings of less than nameplate
capacity.  However, it is expected that relative comparison of cooling
systems  (both open-cycle and the various closed-cycle systems), when
made for the same loading pattern, are generally relevant.  Therefore,
the general results presented herein apply only for the full-throttle
loading pattern for constant demand of nameplate capacity.  Any other
loading pattern may be evaluated directly with the computer models and
an example of a variable loading pattern is presented in Section V. J.

The second assumption enables the establishment of  a reference base in
the cost estimation of closed-cycle cooling systems and their perfor-
mance in comparison with the existing open-cycle system.  In reality,
the power plant will operate under a variety of conditions depending
upon the daily as well as seasonal variations in the temperature of
the stream or water body, but here it is assumed that the original
open-cycle system is designed such that the turbine back pressure can
be maintained at the relatively low levels where the turbine heat rates
are nearly independent of back pressure.  This particular assumption  is
                                   13

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 not unduly restrictive.  Again, both the variability of actual closed-
 cycle system performance and  the  intent to give some generally applica-
 ble results require that this assumption be made.  To consider the
 effects of actual open-cycle  cooling system performance, it would be
 necessary to incorporate actual data for the particular unit under
 consideration into the analysis.  The differential costs presented here
 would have to be modified  accordingly to allow this inclusion.

 The third assumption reflects the practicality of the backfit situation
 since it may not be possible  to consider major modifications in the
 condenser system.   Herein  lies a  difficulty since closed-cycle cooling
 systems are usually designed  and  optimized in conjunction with the con-
 denser design.   Thus, some allowances must be made if the existing
 condensers are to be retained.  In order to ensure compatibility be-
 tween the new closed-cycle cooling system and the old condensers, it
 may therefore be necessary to impose certain restrictions on the design
 of the new equipment.  These  restrictions may take the form of con-
 straints on the allowable  temperature rise  (cooling range) across the
 condenser and the allowable water flow rates through the system.  The
 alternative of  designing new  condensers and salvaging the old ones may
 also be considered,  without the aforementioned constraints.

 The fourth assumption listed  above is, of course, essential if the
 thermodynamic and  economic consequences of backfitting an existing unit
 are to be evaluated  realistically.  The fifth assumption is made to
 conform with the first and with most practical situations.  It may
 simply not be possible to  deliver any capacity loss power, thus incurr-
 ing a  "loss cost."   The economic  loss incurred could then come from
 loss of revenue, cost of contract renegotiation and consequent penal-
 ties,  etc.   These losses are  difficult to determine from a general
point  of view.   However, the  cost of making up lost power from other
 sources or  of building auxiliary  capacity can be estimated.  Further-
more, making up  capacity losses are expected to be the course of action
most utilities will  be required to follow.  The capacity losses are
                                   14

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assumed to be made up from other sources or from building the required
capacity as just mentioned.  They could also be made up by increasing
the capacity of the baseload additions for the system.  In this case,
the additional revenue from operation at off peak periods would also
have to be taken into account.  Such possibilities are not explicitly
considered in the present study although the economics could be easily
adjusted to account for them.

Some of the essential elements of the basic methodology adopted
throughout this work are described in the remainder of this section.
Included here are all aspects of backfitting which are common to all
types of closed-cycle cooling systems.  The subsequent sections deal
with the  four different closed-cycle systems which constitute some of
the available alternatives for backfitting.

A.  TURBINE CHARACTERISTICS
Turbine performance is usually described in the form of a plot of the
                                      *  i
relative fractional change A L= ATU_/T   J, which is the change
                                  HR  HR          v
(AT  , increase or decrease) in the turbine heat rate over some fixed
   HR                ^
reference heat rate T  , versus the back pressure, p.  A typical set
                     HR
of turbine characteristics is shown in Figure 1 for a low back pressure
                                    /
loaded turbine.  This figure and some basic concepts will be used to
define a number of quantities which assume great importance, particu-
larly in backfit considerations.

First of all, the point labelled R corresponds to the, fixed reference
           *                                   *
heat rate T   and the reference back pressure p (AT   = 0) at full-
           HR                                      «R
throttle, or valve-wide-open (VWO) operation.  At this point (for VWO)
                                                 *
power output is equal to the NAMEPLATE CAPACITY P  of the turbine.  The
                                                      *
corresponding heat rejection rate {from the turbine) Q  may then be
obtained from the definition:
               Turbine   _ Heat Input (to the turbine)             .^
               Heat Rate ~        Power Output
                                   15

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             BACK  PRESSURE,p (cm Hg, abs)

         O       2        4       6       8       10
 o
 o
 o
 ex
   cc
  *x
 HI
v— -•
 <
  »
 Z
 O

 o
 UJ
 a:
 a:
 o
 o

 UJ


 a:

 l-

 LU
                    I          2          3

              BACK  PRESSURE,p (in. Hg, abs)
   Figure 1.  Typical turbine heat rate correction curves
                               16

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i.e.,
                            *    *
                    m*  _ CP  + Q
                                    t      (vwo)
                             P
or
                      *    *     *    *
                    cP  + Q  = T_ P ,    (VWO)                     (2)
                                 HR
       *
where P  = nameplate capacity, kW,
     T   = reference turbine heat rate, Btu/kW-hr or kJ/kW-hr,
       c = a conversion factor = 3.413 x  10  Btu/kW-hr =  3.601 x 10
           kJ/kW-hr,
       *
      Q  = reference heat rejection  rate, Btu/hr or kJ/hr.
Secondly, each line in Figure 1  represents a constant steam throttle
setting T  (%VWO) expressed as a  fraction  of the full-throttle condition,
         S
and therefore each line corresponds  to a  constant rate of heat input
to the turbine.  Since the rate  of turbine heat input is  the sum of the
power output and the heat rejection  rate, we have in general:
                                      *    *
               cP + Q = constant =  (cP  + Q )T                     (3)
                                              S
where P = power output, kW,
      Q = heat rejection rate, Btu/hr or  kJ/hr,
     T  = throttle setting  (T  = 1 corresponding to VWO).
      S                      S
Thus, from equations(1),  (2), and  (3) we  have:
               THR P = cP + Q =  (cP* + Q*)Tg = TRR P* Ts           (4)
Now T   can be calculated from the turbine characteristics in Figure  1
     HR
as:
                        THR = THR(1  + A)
Using this definition, equation  (4)  gives
                                 P   T
                               _ 	s                             ,f-\
                                 1 + A
and                                               *
                                               cP  T
                    *   *             *               s
                       P  T  - cP =  TTTT, P T   -
                    UHR '    s    "    XHR '   s   1 + A
                           *
                       = Q
A
                                     Q*   ! + A
                       (6)
                                  17

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 These equations,  together with Figure 1, show that as the back pressure
 rises above  the reference value p  the power output decreases and the
 heat rejection rate  increases.  Since there is usually a range of back
 pressures over which the excess heat rate is negligible or small, for
 simplicity it will be assumed that in open-cycle cooling the stream or
 water-body temperatures are such that the turbine back pressure is main-
 tained in this range.  In order to quantify the performance of the
 plant or unit to  be  backfitted and establish a reference point for the
 subsequent analyses  of closed-cycle cooling systems, it will be assumed
 that the value of Q  , hereafter referred to as the REFERENCE HEAT
                     *
 REJECTION RATE, and  P  , hereafter referred to as the NAMEPLATE POWER
                                      *      *
 OUTPUT,  are  known.   The knowledge of Q  and P  and the heat rate
 correction curves of the form shown in Figure 1 then enable the deter-
 mination of  the power output P and the heat rejection rate Q at any
 steam throttle setting  (rate of heat input to the turbine) and the
 back pressure via equations (5) and  (6).  In particular, equation  (6)
 can be used  to construct the detailed heat rejection characteristics
 in the form  shown in Figure 2.  Since the heat rejection rate is an
 important parameter  in the detailed analysis of the performance of
 closed-cycle cooling systems, the construction of such characteristics
 is an essential preliminary to the evaluation of the consequence of
 backfitting.

 It will  be noticed that the lines of constant throttle setting in
 Figures  1 and 2 terminate abruptly at some high value of the back
 pressure.  For turbines of conventional design this upper limit is
 usually  less  than 5  inches  (12.7 cm) Hg absolute.  This value, denoted
 by Pmax»  is assumed  to be the maximum allowable back pressure which,  if
 exceeded,  will result in some damage to the turbine or a catastrophic
 loss  in performance.  The upper horizontal line EDC in Figure 2 there-
 fore constitutes one of the boundaries of possible operation of the
 turbine.   The other boundary corresponds to the full-throttle line
A'ABC, although most turbines will tolerate a certain amount of over-
load.
                                   18

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0,2    0.4
        HEAT  REJECTION RATE.Q (10* KJ/hr)
      0.6    0.8     1.0     1.2    1.4      1.6
                                        1.8
2.0    2.2
 0.2
0.4
0.6     0.8     1.0      1.2     1.4     1.6  Q* 1.8
 HEAT REJECTION RATE,Q(I09 Btu/hr)
    2.0
 Figure 2.  Typical turbine heat rejection rate characteristics

-------
 The reference heat rejection  rate Q* defined above can, of course, be
 found from equation (2)  when  the nameplate capacity and the reference
 turbine heat rate are known.  Alternatively, it can be estimated from
 the overall plant heat rate in the following manner:  The rate of heat
 input to the boiler (i.e., the heat equivalent of the fuel consumption)
 Q  is given by
                 QT = cP  + Qlp + Q                                 (7)
 and the thermal efficiency n  of the plant  (or plant efficiency) is
 defined by

                           c
=    =                                         (8)
"    ~  HR
                      QT  ~  P
 where P   =  Q /P  =  c/n   = plant heat rate, Btu/kW-hr or kJ/kW-hr.
        HR.    T       p
       Q   =  in-plant  and stack losses.
 The in-plant losses are  usually accounted for by an in-plant or steam
 supply efficiency r\  defined by
                QIP - (i -  VQT                                   o)
 n   is usually 0.85  (0.15 Q  in-plant and stack losses) for fossil units
 and 0.95  (0.05 Q  in-plant  losses) for nuclear units.  From equations
 (7),  (8),  and (9),  we have:

                Q = cP j	1 I  = P (nPHR - c)                    (10)

 which shows  that  the  rate at which heat must be rejected  in the cooling
 system depends upon the  type  (fossil or nuclear) of unit, the power
 level  and  the plant heat rate.  The plant heat rate, of course, depends
 upon  a number of  factors, including the age, size and  the detailed de-
 sign  features of  the  various components as well as the turbine back
pressure.  Figure 3 shows the variation of n   (= c/P   ) with backprese-
                                            p       HR
ure for a  large (800  MW) turbine of contemporary design modified  to
operate up to high  back  pressures.  Such a curve cannot,  however,  be
used  in the backfit situation since the affected units will vary  widely
 in age and size,  and  will have generally higher heat rates.  The  basic
                                                               *
parameter  recommended earlier, namely the heat rejection  rate Q  ,  can
                                   20

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   18
    16
•5   l4
JQ
O
 O»
1U
1C
O
CO
(O
LU
o
<
m
    12
10
    8
ui
5  6
00
cc
          1    I	1	1	TT	1	1	1
          NEW  NUCLEAR

           AND  OLDER

            FOSSIL UNITS
                               NEW

                                FOSSIL

                                UNITS
                  _L
                  _L
_L
 24      26      28      30       32

              PLANT  EFFICIENCY, ^p (%)
                                               34
                                                         44
                                                         40
                               36  -2
                                   X>
                                   o
                                                         o>
                                                     32  x
                                                         28
                                                     24
                                                     20
                                                     16
                                                         12
                                                         8
                             36
                                   E
                                   o
                                                         UJ
                                                         tr
                                                         ui
                                                         cc
                                                         a.
                                                         03
                                                         
-------
 nevertheless be defined  as
                             (\
                       -j- -  11  = p  (n P*  - c)                   dD
                       n     /        J HR
                         P   /
 where n   = plant efficiency at back pressure p  ,
        *                                     *
       Pn_ = plant heat rate  at back pressure p .
  *     HR
 Q  can therefore be  found if the relevant quantities are known.  The
         *                                                          •
 use of Q  as a basic parameter characterizing the "size" of the cooling
 problem, however,  avoids the need to distinguish between different ages,
 sizes and types of units to  be considered in the detailed analysis of
 the performance of closed-cycle cooling systems.  These factors can
                                                       *
 readily be taken into account in the determination of Q  using either
 equation (2)  or (11).

 Returning to the turbine characteristics shown in Figure 2, a number of
 quantities of prime  importance in the backfit situation can now be
 defined.  It has already been mentioned that this particular turbine
 cannot be operated to generate more than the full-throttle power corre-
 sponding to the line ABC and that the back pressure cannot exceed the
 maximum value p   corresponding to the line EDC.  Thus, regardless of
 the cooling system used,  the turbine must operate within the area
 bounded by OA'CE.  Full-throttle operation with the open-cycle cooling
 system corresponds to the point A and to small deviations from it along
 ABC associated with  the  variations in the stream or water-body tempera-
 ture.   The corresponding heat rejection rates are nearly constant and
           *
 equal  to Q .
                                             i
 If  this  unit  is to be backfitted with a closed-cycle cooling system,  it
 is necessary  to recognize that the performance of all such systems
 (mechanical or natural-draft cooling towers, cooling ponds, or spray
canals) depends upon the physical size as well as the prevailing
 meteorological conditions..  The first observation that  can be  made,
 however,  is that  it  is posjsible to design a closed-cycle  system  that  is
 large  enough  to operate  at point A under a specified  set  of  fixed
                                   22

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meteorological conditions.  In this case, the turbine back pressure
remains the same as in open-cycle operation and consequently the tur-
bine delivers nameplate power with the same heat rejection rate Q .
The plant heat rate also remains the same.  Such a size of the closed-
cycle system represents a useful reference and is discussed in greater
detail later.  Now, if either the size of the cooling system is smaller,
or if the meteorological conditions become more adverse than the
specified set, the full-throttle operation point will shift upward
along the line ABC, to a point B, say.  Smaller sizes and/or more severe
meteorological conditions will lead to the operating point C which
corresponds to the maximum back pressure that can be tolerated.  If the
size of the cooling system is still smaller and full-throttle operation
is to be maintained, the operating point C' will fall along the extra-
polated portion of the full-throttle line ABC.  However, since this
implies a back pressure greater than p   , the turbine must be throttled
                                      max
back to operate at a point such as D where the back pressure is p
It is clear that the exact location of the operating point will depend,
among other things, on  (a) the size and type of the closed-cycle
cooling system considered,  (b) the detailed cooling properties of the
system, and  (c) the meteorological parameters which affect the cooling
system performance.  The above considerations, however, enable us to
identify a number of factors that have an important bearing on the
economics of backfitting.
     (1)  The net power available for sale is equal to the gross
          power generated P, minus any power P   that is consumed
                                              C S
          internally in order to operate the closed-cycle cooling
          system, e.g., the pump and fan power requirements in the
          case of mechanical-draft cooling towers.  The power output at
          any operating point (A,  B,-C,  or D)  is,  of course,  given
          by equation  (5) and depends upon the turbine back pressure
          and the throttle setting T .  In comparison with open-cycle
          operation where the power output is the nameplate capacity,
          there is now a CAPACITY LOSS, C  :
                                  23

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               CT  = P*  -  P  4-  P                                (12)
                L             cs
     The evaluation of  the  maximum  capacity  loss  is therefore
     important.
(2)   Since the capacity loss  occurs continuously,  its magnitude
     depending upon the meteorological  conditions, there  is an
     associated ENERGY  LOSS,  ET:
                ____________  ^
               E  =>  (P  -P+P   )At
                L   ^—'           cs
     where At is the duration of  any set  of meteorological  con-
     ditions and the summation is taken over  all  such sets  of
     conditions occurring during  the given period of  time,  e.g.,
     one year.  Again, it is useful  to remember that  this defini-
     tion and succeeding definitions are  made in  the  context of
     an assumed full-throttle loading and a constant  demand for
     the nameplate capacity.   For the general case of demanded
     power, P , capacity loss and  energy loss  would be defined
     respectively in terms of the gross turbine output,  P   as  :
C =
L
E =^
L ^
P - P + P
D cs
r\p - p + p )At
— < D cs
     where P = the maximum possible gross turbine output at full
     throttle or at the back pressure limitation if P  + P   >
                                                     D    cs —
     this max, and P = P  + P   if P  + P   < this max.  Since
                        \J    C S     U    C S
     the assumptions of constant  demand for nameplate capacity
            *
     (P  = P )  and the implied consequence of full-throttle load-
     ing (if possible) (P = max) are made,  then capacity loss and
     energy loss  are defined as in equations (12)  and (13).
(3)   The fuel consumption for full-throttle operation with the
     open-cycle cooling system can be deduced from the reference
                       *
     plant heat rate,  P  .  If the closed-cycle system and the
                       HR
     prevailing meteorological conditions are such that the turbine
                             24

-------
          always operates at  full-throttle  (i.e., along line ABC),
          then the  fuel consumption with the closed-cycle system will
          be the same as that with the open-cycle system  (since Q  is
          constant) .  However,  if the operation is required at less
          than full-throttle  (i.e., at points  such as D) due to the
          back pressure limitation, the fuel consumption will be
          smaller than with the open-cycle  system.  Following the
          usual terminology,  the difference between the fuel consump-
          tions with closed-  and open-cycle systems will be called the
          EXCESS FUEL CONSUMPTION, F_, although, as indicated above,
                                    £*
          it will be either zero or negative.  This peculiarity is
          easily seen to be the consequence of our basic assumption
          that the  plant or unit to be backfitted is operated contin-
          uously at full throttle.
                 ,, =  0  ,   for T  = 1
                 E              s
 1              *    * ,
—  [cP + Q - cP  - Q JAt ,  for T  < 1
                                                                  (14)
Positive  excess fuel consumption  (i.e., a fuel penalty) may result
from backfitting  if this assumption  is relaxed and a specified power
demand curve  is used.  Consider,  for example, the case where the power
demand is constant and lower than the nameplate capacity for part of
the year.  Then during that part  of  the year the demand can be met
even with a closed-cycle system by suitable adjustment of the throttle
setting,  but  the  increased back pressure  (compared to open-cycle cool-
ing) would imply  higher turbine and  plant heat rates than those assoc-
iated with open-cycle cooling, and therefore higher rates of fuel
consumption.  However, during this period the capacity loss and the
energy loss will  not be equal to  those given by equations  (12) and  (13).
These losses  can  indeed be taken  to  be zero since the power level can
be adjusted to equal the demand plus that consumed internally by the
cooling system  (P ) .
                  c s

From the  foregoing discussion it  will be evident that the capacity
loss, the energy  loss, and the excess fuel consumption, which are all
                                  25

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 of great  importance  in the economics of backfitting, depend upon the
 size and  type  of  the closed-cycle cooling system as well as the pre-
 vailing meteorological conditions.  In particular, to evaluate the
 maximum capacity  loss it  is necessary to specify the "most severe"
 meteorological conditions a priori.  The determination of the various
 factors mentioned above is considered in greater detail for each of
 the four  types of closed-cycle cooling systems in later sections.  The
 general discussion presented here, however, emphasizes the importance
 of the turbine characteristics in the overall economic analysis of
 backfitting.

 Any survey of  power  plants now operating with open-cycle cooling will
 indicate  that  a wide variety of turbines will be encountered in
 practice.  Some of these  are considerably older than others, and the
 nameplate capacities vary over a wide range.  In a study such as this,
 it is  obviously impossible to consider each particular situation in
 detail and some generalizations and simplifications must be made.  An
 effort must, however, be  made to make the results as widely applicable
 as possible and retain a  certain amount of flexibility in the method-
 ology  so  that  some of the peculiarities of particular units can be
 incorporated.   To this end, three basic types of turbines which are
 representative of those currently in use are considered in the example
 calculations.   The characteristics of these turbines and their name-
 plate  capacities  have been taken from a recent report prepared by
 Sargent and Lundy [Ref.   7 , Vol. l] and are shown in Figures 4, 5
 and 6.  Turbine A shown in Figure 4 is a high back-end loaded unit of
 contemporary design; turbine B shown in Figure 5 is a low back-end
 loaded  unit representing  some of the older plants, while turbine C
 shown  in Figure 6 is a low back-end loaded unit whose performance is
 only marginally poorer than that of a contemporary unit.  It is ex-
pected  that most  existing turbines can be classified in one of these
three categories.

As indicated earlier, for the detailed evaluation of the capacity and
                                   26

-------
4>
Q.
O
UJ
o:
oc
o
o

UJ
UJ
   20
    16
12
8
   -4
          BACK PRESSURE, p (cm  Hg, abs)

         2        4       6       8       10
             	1	
             "T
    T
                                      T
    Ts*0.65  VWO

   Ts*0.90 VWO

 T8-1.00  VWO

Ts=l.05 VWO
r
      )          I          2         3         4


               BACK  PRESSURE, p (in. Hg, abs)



      Figure 4.  Heat rate characteristics of turbine A
                                  27

-------
 0>
 Q.
O
UJ
oc.
oc
O
O
I-
<
OL

H
<
UJ
           BACK PRESSURE,p (cm  Hg, abs)

              2       4       6       8       10
                I          2          3

           BACK PRESSURE,p(in. Hg, abs)
4
       Figure 5.  Heat rate characteristics of turbine B
                            28

-------
   20
 c
 0>
 u
o
UJ
cc
DC
O
O

UJ
H
Ul
X
    16
3-  12
8
   -4
            BACK PRESSURE,p (cm Hg, abs)

              2468
              T
                 T
T
T
                                         10
                 1234

             BACK  PRESSURE , p (in. Hg, abs)


        Figure 6.  Heat rate characteristics of turbine C
                             29

-------
 energy losses and excess  fuel consumption resulting from backfitting,
 it is necessary to obtain the turbine characteristics in the form
 shown in Figure 2.  This  requires a knowledge of the reference heat
 rejection rate Q  defined earlier, which, in turn, depends upon the
 nameplate capacity,  the overall  thermal efficiency and on whether the
 unit is fossil or nuclear.  For  the purposes of the subsequent example
 calculations, however, it is assumed that the characteristic curves
 shown in Figures 4 through 6 can be applied to fossil as well as
                                              *
 nuclear units, and that the plant efficiency r\  in open-cycle operation
 is 0.302 (30.2%), representative of older fossil fueled units and
 newer nuclear units.  Then equation  (11) leads to the reference heat
 rejection rates given in  Table 1.  At first sight, it would appear
 that the detailed calculations must be performed for both fossil as
                                                        *
 well as nuclear units (using differing values of n  or n ) and repeated
 for a range of values of  the nameplate capacity.  The foregoing assump-
 tions imply,  however, that this  may not be necessary since the
 influence of  changing the type  (fossil or nuclear) of the unit is
                          *
 simply to change n  and n .  However, the calculation of capacity loss,
 energy loss,  and excess fuel consumption depends only upon knowing the
                                                      *
 turbine characteristics,  the nameplate capacity, and Q   (and not on
        *
 n  or n )  for the assumed full-loading pattern.  Thus, it is possible
  1     P                                               *
 to use the results obtained from a particular value of Q   (associated
 with a particular value of  the nameplate  capacity and type of unit)
 to predict the performance  of nuclear or fossil units  (different n  ,
                                   *                              P
 but with turbine heat rejection  = Q ) with different nameplate capac-
 ities.   This  is best achieved by presenting the results in a suitable
 nondimensional form.
From equation  (8) it will be noted that the thermal efficiency assumed
here  (0.302) leads to a reference  (open-cycle) plant heat rate P    of
                                                                HR.
about 11300 Btu/kW-hr  (11920 kJ/kW-hr) for both fossil and  nuclear
units.  While it is recognized that the historical data collected  by
the Federal Power Commission and analyzed in the EPA Development
Document [2, see Figures IV-10 to  IV-12 on pp. 76-78]  indicate a  wide
                                  30

-------
        Table 1.  REFERENCE CONDITIONS FOR TURBINES A, B AND C
                       FOR EXAMPLE CALCULATIONS
TURBINE
A
B
C
NAMEPLATE
CAPACITY
P*, MW
411
275
535
REFERENCE BACK
PRESSURE
p* , inch Hg abs
(cm Hg abs)
1.00
(2.54)
1.00
(2.54)
REFERENCE HEAT REJECTION
RATES @ n* = 0.302
Q*, 10^ Btu/hr
(10 kJ/hr)
Old Fossil
2.545
(2.686)
1.703
(1.797)
1.00 j 3.313
(2.54) ! (3.496)
New Nuclear
3.010
(3.176
2.014
(2.125)
3.918
(4.134)
variation of plant heat rates with the age and size of the units (and
                          *
thus a wide variation in n ), the above values are representative,
as already mentioned, of open-cycle operation of the older fossil units
and the relatively new nuclear units.  The detailed example results
will need correction when they are used to study the consequences of
backfitting units whose reference heat rates deviate substantially
from those used here.  In any case, as will be emphasized repeatedly
in this study, the general methodology adopted here, and particularly
the various computer programs which have been developed, can be used
in conjunction with any set of specified inputs i.e., type and size
of turbine, reference heat rejection rate and therefore the plant
heat rate.

Reference has already been made to the possibility of extending the
validity of the results from a relatively small number of specific
calculations to treat a much wider variety of cases by the use of
                                  31

-------
 suitable  dimensionless plots.  Therefore, it is useful to define the
 REFERENCE SIZE  OF A CLOSED-CYCLE COOLING SYSTEM:  L* = reference length
 of  mechanical-draft cooling tower, S  =reference shell height of nat-
 ural-draft cooling tower, A* = reference area of cooling pond, and N* =
 reference number of module groups along a spray canal.  Formally, the
 reference size  is defined as the size required to reject Q*, at some
 specified meteorological conditions while maintaining the turbine back
 pressure  at some selected value, p1.  It should be noted that because
 of  physical limitations, p' is not necessarily equal to p*, nor is it
 necessary to use the same value of p1 for all systems since the final
 economic  evaluations are independent of the reference sizes.  Thus, for
 example,  the capacity loss for a given turbine system using the mechan-
 ical-draft cooling tower can be plotted nondimensionally as  (C /P*,
                                                              LI
 kW/kW)  vs.  (L/L*), where L denotes the size (length of tower) of the
 closed-cycle system.  It will be seen later that such plots enable the
 presentation of the results in a compact manner.

 B.  GEOGRAPHICAL LOCATION AND METEOROLOGICAL CONDITIONS
 The various factors that influence the economics of backfitting depend
 to  a  large  extent on the size and the performance of the closed-cycle
 cooling system  being considered.  The day-to-day performance of a
 system  of given size, in turn, depends upon the expected variations in
 the meteorological conditions at the site.  Thus, for example, the
 frequencies  of  occurrence of various wet- and dry-bulb temperatures
must  be considered in the analysis of mechanical-draft evaporative
cooling towers, while the performance of cooling ponds is influenced
by  the variations in wet- and dry-bulb temperatures as well as wind
velocities and  cloud-cover.  It is, of course, not possible to make
a detailed evaluation of each site in a study such as the present one.
A few specific  sites have therefore been chosen as being representa-
tive of the  areas in which there is a large concentration of open-
cycle operations.  In particular, the performance of the three basic
types of turbines mentioned earlier will be investigated in detail in
conjunction with the meteorological data from four different sites,
                                  32

-------
namely Chicago, Los Angeles, Miami and St. Louis.  These four stations
also fall in the major climatological regions of continental U.S. [see,
for example, Ref. 7, Vol. II. Appendix to Section IV.A] and are there-
fore expected to give a reasonable representation of other sites in
their respective regions.
      •f

The types of meteorological data usually compiled by the U.S. Weather
Bureau [8]  are shown in Table 2.  Most of the required information can
be obtained from such records.  Thus, for example, it is possible to
obtain the  frequency of occurrence of given values of a particular
parameter or combinations of parameters by simple analysis.  The fre-
quencies of occurrence f(T,. , T   ) of various values of the dry- and
                          db   wb
wet-bulb temperatures at Miami are shown in Table 3.  Note that the sum
of all the  frequencies for all the combinations is equal to unity.
Similar frequency distributions can be generated for other combinations
of meteorological parameters.  It is also possible to calculate the
dry- and wet-bulb temperatures which are not exceeded more than a given
number of hours in a year.  The dry- and wet-bulb temperatures not
exceeded more than 10 hours per year at the four sites listed above are
given in Table 4.

In the design of closed-cycle cooling systems it is customary to quote
what are known as "design meteorological conditions."  Thus, for
example, in the case of mechanical-draft wet cooling towers, a "design
wet-bulb temperature" is generally specified and defined as the value
which is not exceeded by more than a certain percentage (usually
between 2% and 5%) of time during the warmest consecutive four months.
In the United States that period  is taken to be June through September.
Cooling tower manufacturers have  available a list of the design con-
ditions appropriate for various sites in the United States.  Table 5
shows the relevant values for the four sites to be considered here.
While the design parameters give  a good indication of the relative
sizes of cooling systems required for identical duty at different
locations, it will be evident from the considerations of the previous
                                  33

-------
                           Table 2.  ANNUAL SUMMARY OF WEATHER DATA AT MIAMI
                            (REPRODUCED FROM U. S. WEATHER BUREAU RECORDS [8])
                       TEMPERATURE AND WIND SPEED-RELATIVE HUMIDITY OCCURRENCES
WIND
REL.
HUMID.

TEMP
/"^"i r~"\
C°F)

997 95
947 90
897 85
8V 80
797 75
747 70
697 65
6V 60
597 55
547 50
497 45
4V 40
397 35
TOTAL
0-4 M.P.H.



o
on

V



+
+

1
+





1

dp
ON
•^f
1
O
on

2
2
5
5
4
4
2
1




?S

dP
ON
V.Q
i
o
in

4
33
26
24
28
28
11
6
4
2.
1-
+
168

dP
O^\
t^*
1
O
t«-


7
121
55
55
41
26
11
7
3
1
+
3?7

dP
ON
CO
1
O
CO


+
134
329
130
75
50
30
12
4
2
1
76^

dP
o
o
rH

O
ON



6
265
213
106
50
16
5
1
1
+
664
5-14 M.P.H.



o
on

V

1
1
2
3
4
3
2
2
1
+
+

19

dP
ON

1
O
on
1
16
31
46
58
59
36
19
12
7
3
1
+
P89

dP
ON

I
o
LTN
+
82
541
379
340
261
138
65
47
31
15
6
1
L906

dP
ON
. C—

O
C—


104
539
348
211
84
56
45
28
17
6
1
1439

dP
ON
CO
1
O
CO


1
239
465
297
109
83
52
28
17
4
+
L294

o
o
rH

O
ON



8
239
267
124
56
29
7
3
2
+
731
15-24 M.P.H.



o
on

V

+
+
+
+
1
2
1
1
+
+
+

6

dp
ON

1
O
on

3
10
16
26
26
10
9
5
2
1

+
107

dP
ON
MD
I
O
LTN
+
17
137
175
162
71
27
11
11
7
2
1

621

dP
ON
t—
1
O
t-


19
74
85
30
8
4
4
4
2
1

230

dP
a-
CO
i
o
CO


+
17
43
30
7
5
4
2
1
+
+
109

g
0


o
ON



1
LO
16
7
3
1
2
+
1
+
41
25 M.P.H.
AND OVER


tjp
o
on

V















dP
ON
^r
i
o
on

+
1
+
1
1

+





2

dP
ON
VO
1
O
LTN


1
4
4
1
+






10

dp
ON
t-
I
o
D—


+
2
2
+
+






4

dp
ON
CO
1
o
oo



1
1
1
+
+





.4

dP
O
H
1
0
ON




2
1
+
+
+
-1-



3
in
00

^^
|—

i

2
125
888
1795
2463
L708
810
277
147
71
26
4

8767
CO
                           Occurrences are for the average year  (10-year total divided by 10).
        Values  are rounded to the nearest whole, but not adjusted to make their sums exactly
        equal  to column or row totals. "+" indicates more than 0 but less than 0.5-

-------
Table 2 (continued).   ANNUAL SUMMARY OF WEATHER DATA AT MIAMI
  PERCENTAGE  FREQUENCIES OF WIND DIRECTION AND SPEED
Direc-
tion
N
NNE
NE
ENE
E
ESE
SE
SSE
S
SSW

SW
WSW
W
WNW
NW
NNW
CALM
TOTAL
HOURLY OBSERVATIONS OF WIND SPEED
(IN MILES PER HOUR)
0-3
1
1
1
1
1
1
l
+
+
+

1
+
+
+
1
1
4
14
4-7
4
3
2
2
2
3
3
2
1
1

2
1
1
1
1
2

30
8-12
3
2
2
3
4
5
4
3
2
1

1
1
1
1
1
2

34
13-18
1
1
1
3
2
3
2
2
1
1

+
1
+
+
+
1

20
19-24
+
+
+
+
+
+
+
+
+
+

+
+
+
+
+
+

2
25-31
+
+
+
+
+
+
+
+
+
+

+
+
+
+
+
+

+
32-38



+


+
+
+
+


+

+



+
39-46



+
+

+
+


j







+
47
OVER




+
+












+
TOTAL
9
6
6
9
9
11
10
7
5
3

4
3
2
2
3
6
4
100
AV
SPEED
7.8
7-3
8.7
10.4
9.6
9.8
9.7
10.8
10.0
9.4

7.9
9.0
8.4
8.2
7.8
8.3

8.8

-------
  Table 2  (continued) .  ANNUAL SUMMARY OF WEATHER DATA AT MIAMI
PERCENTAGE FREQUENCIES OF SKY COVER,  WIND,  AND RELATIVE HUMIDITY
HOUR
OF
DAY
00
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
AVG
CLOUDS
SCALE 0-10
0-
3
•55
55
58
57
56
53
43
39
37
32
25
23
22
22
23
25
26
29
32
36
43
49
52
54
39
4-
4
23
23
20
21
22
24
25
26
29
33
37
40
40
38
37
35
31
29
27
26
25
24
23
23
28
8-
10
23
23
22
22
22
23
31
35
34
35
37
37
38
40
40
40
43
42
41
38
32
27
25
23
32
WIND SPEED
(M.P.H.
0-
3
20
24
27
28
30
28
28
23
14
7
3
3
2
1
1
1
1
2
5
9
14
17
19
20
14
4-
12
70
67
64
63
62
65
65
67
67
64
60
55
52
50
50
51
56
65
75
78
76
73
72
70
64
13-
24
10
9
8
8
8
8
7
9
18
29
37
41
45
49
48
46
42
33
20
12
10
10
9
10
22
25-
g
OVER
+
+
+
+
+
+
+
+
+
+
+
1
1
1
1
1
1
+
+
+
+
+
+
+
+
RELATIVE HUMIDITY (%)
0-
29









+
+
1
1
1
1
1
1
1
+
+




+
30-
49
+
+
+
+
+
+
+
+
1
3
7
11
15
16
17
15
12
8
c
3
1
T
1
+
5
50-
69
10
8
7
6
6
6
6
7
20
44
60
66
64
62
61
59
58
54
43
31
22
17
14
12
31
70-
79
25
20
18
16
15
13
14
20
35
33
22
14
12
12
13
15
18
24
32
39
39
36
33
29
23
oO-
89
43
43
42
40
37
37
37
42
31
15
8
5
5
5
5
6
8
10
15
20
28
33
38
41
25
90-
100
22
28
33
38
42
45
44
32
13
5
3
3
2
3
3
3
4
4
6
8
10
12
15
18
16
                                  36

-------
                          Table 3.  FREQUENCY  OF OCCURRENCE OF T ,, T,,  AT MIAMI
                                                                wb   db
                                            Wet Bulb Temp,  Twb °F

20-30
([-6.7]-[-l.l])
30-40
([-1.1] -4. 4)
40-50
(4.4-10.0)
50-60
(10.0-15.6)
60-70
(15.6-21.1)
70-80
(21.1-26.7)
80-90
(26.7-32.2)
90-100
(32.2-37.8)
100-110
(37.8-43.3)
1-1
0 r-5
cn i
I T
0 rT
CM .
vO
\_x
0.0








/— s
vt
o •
•* -*
i J^
0 ^H
co •
iH
1
^*s

0.0003
0.0027






<->
o
o •
in O
iH
' 1
O -d-
•* •

O .
\D IT)
H
1 1
0 0
m •
0
f-t
v_x



0.0283
0.0570
0.0146
0.0002


^-N
H
O •
r^ iH
CM
' 1
O vO
vO •
m
iH
N^




0.0838
0.1945
0.0333
0.0001

/~\
i-^
o •
00 vO
CM
1 1
O rH
r>. .
H
CM
v^





0.2667
0.2632
0.0064

/~y
CM
o .
ON CM
en
1 i
o r-
CO •
vo
CM
vx






0.0092
0.0078

^N
O 00
0 •
iH r-.
m
O CM
en .
CM
CO
v-x








0.0
I
PQ
14

Q

-------
     Table 4.   TEMPERATURES EQUALLED OR EXCEEDED LESS  THAN 10  Hrs/Yr
Site
Chicago
Los Angeles
Miami
St. Louis
A
wb
82
73
83
83
(27.8)
(22.8)
(28.3)
(28.3)
T. . °F (°C)
db
96
93
97
103
(35.6)
(33.9)
(36.1)
(39.4)
           Table 5.   "DESIGN" TEMPERATURES FOR COOLING TOWERS
   SITE
              WET-BULB  TEMPERATURE, °F (°C)
                1%
        2.5%
5%
10%
                             DRY-BULB  TEMPERATURE, °F (°C)
1%
2.5%
5%
10%
 Chicago


 Los  Angeles


 Miami


 St.  Louis
 78     76     75      73
(25.6)  (24.4)  (23.9)  (22.8)

 71     69     68      67
(21.7)  (20.6)  (20.0)  (19.4)

 79     79     78      78
(26.1)  (26.1)  (25.6)  (25.6)

 79     78     77      75
(26.1)  (25.6)  (25.0)  (23.9)
             94     92     89     85
            (34.4)  (33.3) (31.7) (29.4)

             84     81     78     75
            (28.9)  (27.2) (25.6) (23.9)

             91     90     89     88
            (32.8)  (32.2) (31.7) (31.1)

             98     95     93     89
            (36.7)  (35.0) (33.9) (31.7)
 section that a realistic evaluation of the performance  of  the power
 plant or unit must consider  the detailed variations  in  the meteor-
 ological conditions from their design values  as  well as load variations
 (if considered).  This is particularly so in  a backfit  situation where
 quantities such as capacity  and energy losses and  excess fuel consump-
 tion are of prime importance and must be predicted accurately.


 In the example calculations  described here, the  MAXIMUM CAPACITY LOSS,
against which the capital cost of replacement is assessed, is evalu-
ated at the meteorological conditions which are  not  exceeded more than
                                   38

-------
10 hours during the year.

It is important to realize that other definitions have been and are
being used for determining the maximum capacity loss for use in sizing
the additional required capacity.  Most definitions involve a specif-
ication of the sort made here; i.e., maximum capacity loss is the
capacity loss at meteorological conditions which are not exceeded more
than some number of hours during the year.  Any other definition can
be easily incorporated into the computer models, but the example
calculations are based on the 10 hours per year figures of Table 4.
The total energy loss and the excess fuel consumption are calculated
by summation, with respect to time, of the capacity loss and the excess
rates of fuel consumption, respectively, over all possible combinations
of meteorological conditions.

C.  ECONOMIC CONSIDERATIONS
For the purposes of this section, the method outlined earlier is used
to determine the maximum capacity loss  (C  in kW), the annual energy
                                         L
loss (E  in kW-hr) and the excess fuel consumption (F  in kW-hr) for
       L                                             E
the situation in which a particular power plant or unit (of known name-
plate capacity at a specific site) is to be backfitted with a closed-
cycle cooling system of known type and size.  The problem to be con-
sidered is then the determination of the total extra cost, in mills per
kilowatt-hour, of backfitting.

The TOTAL DIFFERENTIAL CAPITAL COST, CC in dollars, to be charged
against the project will involve the following:

(a)  The differential capital cost of the closed-cycle cooling system
     minus salvage values, CC .  This cost, depends upon the type and
                             o
     size of the system, and it includes the cost of site acquisition
     and preparation, the purchase and installation of the cooling
  1   equipment and associated auxiliaries, as well as the start-up and
                                  39

-------
     testing costs.   For most closed-cycle  systems the capital costs
     can be estimated by recourse to  the  experience of the  industry
     concerned,  and  although a number of  site-dependent  factors need
     to be considered, reasonable estimates can be made  using standard
     procedures.  The methods used here for the different types of
     cooling systems will be described in detail  in subsequent sections.
     The differential capital costs of the  closed-cycle  cooling system
     can be estimated as follows.  The salvage worth of  the old con-
     denser (which equals the estimated sale price if sold  or the re-
     placement cost  if salvaged for new construction) is subtracted
     from the capital cost of the new condenser,  if a new condenser is
     indicated,  to calculate the differential condenser  cost.  The
     differential capital cost of the pumps and piping system is cal-
     culated either  by subtracting the estimated  sale price of the old
     system from that of the new, or  by estimating capital  cost of an
     additional  system to make-up additional pumping capacity.  The
     differential cost of the cooling system  (excluding  pumps, piping
     and condenser)  is estimated by subtracting the salvage worth of
     all old cooling system components, excluding pumps, piping and
     condenser,  (which again equals estimated sale price if sold or
     replacement cost if salvaged for new construction), from the cap-
     ital cost of the new system.  Land requirements are limited to
     consideration of only the additional land required  for the new
     system.  Any hook-up and testing costs (exclusive of lost revenue)
     which would be  incurred in the backfit are also differential
     capital costs to be considered.   Adding all  of these differential
     capital costs results in the determination of the differential
     capital cost of the closed-cycle cooling system, CC .
                                                        s

(b)   The differential cost associated with  the plant or  unit  shut down
     at the time of  the changeover from the open-cycle to the closed-
     cycle cooling system,  CCDT.   It  is obvious that this will depend
     upon the  affected capacity and the duration  of the  outage.  The
     time required for the changeover will  depend on the layout  and
                                 40

-------
     accessibility of the existing system.   The EPA Development
     Document [Ref. 2, p. 598 ]  estimates that the time required  for
     this purpose will vary from 2 to 5 months, depending upon the
     site conditions, with an average time  of 3 months.   This time
     generally depends upon the cooling system being used,  the unit
     being backfitted, and many site-specific factors.   However, this
     estimate appears reasonable, and since more definitive estimates
     could not be obtained during the course of this study,  it was
     decided to make downtime a variable parameter whose influence on
     the overall economics of backfitting could be examined. It is
     obviously beneficial to schedule the backfit operation such that
     the changeover coincides with periods  of low power demand and with
     the annual maintenance period (of the  order of one month) during
     which the plant is down in any case.  Perhaps the most logical way
     in which the downtime cost can be evaluated is to equate it to
     the cost of energy lost during the outage, i.e.,  the product of
     the downtime, the affected capacity, the overall capacity factor
                                 •
     during the outage and the unit differential cost of energy  loss,
     e' (the purchase price minus the usual generating cost).  This is
      Xf
     basically the procedure adopted here.   It should,  however,  be
     mentioned that the recent Sargent and  Lundy study [Ref. 7,  Vol. I,
     p. 11.28] incorporated an outage capital cost of $4.00 per  kilo-
     watt for fossil capacity and $7.00 per kilowatt for nuclear
     capacity (1970  dollars) for the installation of cooling towers oh
     a retrofit basis, although it was suggested that outage costs can
     easily range from $1-$21 per kilowatt  and cannot be assigned on
     an a priori basis.  The procedure suggested here would therefore
     appear to be more satisfactory.

(c)   The capital cost of installing additional generation capacity to
     replace the lost capacity, CC:.  Once  the maximum capacity  loss
                                  .K
     C  has been determined, the assessment of the capital cost  depends
      L
     largely on the choice of an appropriate unit cost in dollars per
     kilowatt.  It has generally been assumed that the lost capacity
                                  41

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      and  the  energy  loss resulting from backfitting will be replaced
      by installing gas-turbine peaking units.  In this connection,
      two  additional  factors need to be recognized.  First, the antic-
      ipated demand of gas turbines may exceed the available production
      capacity, resulting in an escalation of prices over present
      estimates.   Secondly, it is likely that many of the larger
      utilities might consider building additional fossil-fuel or nuclear
      power plants to replace their cummulative capacity losses occa-
      sioned by backfitting.  In this case, the increased revenue from
      operation at noncritical periods would also have to be taken into
                                                                  it
      account.  Thus, it is possible that the capital as well as op-
    ,  erating  costs of the replacement capacity will vary over a wide
      range.   Table 6, taken from Ref. 7 (Vol. I, p. 11-33)., shows the
      cost estimates  for various types of replacement methods in 1980
      dollars.  In the present study, the unit costs associated with
      the  replacement capacity are treated as basic variables since they
                                 •
      can  exert a  significant influence on the economics of backfitting,
      and  it is suggested that their inclusion in the final economic
      analysis be  based on the particular circumstances of the affected
      utility.  Since the amount of capacity loss, in megawatts, can
      be calculated by the procedure described earlier, it is a simple
      matter to study the influence of varying the unit costs of re-
      placement capacity.  As previously mentioned, if capacity losses
      are  to be made  up using increases of the base load additions
      for  the  system  then the economic procedure outlined in this report
      does not strictly apply because of the necessity of including the
      increased revenue that would accrue at off-peak conditions.
      Therefore, for  this situation, it is advised that the cost of the
      new  cooling  system be calculated including these increased
      revenues and the differential costs be evaluated in a more
      appropriate way.

The TOTAL DIFFERENTIAL CAPITAL COST can therefore be written in the
following form:
                                  42

-------
Table 6.  CAPITAL COST OF REPLACEMENT CAPACITY AND FUEL  (1980 estimates)
                         [Ref. 7, Vol. I, p. 11-33]
TYPE OF
REPLACEMENT POWER
Coal
Oil
Nuclear
Gas or Combustion
Turbines
UNIT CAPITAL COST OF
REPLACEMENT POWER
$ per kW
376
292
457
154
UNIT COST
$ per 10
A*
0.73
1.56
0.30
2.90
OF FUEL
6 Btu
B*
1.04
1.91
0.30
2.06
 *The two sets of values correspond to different assumptions concerning
  the price of oil  (depending on the market conditions) and the price
  of coal (reflecting possible effect on environmental regulations).
  These may therefore be regarded as the upper and lower limits.
cc = cc.
CC
  DT
                                        CC
                                          R'
(15)
 The DIFFERENTIAL OPERATING COSTS, OC in dollars per year, to be
 assessed against backfitting, consist of the following:

 (a)  The operating and maintenance costs of the replacement capacity,
      OC .  As explained earlier, it is assumed that a peaking unit
        R
      needs to be installed such that its peak power is equal to the
      maximum capacity loss (C_) , and the energy supplied by it is
                              ii
      equal to the energy loss  (E ), sustained by the basic unit as a
                                 L
      result of backfitting.   (Again the definitions of capacity loss
      and energy loss are relevant only for the assumptions of constant
      power demand for nameplate capacity and the implied consequence
      of full-throttle loading).  More generally, installed replacement
      capacity would be required to have its peak power equal to the
      maximum (10 hour exceedance, say) value of
                                    43

-------
                           c  =  p   _  p  + P
                            L   D        cs
     and supply energy equal  to
                       E  -    (P^  -  P  +  P   ) At
                        L   Z_>   D        cs'
     Both of these expressions  are  zero (i.e., P = PD + PCS)  if PD +
     P   is smaller than the possible full-throttle output, P.  Since
      cs   *
     P  = P  and P = the maximum possible gross turbine output at full
     throttle or at the back pressure limitation, equations  (12) and
     (13) are used.
     It is important to note that  the capacity and energy losses can
     be made up in other manners,  besides  supplying a peak unit, as
     mentioned earlier.  In the case of  increasing the base  load
     additions to the system,  the  operating and maintenance  cost of the
     "increased system capacity" will be included in the operation
     and maintenance cost of the new system and must be considered.
     Such evaluations are not attempted  in the present study.

     While the annual operation and maintenance of such a peaking plant
     will depend upon a number of  complex  factors, it is certain that
     the cost of energy produced by it will be substantially greater
     than that produced by the basic, base-loaded unit.  It  is  usually
     assumed that these costs can  be taken into account by assigning
     a single unit cost of replacement energy produced.  For the case
     of gas-turbine peaking units, a value of 10 mills per kilowatt-
     hour appears to be a reasonable figure.  In the present study,
     however, this unit cost is again left as a variable parameter
     since it has a significant influence  on  the final economic
     assessment of backfitting.

(b)   The cost of excess fuel consumption,  OC__.  It has already been
                                           EF
     mentioned that the rate of fuel consumption with a closed-cycle
     cooling system will be different from that with the open-cycle
     system.   The annual cost  associated with the difference is
     easily  found by multiplying the excess fuel consumption, F,. (in
                                                               Ei
                                  44

-------
     kW-hr thermal or  Btu)  by the unit  cost of fuel  (in  $ per kW-hr
     or  § per  Btu).  Table  6,  taken  from Ref. 7  (Vol. I, p. II-33) ,
     includes  the unit costs  expected to prevail  in  1980 for various
     types of  fuel.  These  cost  estimates are included here simply
     as  a guide.  Better  estimates can,  of course, be obtained from
     the affected utility for any particular unit.

 (c)  The differential  cost  of operation and maintenance of the new
     closed-cycle cooling system over the existing open-cycle cooling
     system, OC  .  This will  obviously  depend on  the type of closed-
               o
     cycle system that is considered.   Taking the specific example of
     mechanical-draft  wet cooling towers, the operating costs will
     include the cost  of  make-up water  (evaporation, drift and blow-
     down) , the cost of blowdown treatment, and the  maintenance of the
     tower structures  and related equipment such  as  fans, pumps and
     controls.  The differential operating and maintenance costs will
     then be these costs  minus those associated with the present
     system.   It will  be  clear,  however, that the cost of the power
     consumed  by the fans and pumps  need not be considered since that
     has already been  taken into account in the evaluation of the
     costs of  capacity and  energy replacement.  The  assessment of the
     operating and maintenance costs of the different closed-cycle
     cooling systems will be  considered in greater detail in later
     sections.

From the foregoing, the TOTAL DIFFERENTIAL OPERATING COST to be
assessed against backfitting  can be  written as follows:
               OC = OC + OC__ + OC_,    $ per year               (16)
                       R    EF    b
Once the differential  capital cost CC  (in dollars) and the differential
operating cost OC (in  dollars per year)  have been determined for a
specific power plant or unit,  the problem reduces to that of assessing
the total differential cost,  in  mills per kilowatt-hour, to be charged
against  the NET energy delivered.  The  manner in  which the capital and
                                   45

-------
 operating costs are combined to obtain the total cost depends pri-
 marily upon the general economic situation of the utility and the age
 of  the affected unit.  Adopting the levelized annual cost method of
 accounting, the total differential cost, in dollars per year, can be
 written
                 TC = OC + CC x FCR,       $ per year             (17)
 where FCR is  the "fixed charge rate" which reflects the annual cost of
 raising  the required capital and includes such factors as interest on
 debt, required return on the stockholders' equity, depreciation of the
 equipment, and salvage value  (useful life of the plant or unit) , prop-
 erty taxes, property and income tax rates, etc.  Although these factors
 vary from utility to utility, the value of the fixed charge rate to be
 used in  the backfit analysis is determined mainly by the remaining
 life of  the plant or unit to be backfitted.  The rates recommended
 and utilized  in the EPA Development Document [Ref . 2, p. 597] and in
 the Sargent and Lundy study [Ref. 7, Vol. I, p. 11-32] ace compared
 in  Figure 7.  The two separable projections made in Ref. 7 reflect the
 influence of  making different assumptions concerning the rates of
 return on the capital investiment.  For the purposes of the present
 work, it is recognized from equation  (17) that the precise value that
 is  chosen for the fixed charge rate will greatly influence the total
 cost assessed against backfitting, and consequently it is retained as
 a basic  variable that needs to be ascertained with some care by a
 detailed examination of the financial structure of the utility conr
 cerned.

 The  total cost, in dollars per year, obtained from equation  (17) can
 now  be prorated over the rated net energy output of the affected unit
 or over  the actual net energy output of the affected unit.  The rated
 net  energy output for one year is simply
Likewise, the actual net energy generated by the affected unit  for  one
                                 46

-------
or
o
u.
   0.40
    0.35
   0.30
    0.25
   0.20
x
o

o   0.15
UJ
X
    0.10
    0.05
\\
                                   -O	REF.  7
                           -0-.	"
                         10       15      20      25

                        REMAINING  LIFE, (years)
                                             30
       Figure 7.  Variation of the fixed charge rate with remaining

                 life of plant or unit [2/7]
                                  47

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year  is given by

             EA = 8760£[PD x f (Twb, T^, PD) ] -
                        (P-Pcs) x f(Twb, Tdb, P-Pcs)]             (19)
                        «
where the frequency, f , depends upon both meteorological conditions
and power, accounting for fluctuations in output (or demand, as the
case may be) as well as scheduled or unscheduled outages for repairs
and maintenance.

There is some question as to what basis to use in prorating the total
cost:  actual or rated net energy output.  The answer depends upon
the purpose for which prorated costs are calculated .  For purposes of
comparing total costs of a cooling system for different nameplate
capacity power plants, the rated net energy basis would prove more
useful, allowing cost comparisons which do not penalize twice for
energy losses.  For purposes of estimating costs of power to consumers,
                                            I
the actual net energy output basis would be more useful, allowing
a more realistic expression of real costs.

It will be recalled from the introduction to this section that in order
to maintain a certain amount of generality the analysis has been
restricted to the idealized situation in which the power plant or unit
delivers maximum power possible throughout the year, for which P  = P*
and £ f (Twb/ Tdfa, P*) equals unity.  The rated net energy output for
one year then becomes ER = 8760 P* and the actual net energy output
for one year, EA = 8760 P* - E .  The prorations are arbitrarily made
                              L
in terms of the rated net energy output in the various examples which
follow.  Conversion to the basis of actual net energy output can be
easily accomplished using the above two equations.  The UNIT EXCESS
COST OF ENERGY PRODUCTION resulting from backfitting, tc, is then
                                  48

-------
     .	OC + CC x FCR
     cc   8760 VfP  x f (T	T	P~TT  (for any Ioadin9 pattern)
               ^L D      wb'  db'  D;J
                                                                  (20)
or
     .   _ OC + CC x FCR
     cc	8760 P*	                   ^or idealized full-throttle
                                          loading pattern)
The various relations proposed in this  section on economic analysis
are summarized in Appendix I.  A discussion of the treatment of var-
iable loading conditions follows in part D of this section, and a
numerical example is presented in Section V.J.

D.  TREATMENT OF A VARIABLE LOADING PATTERN
Although it has been assumed in the present study that the power plant
or unit operates at full throttle throughout the year and satisfies
a constant demand for nameplate capacity, a discussion of variable
loading patterns is included for completeness.  It should also be
mentioned that the computer programs used in the analysis of the
closed-cycle cooling systems are written in general terms and can
accept any variation in power demand and meteorological conditions;
i.e., input data for the programs include the relative frequency of
occurrence of various meteorological conditions and corresponding
power demands.  It is, therefore, quite straightforward to analyze
variable loading patterns by the programs given in the present study.

For the case of a variable loading pattern, the rated net energy
generated in a year is given by equation  (18) , and the unit excess
cost of energy production resulting from backfitting may be calculated
by the first of equations  (20) .  For use in that equation, the differ-
ential operating cost, OC, is calculated in the computer program with
the proper accounting for the variable  operating schedule.  However,
if the graphical results are used, it must be remembered that the
value of OC will correspond to the idealized full-throttle case and
will be over-estimated for the variable loading application.
                                  49

-------
 Another  term commonly employed in the power industry called capacity
 factor,  CF, should now be mentioned.  Use of the capacity factor
 offers a simplified empirical method to account for fluctuations in
 power demand as well as scheduled or unscheduled power outages.
 However,  in the present study, it is not necessary to apply CF in the
 computation of annual energy output because of the use of the general
 expression in equations  (18),  (19), and  (20).

 The major factors that influence the economics of backfitting a power
 plant with a closed-cycle cooling system have been identified in this
 section.  It should be emphasized that the general method of approach
 described here is common to all types of closed-cycle systems.  In
 order to  evaluate the total cost of backfitting any particular type
 and size  of cooling system to a plant or unit with given characteris-
 tics, however, it is obvious that it is necessary to perform the
 detailed  calculations described in parts A and B in conjunction with a
 knowledge of the thermodynamic characteristics of the cooling system.
 These computations form the subject matter of the next four sections.
 In each case, the application of the general methodology is illustrated
                                             \
 by a hypothetical example.

 An important aspect of the work described here is the development of
 major computer programs which are flexible enough to allow the analysis
 of the economics of backfitting given any set of site and utility
 dependent inputs.  It goes without saying that the proper identifica-
 tion of these inputs is a significant part of the problem and the re-
 sults are no better or worse than the inputs themselves.  Although
 results have been obtained using the best available information, and
presented in graphical form wherever possible, it is important to note
 that for  any particular situation it is preferable to use the computer
programs.  The example results nevertheless give a quick estimate of
the cost of backfitting.
                                  50

-------
                                SECTION V

                  MECHANICAL-DRAFT WET COOLING TOWERS

It  is well known  that  the amount of  cooling performed by a wet  (or
evaporative)  cooling tower depends primarily upon the ambient wet-bulb
temperature,  the  temperature of the  hot water entering the tower, and
the size and  thermodynamic characteristics of the "wet pile" inside
the tower.  Although the basic  theory of evaporative cooling has been
presented in  considerable detail in  the literature, the actual perfor-
mance of towers designed and built by various manufacturers will differ
due to the differences in the internal construction of the wet piles
and in the air and water  loadings recommended.  Much of the empirical
information on the heat transfer properties of particular designs and
the criteria  used to determine  the air and water loadings, which are
required to complete the theoretical models, are, however, regarded as
proprietary by the manufacturers for obvious reasons.  In what follows,
an  attempt has been made to develop  a methodology that is capable of
accepting any set of design parameters so that the performance of
towers of different designs can be analyzed.  Detailed example results
are then presented for a particular  set of input parameters which were
obtained through  the cooperation of  a leading manufacturer of cross-
flow cooling  towers.   These results  therefore apply to CROSSFLOW,
MECHANICAL-DRAFT  WET TOWERS.  It is  hoped, however, that the different
designs of such equipment are not so radically different so as to
limit the applicability of the  results to the product of a single
manufacturer.
                                   51

-------
 For the purposes of backfitting a power plant or unit with crossflow
 mechanical-draft cooling towers, it is first necessary to ask the
 question:   how large a tower is being built?  Although the answer to
 this is not simple, it is obvious that owing to the peculiarities of
 the backfit situation, the actual size will be different from that
 which will  be  recommended for a new plant or unit of identical design.
 Throughout  this section, therefore, the physical size of the tower is
 regarded as a  primary variable so that the various quantities of inter-
 est, such as the capital costs, maintenance costs, capacity and energy
 losses,  and excess fuel consumption, can be calculated for a range of
 sizes.   These  quantities can then be used, in conjunction with the
 economic considerations outlined in the previous section, to identify
 the project costs.

 A typical mechanical-draft, crossflow, evaporative cooling tower is
 shown in Figures 8 and 9.  From Figure 8 it will be seen that the
 overall  tower  structure consists of a number of distinct "cells", each
 with its own fan.  The physical size of a tower is specified if the
 number of cells and the dimensions of the fill in each cell are known.
 Alternatively,  the size can be specified by the height H, the width W
 and the  total  length L of the fill, the length of each cell being L/N,
 where N  is  the  number of cells.  The quantities H, W and L will be
 used as  the primary indicators of the size of the cooling tower.  It
 will be  clear  that H is the length of the water path and is also a
 measure  of  the  pumping height required.  W is a measure of the length
 of  the air  path and therefore will influence the size and the horse-
 power of the fans required to maintain the desired air flow rates.
 Finally, L  determines the number of fans, the length of the piping
 required, the total water flow rate and therefore the total pumping
power needed to circulate the cooling water.  When the dimensions of
the  fill, the air and water flow rates, the empirical heat-exchange
characteristics of the fill, and the temperature of the hot water at
the  tower inlet are specified, the basic theory of Merkel [9,10,11,12,
13,14,15] can be used to calculate the temperature of the cold water
                                  52

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 Figure 8.  Overall view of typical mechanical-draft tower
                         AIR
                       OUTLET
            WATER
             INLET
                                     FAN
                                    WATER
                                     INLET
WATER OUTLET c
                                    I'/  INLET
                                COLLECTING  BASIN
      Figure 9.  Mechanical-draft crossflow tower


                             53

-------
 at the tower  outlet, the temperature and humidity of the exit air,
 and the rate  of  heat rejection from the water to the air.  The manner
 in which such calculations are used to determine the overall perform-
 ance of a power  plant or unit fitted with cooling towers will be
 discussed in  the subsequent  sections.  For the present, however, it
 may be noted  that the basic  calculation scheme is described in detail
 by Croley, Patel and Cheng [15], and that reference will be made to
 that work from time to time.

 A.   CAPITAL COST OF TOWERS (C  ) AND AUXILIARY EQUIPMENT
                             cs  -
 From the preliminary considerations outlined above it would appear that
 the capital cost of a mechanical-draft cooling tower will be deter-
 mined primarily  by its size  since the fill dimensions H, W and L fix
 not only the  cost of the tower structure itself but also the cost of
 site acquisition and preparation, water basin, and auxiliary equipment
 such as fans, motors, pumps, controls and pipes.  While this is so,
 manufacturers of such cooling towers recommend sizing and pricing
 procedures which bear no direct relation to the physical size of the
 tower.   Instead,  the cost of the tower is linked to the "design"
 meteorological conditions  (here, the design wet-bulb temperature) and
 parameters describing the overall performance of the tower at these
 design conditions, notably the RANGE and APPROACH.  The rating-factor
 tower-unit method [16] and the K-factor method [17] are examples of
 such procedures.   In the former method, which is the most well pub-
 licized,  the manufacturers present charts, such as those shown in
 Figure  10,  from which a rating factor can be found for any given range,
 approach  and wet-bulb temperature.  The rating factor may be inter-
 preted  as  the relative degree of difficulty of heat rejection.  The
product of  the rating factor and the water flow rate  (GPM, gallons
per minute) then  gives the "required tower units," i.e.,
                  TU = RF x GPM                                    (21)
The capital cost of the tower, C  , can be found simply by multiplying
                                C S
                                  54

-------
74  WET BULB
 40
                     UJ
                     CD
                     Z
                     <20
                         10
                                    ,fc*
           /
                                                                    76 WET  BULB

                                                                     40
                                                                     30
                                            UJ
                                            o
                                              20
   0.5 0.6 0.7 0.8 0.9 1.0  I.I  1.2  1.3  1.4  1.5  1.6

               RATING  FACTOR
                                                                     10
                                                     //
                      y
                                                                         £/\
                                                                      0.5  0.6 0.7 0.8  0.9  1.0  I.I  1.2  1.3  1.4 1.5  1.6

                                                                                  RATING FACTOR
Ul
ui
78  WET BULB
 40
                      UJ
                      0
                      Z
                      < 20
  10
     *v/  /
     //,
                                     '4
                  X
                                        x
                            f/
                                             80  WET  BULB
                                              40
0^30

UJ
O

< 20

                                                  $/a
                                                        O /
   0.5  0.6 0.7 0.8  0.9 1.0  I.I  1.2 1.3  1.4  1.5 1.6

               RATING  FACTOR
                                                                     NO/
                                                                      10
                                                                      0.5  0.6 0.7 0.8  0.9  1.0  I.I  1.2 1.3  1.4  1.5 1.6

                                                                                  RATING FACTOR
                                 Figure  10.  Typical rating factor charts for mechanical-
                                              draft crossflow towers [Ref.  16]

-------
 the tower  units  by a unit cost c  in $/TU, i.e.,
                 C   = TU x c                                      (22)
                 cs         t

 From an analysis of previous experience, Dickey and Gates  [16] have
 found that the installed cost per tower unit is of the order of $7.50
 with a scatter of ± 12 percent for 1976 erection.  This figure includes
 the structure, fans and motors, concrete basin with sump,  the construc-
 tion costs,  and  the necessary electrical components and controls.  It
 is assumed that  this cost also includes the cost of hook-up and testing;
 The scatter of 12 percent in the unit cost was observed for the best
 85 percent of data obtained from 22 generating units and represents
 the influence of site-dependent conditions.  It will be noticed that
 this procedure for the estimation of the capital cost of cooling
 towers is  very simple, and since the unit cost is based on past exper-
 ience of the industry, it yields realistic results.  The rating factor
 charts can also  be used to predict the performance at specific off-
 design conditions but their use is restricted to the particular class
 of towers  for which they were constructed.  This procedure gives no
 indication of the physical size of the tower structure nor does it
 indicate the performance of towers which are radically different in
 internal design.

 In order to  proceed further and establish a capability for handling
 towers of  different designs it is necessary to return to a more basic
 approach in  which the Merkel theory is used to predict the amount of
 cooling delivered by a tower fill of given type and dimensions.  Such
 a  procedure  is described in detail in Ref. 15 and will not, therefore,
 be repeated  here.  There it is shown that when the dimensions  (L, W, H)
 and  the heat transfer coefficients of the fill are specified it is
possible to  calculate the cold-water temperature, and therefore the
 heat rejection rate, range and approach, for any given set of values
of the  hot-water temperature, air- and water-flow rates and ambient
wet-bulb temperature.  When the calculations are performed for the
                                  56

-------
design wet-bulb temperature over a range of values of the design heat
rejection rates and tower dimensions, and use is made of the rating-
factor tower-unit method, it is possible to express the tower units
as a function of the tower dimensions as shown in Figure 11.  These
results were obtained using a known  set of heat transfer
coefficients, air- and water-loadings on the pile, pile resistance
and fan characteristics.  A fixed one-side fill width, W = 18 ft
 (5.49 m), had to be used since the available pile resistance and fan
performance data were restricted to that particular value.  It
                    /
should be emphasized that Figure 11 results from a large number of
calculations performed using a range of values of heat rejection
rate, fill height and fill width, and a number of values of the design
wet-bulb temperature.  For each set of conditions (0, L, H, T   ) , the
                                                               /i
thermodynamic model of the evaporative pile, described in detail in
 [15], was used to calculate the corresponding range and approach.
This, in turn, was used to find the corresponding rating factor from
the charts shown in Figure 10.  The total water flow rate, computed
from the water loading and the plan area of the fill, was then used
in equation (21) to find the tower units corresponding to the specified.
set of input conditions.  For each design wet-bulb temperature and pile
height, the number of tower units was found to be a linear function
of the pile length, irrespective of the heat rejection rate.  A small
scatter was observed between the results obtained with different
design wet-bulb temperatures which is shown by the shaded area in
Figure 11.  While the scatter is somewhat consistent, insofar as
smaller tower units correspond to lower design wet-bulb temperatures,
its origin lies mainly in the fact that a highly complex phenomenon
is being represented in a relatively simple form.  In any case, the
scatter is small and well within the accuracy expected from the various
assumptions made in the thermodynamic model of evaporative cooling.
The most remarkable feature of Figure 11 is that the number of tower
units, and therefore the cost of the tower, is primarily a function of
of the dimensions of the fill, as was conjectured earlier.
                                   57

-------
I.S
      100
      TOTAL TOWER LENGTH, (m)
200    300   400    50O   600   700   800	900
       400
              BOO     1200     1600    2000
                 TOTAL TOWER LENGTH, (ft)
                              2400    2800
    Figure 11.  Relation between tower  units  and
                 physical dimensions of  the tower
                     58

-------
Thus, for the estimation of the capital cost of mechanical-draft cool-
ing towers, either Figure 10 or Figure 11 can be used, depending
upon the information that is known.  The range and approach which were
calculated as an intermediate  step in the development of Figure 11
are shown in Figure 12 for three different design wet-bulb temperatures.
The capital cost of pump and pipe system, C   , depends primarily upon
the total water flow rate  (GPM), although some variations will result
due to different pumping heights, structure length, distance between
the power plant and the towers, and other site-related factors.
Figure 13 which is based on the estimates made in Ref. 16, shows the
dependence upon the water  flow rate.  If the  water loading on the
fill, in gpm or m /min per unit plan area, is known, then of course
the total water flow rate  can be related to the length and width of
the tower.  Figure 13 also shows the cost of  pump and pipe system
                                                                   2
plotted against the tower  length for a water  loading of 12.5 gpm/ft
(0.509 m /min/m ) and a fill width of 18 ft (5.49 m) per side.
When cooling towers are designed for a new power plant, the design is
usually optimized  in conjunction with the condenser design.  The new
condenser area A required for compatibility with cooling towers is
                c
shown in Figure 14 as a function of the tower size and the reference
heat rejection rate  (for a heat transfer coefficient, 0  = 630 Btu/hr/
  2
ft /°F) .  The capital post C  of new condensers can then be found from
                            C

                             C  = A  c                            (23)
where c  is a unit cost.  In an example, Dickey and Gates [16] use an
       C                   22
installed value of $4.00/ft   ($43.00/m ) for c  for 1976 construction,
                                              G
and that figure is utilized in the present study even though it
appears low compared to other sources.  The information presented in
Figure 14 can be used if new condensers are considered in the retro-
fit situation.  In that case, the differential cost to be charged
against the project will be the difference between GC an4 any salvage
                                  59

-------
20 r
               100
                       200
TOTAL TOWER  LENGTH, (m)
300    400    500    600
                                          HEAT  REJECTION  RATE.O
                                         10* Btu/hr     10* KJ/hr
                                                       6.668
                                                       4.748
                                                       3.165
                                                       2.110
                                                       LOSS
                                                        HEAT  REJECTION
                                                       (2)        RATE  (I)
                                                 	.SO	85      	50 _
                                                 — — ";I"     _- — --•"""""     4*
                                                       HEIGHT , H
                                                           35 FT (10.67m)
                                                           40 FT (12.19 m)
                                                           45 FT (13.72m)
                                                           50 FT (15.24m)
                                                           55 FT (16.76m)
                  Example:
                  Tower Length of 400m; Q«(2), H-50H
25
               400
                         800      1200     1600     2000
                             TOTAL TOWER LENGTH, (ft)
                              2400
                                                                   2800
              Figure  12(a).   Range,  approach  and water  flow rate
                                as functions of  tower  size,
                                    wb.
                                         = 60°F  (15.56  °C)
                                          60

-------
20
 15
 10
                             TOTAL  TOWER  LENGTH, (m)
                             300    400    500     600
 10
 15
20
25 -
                                             1	1
                                          HEAT REJECTION
                                    10' KJ/hf
                                      6.868
                                      4.748
                                      3.165
                                      2.110
                                       .055
                                               HEAT REJECTION RATE (I)

                                                     40
                                                        HEIGHT , H
                                                           35 FT  (10.67m)
                                                           40 FT  (ia.!9m)
                                                           45 FT  (13.72m)
                                                           50 FT  (15.24m)
                                                           65 FT  (16.76m)
Example:
Tower Length of 400m; Q«I2), H'OOfl
                400
       800
                                 1200
                        1600
2000
                                                           2400
                                                  2800
                             TOTAL TOWER  LENGTH, (ft)
               Figure 12(b).
               Range, approach and  water  flow rate
               as  functions of tower size,
                 T ,   =  70°F  (21.11 °C)
                   wb,
                     a
                          61

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                                    TOWER LENGTH, (m)
                                     400    500    600
                                             1	1
                                           HEAT  REJECTION
                                          I09 Blu/hr
                                       ( I )    6.50
                                       (2)    4.50
                                       (3)    3.00
                                       (4)    2.00
                                       (5) 	 1.00
                                                     HEAT REJECTION RATE (I)
                                                     	45             _JP
(5)    (4)  (3)
                  Example:
                  Tower Length of 250m; 0«(2), H«50ft
20
25
                                                        HEIGHT, H
                                                            35 FT (l0.6Tm)
                                                            40 FT (12.19 m)
                                                            45 FT (13.72m)
                                                            50 FT (15.24m)
                                                            55 FT (16.76m)
                400
               800      1200     1600     2000
                   TOTAL TOWER LENGTH, (ft)
                                                                        S
                                                                        a.
                                                                        g
                                                                        6
                                                           2400
2800
                Figure 12 (c).
                        Range,  approach  and water  flow  rate
                        as functions of  tower  size,
                          T     = 80°F  (26.67 °C)
                           W0,
                             d
                                   62

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   TOWER LENGTH FOR  CONSTANT PILE  WIDTH, L (m)
         200           400          600          800
          T
                       T
           WATER  FLOW RATE, (I06 liters/min)
        1.0          2.0         3.0          4.0
         I	1
WATER LOADING =12.5 gpm/ft8
                (0.509 m3/min/m2)
PILE WIDTH = 18 ft (EACH SIDE)
            (5.49 m)
              0.4      0.6      0.8       1.0
             WATER  FLOW  RATE (10*  gpm)
                                             _L
 J
    400     800     1200    1600    2000    2400
   TOWER LENGTH FOR  CONSTANT PILE  WIDTH, L (ft)

   Figure 13.   Capital  cost of pump and pipe system
2800
                      63

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             100
200
TOTAL TOWER LENGTH,(m)
300    400    500    600
700
800
900
«i
                                                    HEAT REJECTION  RATE
                                                                10' KJ/hr
                                                                  6.86B
                                                                  4.748
                                                                  3.165
                                                                  2.110
                                                                  1.055
              400
   800      1200      1600     2000
        TOTAL TOWER LENGTH, (ft)
                                2400
           2800
               Figure 14.  Required surface area of new condensers

-------
value (T of the existing equipment,  if the old condensers are to be
retained, however, the tower sizes which can be employed in any partic-
ular application will be constrained by the temperature rise and water
flow rate that can be tolerated by the old condensers.

The additional land area required for backfitting with a mechanical-
draft cooling tower depends upon the plan area of the tower and upon
considerations of interference with adjacent towers and neighboring
structures, plume recirculation, and fan noise.  The problem of recir-
culation is primarily dependent upon meteorological conditions and
tower length  [2, p. 630].  Minimizing recirculation, therefore, depends
more upon tower orientation with respect to wind direction and tower
design than upon the land area.  One exception is the case when a long
tower is split into multiple smaller units.  In that case sufficient
land should be available for adequate spacing of the towers to avoid
interference.

The EPA Development Document [2, p. 628] suggests that from 100 to 200
ft  (30.5 to 61 m) of clearance is required around a single mechanical-
draft cooling tower to avoid interference.  If two or more towers are
needed, tower separation should range from 400 to 600 ft  (122-183 m) .
Based on this criterion, the required land area, A  , for a single
                                                  JU
mechanical-draft wet cooling tower of length, I», and breadth, B, may
be expressed as
                                          o
                    A  = BL + 2D(B+L) + 4D                        (24)
          )           L
where D is the width of the clear area around the tower.  Other land
requirement critera are given in Ref. 2  (p. 631) based upon power
plant size.  In a Federal Power Commission survey, a land requirement
of 1000 to 1200 sq. ft  (93 to 112 sq. m) per megawatt, including area
for spacing, is mentioned.

Additional land area determined from the standpoint of acceptable noise
levels may be necessary, particularly in populated  regions.  A detailed
                                  65

-------
study of this criterion may be found in Ref. 7 (Vol. I, Appendix G).
In the hypothetical test case presented in part H of this Section,
additional land area is computed on the basis of a noise level limit of
60 dBA; the specific land area thus required is 0.1 acre/MW (0.04
hectare/MW).  It is readily seen that land area requirement based on
this noise level is approximately four times larger than that based on
equation (24) with D = 200 ft (61 m) and that problems of interference
and recirculation can be handled adequately.  The estimates based on
noise apply only to situations where the availability of land is not a
major problem.  In many backfit cases, however, limitations of avail-
able space may dictate the use of noise suppression devices.

Since criteria for the determination of additional land area needed for
backfitting differ so much, the specific land area requirement, in
acres/MW or hectares/MW, is left as a variable parameter in the
present study.

The total differential capital cost of the closed-cycle cooling system,
CC , can now be expressed in the form
  s
         CC0 = C-C'+C   - C'  +C   - C1 + A a.. + C           (25)
           S    c   c    pp    pp    cs    o    L I    HT
where  CC  = differential capital cost of cooling towers
         &
        C  = capital cost of new condensers (see equation (23) and
             Figure 14)
        C'  = salvage value of old condensers (C  - C' = 0 if old
         c                                      c    c
             condensers are retained)
       C   = capital cost of pumps and piping  (see Figure 13)
       C1   = salvage value of pumps and piping used in open-cycle
             cooling
       C   = capital cost of towers, including tower structure, fans,
        G S
             motors, controls, basin; installed cost (see Figure 10
             or  Figure 11)
        C'  =  salvage worth of old system components, excluding
             condensers, pumps and piping
                                  66

-------
        AL ~ land area required  for  towers  [see equation  (24) or Ref. 7
              (Vol.  I, Appendix G)]
        a^ = unit land cost
       CHT ~ cost of hook-up  and testing of towers

All cost figures used in  this study  are based on 1974 values unless
otherwise specifically stated.   If estimates of inflation, labor costs,
construction costs, material  costs,  etc. can be made, standard methods
of proration may be used  to project  costs to a future date.

As explained in the previous  section, the total capital cost to be
assessed against backfitting  consists of the cost of the cooling system
considered above, the cost of downtime CC   which has already been
discussed, and the  capital cost  of replacement capacity CC.  The
                                                          R
evaluation of the last quantity  is considered in later sections.
              -^
B.  REFERENCE LENGTH OF COOLING  TOWERS, L*
A number of quantities which  characterize the operation of an existing
power plant or unit using open-cycle cooling were defined in the
previous section.   For a  specific turbine  (A, B, or C; Table 1) , P*
is the rated or nameplate capacity which is obtained at the reference
               *
back pressure p  where the excess turbine heat rate A is zero, and the
                                      *
corresponding heat  rejection  rate is Q .  Here, it is useful to define
a reference size of the cooling  towers.  For any given pile height H
                                                 *
and pile width W, the reference  length of tower L  can be defined as
                               *
the length required to remove Q   at  some reference ambient wet-bulb
temperature while maintaining the back pressure at p' which can be
selected arbitrarily without  loss of generality.  For the example
calculations, L  is determined holding the  pile width, W, constant at
18 ft (5.49 m) for  reasons discussed earlier; the reference wet-bulb
temperature is set  equal  to 60°F  (15.6°C),  and p1 is taken as 2 in. Hg
abs (5.08 cm Hg abs).

It is clear that L* can be found  for any given set of values of Q*
                                  67

-------
 and H using  the  theory  of Merkel  in conjunction with the known heat
 transfer  properties  of  the  condenser and the evaporative pile, and
 the air-  and water-loadings recommended by tower manufacturers.  A
 computation  construction which has proved useful in calculating the
                   *
 reference length L  is  as follows.  In the thermodynamic model, the
 turbine characteristics curves  (as in Figure 2) are replaced with a
                                                         *
 vertical  line (corresponding to the heat rejection rate Q ) as in
                                                             i
 Figure 15.   The  operation of the  cooling system  (with condenser) then
                                      *
 corresponds  strictly to rejection of Q   (regardless of what turbine it
 is rejected  from or  what power level or throttle opening is being used).
               *
 Rejection of Q  from any specified cooling system occurs at a unique
 set of values of hot-water  temperature and cold-water temperature
 (and thus corresponding steam temperature and pressure) for a specified
 design wet-bulb  temperature.  By  repeating the calculations for a
                 *
 given value  of Q  and several different cooling system sizes, at a
 specified wet-bulb temperature, the system size that corresponds to
 the specified back pressure,  p1,  for the given heat rejection rate,
  *
 Q ,  can be determined.  This cooling system size is the reference
               *
 system size  (L  for  mechanical-draft crossflow wet cooling towers)
 used to nondimensionalize succeeding example operation results.  With
 an air-loading of 1800  Ib/hr/ft -face area  (8790 kg/hr/m -face area),
                             2                  32
 water-loading of 12.5 gpm/ft -plan area  (0.509 m /min/m -plan area),
 and typical  (proprietary) information concerning the heat transfer
                               *     *
 properties,  the  dependence  of L   on Q  and H is shown in Figure 16.  It
 will be seen that the reference length is a nearly linear function of
  *                                                  *
 Q  which  decreases with increasing H for a constant Q .  in what
                               *
 follows,  the reference  length L   will be used to normalize the tower
 size so that the example results  can be used to assess the performance
 of power  plants  or units with different nameplate capacities and heat
 rejection rates.   It is perhaps useful to emphasize that the foregoing
 considerations apply regardless of the type of turbine that  is employed
                                        *
 since the definition and evaluation of L  is independent of  the source
     *                       *
of Q  .  The definition of L   thus depends on the values of wet-bulb
temperature and p1 used in the definition.  It makes no difference
                                  68

-------
Cfl
jQ
O
 .  3.0
X
c

Q.


IT

CO
CO

tr


o

00
                                                *
                                                oi
                                                II
                                                OI
                                   OPERATION
                                   AT  REFERENCE
                                   CONDITIONS
1.0
                 0.4        0.8         1.2         1.6

               HEAT REJECTION  RATE,Q(109 Btu/hr)
                                                         2.0
           Figure 15.  Construction for the definition of
                      reference tower length,  L

-------
   2000
               REFERENCE  HEAT  REJECTION  RATE, Q* (I09 KJ/hr

                1.0       2.0       3.0       4.0       5.0       6.0
                                                                            600
    1600 -
LU
O
UJ
u

UJ
CC.
UJ
u.
UJ
CC
    1200 -
             1	1	1	1

       p' » 2.0  in. Hg  abs (5.08 cm Hg  abs)
    800-
400 -
                 1.0       2.0       3.0       4.0       5.0        6.0

                 REFERENCE  HEAT  REJECTION RATE, Q* (I09 Btu/hr)
                    Figure 16.  Reference length of towers

-------
which reference temperature or back pressure is used in defining
L  as long as all such references are consistent.  As mentioned, the
reference length is defined for a 60°F  (15.6°C) reference wet-bulb
temperature and p'=2. in. Hg abs  (5.08 cm Hg abs) .  All calculations of
 *      .                                              *
L  consistently use these same references.  Thus, an L  from Figure 16
is suitable for "dimensionalizing" results obtained from succeeding
nondimensional plots.

C.  OPERATION OF A TOWER OF GIVEN SIZE  (L, H)
When the width of the pile W is fixed, the physical size of the
cooling tower is characterized by only two parameters, namely the
length L and the height H.  In turn, the length determines the number
of fans required, while the plan area  (2WL) and the face area (2HL)
determine the total water and air flow rates when the appropriate
water and air loads per unit area are prescribed.  For the example
calculations presented herein, the air- and water-loadings mentioned
in the previous paragraph and proprietary heat transfer properties of
the pile are used.  For different loadings the results can be expected
to change; however, these data are characteristic  of currently manu-
factured cooling towers and are expected to be representative of
available units.

In this part, consideration is given to the operation of a cooling
tower of a given size  (L and H) in conjunction with a turbine whose
performance characteristics are known.  Thus, it is assumed that the
following quantities are prescribed:
     1.  Nameplate capacity, P   (kW),  (see Sections IV.D and V.J for
         variations in loading pattern)
                                         *
     2.  Reference heat rejection rate, Q   (Btu/hr or kJ/hr),
     3.  Turbine heat rate correction curves, A vs. p  (as in Figure 1),
     4.  Frequency of occurrence of dry- and wet-bulb temperatures
         (as in Table 3),
     5.  The size of the cooling tower, L and H  (ft or m).
                                  71

-------
 Then,  items  2 and 3 can be combined to obtain the heat rejection rate
 characteristics of the turbine in the form shown in Figure 2 using
 the procedure described in the previous section.  The information in
 item 4 can be used to find the various design temperatures and also
 the extreme  temperatures which are not exceeded or equalled more than
 10 hours per year.  The basic theory of Merkel can then be used to
 find the turbine back pressure p which will occur at each set of values
 of the dry-  and wet-bulb temperatures.  These calculations again
 involve a certain amount of iteration since the rate of heat rejection
 from the turbine must be balanced by the cooling capacity of the
 towers.  It  is also necessary to assume the performance characteristics
 of the condensers so that the temperature of the hot water entering
 the tower can be related to the steam condensing temperature correspond-
 ing to the back pressure p.  The detailed procedures adopted and the
 computer programs developed to accomplish such calculations are de-
 scribed in Ref. 15  (see Sections III.B, E, and F) and will not be
 presented here.  It should be noted, however, that these steps are
 included in  the major program listed and described later for the
 analysis of  the backfit situation.

 For each set of dry- and wet-bulb temperatures, these calculations
 identify a corresponding operation point on the turbine characteristics
 curves shown in Figure 2.  Consequently, it is possible to determine
 all quantities of interest including the back pressure p, heat re-
 jection rate Q, power output P, the rate of evaporation of water from
 the tower, the hot-water temperature, the cold-water temperature, the
 range  and approach, and the power required by the fans and pumps.  When
 such calculations are performed for all possible combinations of the
dry- and wet-bulb temperatures occurring at the site, it becomes
                                                      " »
possible to  evaluate the following (these definitions apply for the
assumed "full-throttle" power loading; for consideration of variations
                                              i
in power loading related to meteorological conditions, see Section V.J):
     (a)  The maximum capacity loss, C  is given by
                                  72

-------
                      *
                CL=P  -Pmin+Pcs  '    kW                (26)




     where Pmin is the gross output from the turbine at the


     extreme temperatures T  , T ,  which are not exceeded or
                           db   wb

     equalled more than 10 hours per year, and P   is the power
                                                cs

     required to operate the pumps and fans.





(b)   If the time duration (in hours) of each set of meteorological


     conditions (Tdb/ T  ) is At, then the annual loss of energy,


     E  is given by
      Li



            E  = V* (P* - P + P  )At  ,    kW-hr             (27)
             L   /—/           cs



     where the summation is carried out over all sets of T,, ,  T
                                                          db   wb

     Note that At = f(T,, , T , )  * 8760 hrs, where f is the fre-
                       db   wb

     quency of joint occurrence of the temperatures T_, , T , .
                                                     db   wb
(c)   Similarly, the difference between the annual fuel consumption


     using cooling towers and that with open-cycle cooling F  is
                                                            £j

     given by

       \


            n  F  = V'* (cP 4- Q - cP  - Q )At  ,    kW-hr     (28)




     As explained in section IV, the contribution to this quantity


     will be zero during periods of full-throttle operation,


     T  =1, and negative when the turbine is throttled back,
      s

     T  < 1.
      s




(d)   The annual water loss due to evaporation from the towers is


     given by




            W  = V* c, (w  - w.)G At  ,   m /year             (29)
             L   / j  1  o    i



     where w.  and w  are, respectively, the absolute humidities
            i      o

     of the air entering and leaving the tower (in kg water/kg dry
                             73

-------
          air), G is the total air flow rate through the tower
          (in kg/hr) and c  is a numerical conversion factor
                    3     1
          (= 0.001 m  water/kg water).   The theoretical development
          of equation (29) and the method used to calculate wi and WQ
          are described in Ref. 15 (Section III.G).
D.  PARAMETRIC STUDIES
Detailed calculations of the type described above can of course be
performed for a range of values of the tower length and height.
Figures  17 through 20 show the variations, with tower size,  in the
maximum capacity loss C , the annual energy loss E ,  the annual fuel
                       L                          L
penalty F , and the annual water loss due to evaporation W ,  for the
         E                           *            *       L
particular case of turbine A (whose P  = 411 MW, p  = 1.00 in.  Hg abs
= 2.54 cm Hg abs, and Q  = 2.545 x 1Q9 Btu/hr =  2.686x 10  kJ/hr for
fossil-fuel operation, see Table 1) with the meteorological condi-
tions at Los Angeles  (Tables 4 and 5) for the assumed "full-throttle"
loading.  Also shown in these figures are the results obtained  for a
hypothetical turbine whose nameplate capacity and reference heat re-
                                                  *            *
jection rate are twice those of turbine A (i.e., P  = 822 MW, Q  =
5.090 x 10  Btu/hr = 5.372 x lo9 kJ/hr) but whose basic heat rate
characteristics are the same as those of turbine A (Figure 4).   For
consideration of variations in power loading, see Section V.J.   The
following important observations can be made from these results:
     (a)  The range of values of tower heights and lengths considered
          here were dictated by the guidelines on practicable con-
          figurations suggested by the manufacturers of conventional
          equipment.
     (b)  From Figure 17 it will be seen that the maximum capacity
                                                       *
          loss C  varies markedly with tower size and Q .  For  a given
                L           *
          tower height and Q ,  C  decreases rapidly with increasing
          length, reaches a minimum and then increases slowly.   The
          high values of C  at the smaller lengths arise primarily due
          to the maximum back pressure limitation, requiring the
                                   74

-------
  140
   120
^  100
o
«  8O

O
>-
I-
o



o
   60
   40
   20
            100

            —I—
 TOWER LENGTH, L (m)

200     300    400    500
     	1	,	.—
                    T
                                                 600
                                 LOS ANGELES

                                   TURBINE A
                                 PILE HEIGHT, H


                                     45ft, 13.72m

                                     55ft, 16.77m
             400      800     1200     1600


                   TOWER LENGTH, L(ft)
                                                 2000
           Figure 17.  Variation of capacity loss with

                      tower size and plant capacity
                               75

-------
             100
 TOWER  LENGTH, L (m)

200     300     400
                     T
 500
—I—
   700
    600
 ~  500
KJ
 O
 UJ
   400
 
-------
    -50
 .  -100
p-
X
2
O
I-
O.
(0
O
O
UJ
a.
V)
UJ
UJ
u.
O
UJ
-150
   *
h  O-
   -200
   -250
   -300
   -350
                       TOWER LENGTH, L (m)
                      200     300    400
                                         500
                600
             oo
              II
                                       I	1	
                                    LOS ANGELES
                                     TURBINE A
 PILE  HEIGHT, H
	45 ft,  13.72 m
	 55ft,  16.77m
                400      800      1200
                      TOWER LENGTH, L(ft)
                                        1600
                2000
        Figure 19.  Variation of excess fuel consumption
                   rate with tower size and plant capacity
                              77

-------
14
                    TOWER LENGTH, L (m)

            100    200     300    400    500
                       	,	




                                 LOS ANGELES

                                  TURBINE A
                                               600
                                                  14
                                                     12
 o 12
 
                                                     to
      ID

      O
                                                     oc
                                                     o
                                                     Q.
                                                     UJ

                                                     01
                                                     Ul

                                                     i
             400      800     1200


                   TOWER  LENGTH, L(ft)
                                      1600
2000
         Figure 20.  Variation of evaporation with

                    tower size and plant capacity
                               78

-------
     turbine to operate at less than full-throttle  to maintain
     P =  Pmax durin9 periods of severe meteorological conditions.
     The  increase in CL at larger values of  tower length, on the
     other hand, results primarily from the  increase in  the pump
     and  fan power required to operate the larger towers.
(c)   Figure 18 shows that the behavior of the annual energy loss,
     EL, is similar to that of the maximum capacity  loss.  The
     reason for this is obvious from equations (26) and  (27).
(d)   Figure 19 indicates that, for given P  and  Q  , there is a
     range of tower sizes over which the turbine operates at full
     throttle at all sets of meteorological  conditions so that
     the  annual fuel consumption is the same as  that in  open-
     cycle operation.  For smaller towers, however, the  reduced
     throttle operation during periods of severe temperatures
     implies that the fuel consumption will  be smaller than with
     the  open-cycle cooling system.
                                      *      *
(e)   Figure 20 shows that, for fixed P  and  Q ,  the annual water
     evaporation increases  with tower size.  This  is mainly due
     to the larger water flow rates and smaller  cooling  ranges
     associated with the larger towers.
(f)   Comparison between the results obtained with the two values
     of the nameplate capacities, and corresponding reference heat
     rejection rates indicates that the precise  values of the
     capacity and energy losses, excess fuel consumption, and
     water loss due to evaporation are dependent upon the SIZE
     AND  TYPE of the power plant or unit that is considered, even
     though the distribution of the meteorological  conditions and
     the  turbine heat rate characteristics may be  identical.  In
     other words, calculations of the type shown in Figures  17
     through 20 need to be repeated for any  specified values of
      *      *
     P and Q .  These calculations can of course be accomplished
     by means of the computer program which  was  developed and used
                             79

-------
          to obtain the example results.  Fortunately, however, it
          turns out that the usefulness of these results can be greatly
          enhanced if they are rendered "nondimensional" by employing
          suitable "scaling parameters."  Thus, if the tower length is
          normalized with respect to the reference length L  (which,
          as shown in Figure  16  is a function of the pile height and
            *
          Q ), the capacity loss is normalized with respect to the
          nameplate capacity, and the energy loss and excess fuel
                                                                 *
          consumption are normalized using the maximum energy  (PE )
          that can be produced in a year, i.e.  (8760 hr/year) x p  (kW),
          then the two sets of results shown in Figures  17 through  20
          can be plotted as shown in Figures  21 through  24.  The prob-
          lem of the water evaporation is somewhat difficult since
          there is no suitable reference value that can be used.
          Various alternatives, such as evaporation per unit flow rate,
          or evaporation per unit nameplate capacity, were attempted,
          but it was found that best results were obtained by defining
          a "specific rate of water evaporation" by W /Q , i.e. evap-
                                                     L
          oration per unit reference heat rejection rate.  This quanti-
          ty is of course not dimensionless.  However, Figure 24 shows
                        *        *
          a plot of W /Q  vs. L/L  for the two sets of results given in
          Figure 20.  It will be seen from Figures 21 through 24 that
          there is a remarkable coincidence between the results ob-
          tained with the two different sets of values of P  and Q  .
          The major implication of this is that for a given set of
          turbine heat rate characteristics and meteorological data
          there is no economy of scale in the detailed operation of a
          particular type of turbine.  A similar collapse of the re-
          sults was also observed when the calculations were repeated
                                  *
          with the same value of P  (411 MW) but a different, higher
                    *            9                    9
          value of Q - (3.010 x lo  Btu/hr = 3.176 x 10  kJ/hr) corres-
          ponding to a nuclear unit.

It will be recalled that the foregoing discussion applies to the re-
                                  80

-------
   0.20
                                     T
                       T
CO
8
o
   0.18
   0.16
   0.14
   0.12
S  ojo
o
UJ
n  0.08
o
z
   0.06
   0.04
   0.02
                                     LOS ANGELES
                                       TURBINE A
                x P* = 411 MW
               O P*=822 MW
                 PILE HEIGHT,  H
               	45 ft, 13.72 m
                    55 ft, 16.77 m
              0.2
0.4
0.6
0.8
1.0
               NORMALIZED TOWER LENGTH,  L/L*
             Figure 21.   Normalized capacity loss
1.2
                                  81

-------
  0.20
   0.18
                                    LOS  ANGELES
                                      TURBINE A
  0.16
                                  x P*= 411 MW
                                 O P* = 822 MW
o
o
UJ

a
   0.14
   0.12
   o.io
  0.08
                                     PILE HEIGHT,  H
                                   	45 ft, 13.72 m
                                   —	55 ft, 16.77 m
                      ITOTAL (INCL. FAN  a PUMP
                                         ENERGY)
  0.06
  0.04
0.02
             FAN 8 PUMP
              ENERGY
             0.2     0.4     0.6     0.8

              NORMALIZED TOWER LENGTH,
                                         1.0
                                         . *
             Figure 22.  Normalized energy loss
                                 82

-------
*ui  -0.02
 a.
    -0-04
 x  -0.06
 z
 o
 to
 z
 o
 o
 UJ
    -0.08
    -0.10
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 X
 UJ



 y  -°-14
 O  -0.16
    -0.18
    -0.20
                          ®
 LOS ANGELES

  TURBINE A
 x P* = 411 MW

 0 P*=822 MW
  PILE HEIGHT, H

	45ft, 13.72m

	55ft, 16.77m
         0      0.2     0.4     0.6     0.8


                 NORMALIZED TOWER LENGTH,  L/L*
        1.0

          *
           Figure 23.   Normalized excess fuel consumption
                                  83

-------


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o
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^
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1 1 1 1 • 1 I
LOS ANGELES
TURBINE A
«•

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1
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//

PILE HEIGHT, H
	 45 ft, 13.72 m
	 55 ft, 16.77 m
MB



•m


•IB»


1 1 1 1 1 1
0.2     0.4     0.6      0.8     1.0


 NORMALIZED TOWER LENGTH,  L/L*



   Figure 24,  Normalized evaporation
1.2
                                           8000
                                           3000
                                           2000
                                           1000
                                                  E
                                           7000
                                           6000
                                           5000
                                                 10
                                           4000  2
                                                 oc
                                                 o
                                                 a.
            CC
            UJ

            I

            o
            UJ
                                                 CC
                                                 o
                                                 Z
                   84

-------
suits obtained with the heat rate characteristics of turbine A
(Figure 4) and the meteorological data corresponding to Los Angeles.
It is obvious, however, that even the normalized quantities shown in
Figures 21 through 24 will change if either the heat rate character-
istics or the meteorological conditions are different.  In order to
build up a representative library of the operating characteristics of
cooling towers, therefore, a parametric study was conducted using the
following:
        Heat rate characteristics of turbines A, B, C.
         (Figures 4, 5, 6)
        Meteorological data at Chicago, Los Angeles,
        Miami, and St. Louis.
As indicated in Section IV, these studies of full-throttle loadings,
are expected to represent a majority of the situations which will be
encountered in the considerations of backfitting in this country; for
discussion of variations in loading, see Section V.J.  The final
results are presented in Figures 25 through 28.

E.  OPERATING COSTS WITH COOLING TOWERS
As discussed in Section IV.C, in the consideration of the costs of
backfitting a power plant or unit with cooling towers, the maximum
capacity loss  (Figure 25) contributes to the capital cost of the
project, while the energy loss, the excess fuel consumption, and the
loss of water due to evaporation all contribute to the operating costs
after backfitting.  From Section IV.C, it will be recalled that the
total operating cost resulting directly from backfitting can be
written as
               OC = OCR + OCEF + OCS                              (16)

where OC  is" the cost of replacing the energy loss EL/ OCEF is the
cost resulting from the excess fuel consumption F£ and OCg is the
differential operating cost of the cooling towers.  The first two of
these can be found from Figures 26 and 27, respectively, when the
tower size, nameplate capacity, reference heat rejection rate, and
                                  85

-------
   0.22
   O.20
   0.18
   0.16
u
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   O.14
 > O.12



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 0 0.10
 a
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 N

 U

 | 0.08


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   0.06
   0.02
                     -i	1	r


                         CHICAGO




                       PILE HEIGHT, H

                     	35  ft, 10.67m

                     	45  ft, 13.72m

                     	 55  ft, 16.77m
                           _L
J_
JL
                                    J_
0.2     0.4    0.6     0.8     1.0     1.2


           NORMALIZED TOWER LENGTH,  l
                                                        1.4
                             1.6
                             1.8
                Figure 25(a).   Normalized  capacity loss, Chicago
                                        86

-------
   0.22
   0.20
   0.18
   0.16
o
 CO
 CO
 p
   0.14
>; 0.12

5
   0.10
o
IU
N
   0.08
o:
o
   0.06
  0.04
   0.02
                                                          LOS  ANGELES
                               PILE HEIGHT, H

                               — 35 ft, 10.67m

                                   45ft, 13.72m

                                   55 ft, 16.77 m
             0.2     O.4
0.6     0.8
1.0
1.2
1.4
1.6
1.8
                                                    LA*
                        NORMALIZED TOWER LENGTH,  U/L*




        Figure  25(b)•   Normalized capacity loss, Los Angeles
                                          87

-------
   0.22
   0.20
   O.I 8
   0.16
o


 co
 w
 Q
0.14
   0.12
   0.10
 o
 ui
 N
   0.08
cc
o
   0.06
  0.04
   0.02
                                                            MIAMI





                                                        PILE HEIGHT, H

                                                       	35 ft, 10.67m

                                                       	45 ft, 13.72 m

                                                            55 ft, 16.77m
                             I
                                    I
                                            I
             0.2     0.4     0.6     0.8    1.0     1.2


                         NORMALIZED  TOWER  LENGTH, L
                                                      1.4
                                                  -XL«
1.6
1.8
                Figure 25(c),  Normalized capacity loss, Miami
                                        88

-------
   0.22
   0.20
   0.18
    0.16
u
 CO

 8
 o

 2

 6

 Q
 111
 (si
    O.14
    0.12
0.10
   0.08
 cc
 o
   0.06
   0.04
   0.02
                                                          ST. LOUIS




                                                         PILE HEIGHT, H

                                                      	35 ft, lO.67m

                                                      	45 ft, 13.72m

                                                      	55 ft, 16.77 m
             0.2     0.4     O.6     0.8      IjO      1.2     1.4

                         NORMALIZED TOWER LENGTH,  L/L*
                                                              1.6
1.8
         Figure  25 (d).  Normalized  capacity loss,  St. Louis
                                        89

-------
  0.22
  0.20
  0.18
   0.16
                                                               I       T

                                                          CHICAGO


                                                        PILE HEIGHT, H
                                                        	35 ft,  10.67 m
                                                        — 45 ft,  13.72 m
                                                            55 ft,  16.77m
 UJ
 a.
  0.14
OT
co
   0.12
UJ

Q
UJ
0.10
  0.08
  0.061
  0.04
  0.02 h
       PUMP 8 FAN
          ONLY
O.2    0.4     0.6     0.8     1.0     1.2      1.4

             NORMALIZED TOWER  LENGTH, L/L*
                                                                1.6
                                                                     1.8
            Figure 26 (a).   Normalized energy loss,. Chicago
                                     90

-------
0.22
0.20  -
                                                     LOS ANGELES
                                                     PILE HEIGHT, H
                                                    	35 ft, 10.67m
                                                    	45 ft, 13.72m
                                                         55ft, 16.77m
                                        TOTAL (INCL.  PUMP 8 FAN)
       PUMP a FAN
          ONLY
                        0.6     0.8     1.0     1.2
                       NORMALIZED TOWER LENGTH,
       Figure 26(b).  Normalized  energy loss, Los  Angeles
1.8
                                 91

-------
0.22
0.20  -
                                                     PILE  HEIGHT, H
                                                   	35 ft, 10.67m
                                                   	45 ft, 13.72m
                                                        55ft, 16.77m
                                          TOTAL (INCL.  PUMP a FAN
       PUMP ft FAN
          ONLY
                        0.6     0.8     1.0     1.2

                      NORMALIZED TOWER  LENGTH,
             Figure  26 (c).   Normalized energy loss,  Miami
                               92

-------
  0.22
  0.20
   0.18
   0.16
 UJ
 a.
   0.14
co
CO
O
   0.12
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< 0.08

i
   0.06
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  0.02 -
                 ST. LOUIS


                PILE HEIGHT, H
                — 35ft, 10.67m
                — 45 ft, 13.72m
                	55 ft, 16.77 m
TOTAL (INCL. PUMP 8  FAN)
          PUMP 8 FAN
             ONLY
0.2     O.4     0.6     0.8     1.0     1.2

              NORMALIZED TOWER LENGTH, '
                                                          1.4
                     1.6
1.8
          Figure  26(d).  Normalized  energy loss, St,  Louis
                                                    •
                                        93

-------
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 ~  -0.04
K

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    -0.06
o
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                                         CHICAGO


                                        PILE HEIGHT, H
                                       	35 ft, 10.67 m
                                       — 45 ff, 13.72m
                                       	55ft, 16.77m
0.4
 i	
0.6
 i
0.8
 i
1.0
 i
1.2
1.4
1.6
1.8 (A,B)
                              0.2     0.4      0.6     0.8      1.0

                            NORMALIZED TOWER  LENGTH, L/L*
                                              1.2
                                              1.4 (C)
        Figure  27(a).. Normalized  excess fuel consumption,  Chicago
                                    94

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  : -0.04
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   -0.08
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                                   O
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                                   CC

                                                 7/
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                          I
                              LOS ANGELES

                               PILE  HEIGHT, H
                             	35ft, 10.67m
                             	45 ft, 13.72 m
                             	55ft, 16.77m
0.4
0.6
0.8
1.0
1.2
1.4
                             0.2
               0.4
               0.6
                       1.0
                                                      L, *
                            NORMALIZED TOWER LENGTH, U/L'
1.6
                                            1.2
1.8 (A,B)
1.4 (C)
       Figure 27(b).  Normalized  excess fuel consumption, Los Angeles
                                        95

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  : -o.04
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8  -0.08
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                                                               MIAMI



                                                            PILE HEIGHT, H

                                                         	35 ft, 10.67m

                                                         	45 fj, 13.72 m

                                                         	 55ft, 16.77m
                                                                          I
               0.2
0.4
                             0.6
                              i
          0.8
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 i
1.2
1.4
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                         0.8
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                                                      L, «
                            NORMALIZED TOWER LENGTH, L/L*
        Figure  27 (c).   Normalized excess fuel consumption, Miami
                                      96

-------
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                                 ST. LOUIS




                               PILE  HEIGHT, H

                             	35ft, 10.67m

                             	45 ft, 13.72 m

                             	 55 ft, 16.77 m
                                                                           I
0.4
0.6
         0.8
1.0
1.2
1.4
1.6
1.8 (A,B)
  0.2     0.4      0.6     0.8


NORMALIZED TOWER  LENGTH, '
                                                            1.0
                                            1.2
                                            1.4 (C)
        Figure 27(d).   Normalized excess  fuel consumption,  St.  Louis
                                       97

-------
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                                                          CHICAGO
                                                     PILE HEIGHT, H
                                                  —- 35ft, 10.67 m
                                                  	— 45ft, 13.72m
                                                  ——55ft, 16.75m
                                                                       9000
                                                                             19000
                                                                              6000
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                                                                              6000
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                                                                                    6000
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                         NORMALIZED TOWER LENGTH, L/L*
                                                            1.6    1.6
                                                                              3000
                                                                              2000
                                                                              1000
                                                                       4000  -I i
                                                                       3000
                                                                                         OC

                                                                                         i
            Figure 28(a).   Normalized  evaporation,  Chicago
                                             98

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                                                                         111
          02   0.4    0.6   0.8    1.0    1.2
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Figure  28(b).  Normalized evaporation,  Los Angeles
                                99

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                                          —— 55 ft. 16.75 m



                                         I      I	I
          0.2    OA    0.6   0.8    IX)    1.2


                   NORMALIZED TOWER LENGTH,
                                                       1.4
                                                             1.6
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                                                                        9000  H
                                                                        BOOO  H
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                                                                        6000  H
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                     Figure 28 (c).   Normalized evaporation,  Miami
                                            100

-------
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Figure 28 (d).  Normalized  evaporation,  St. Louis
                       101

-------
 unit costs of replacement energy and  fuel  are known.   Before des-
 cribing the general procedure for the detailed economic assessment of
 backfitting, however,  it is necessary to examine the  operating costs
 of the cooling towers,  OCC, in some detail.
                          O

 First of all, it will  be noted that the power required to run the fans
 and pumps has already  been accounted  for in  the evaluation of the
 energy loss (and also  in the calculation of  the capacity loss) .   The
 tower operating costs  can therefore be further due  only to the addi-
 tional quantities:
         The cost of makeup water (evaporation + blowdown;
            drift is neglected) ,
         The cost of blowdown treatment,
         Maintenance of the towers and associated equipment.
 The water loss due  to  evaporation W   can be  found directly from
                                   L                     ,
 Figure 28.   The makeup water required,  W , is then  the sum of the
 evaporation WT  and  the blowdown W :
              i>                   b

               Wm "  WL  + Wb                                       (30)
 The amount  of blowdown will depend upon the  concentration k (in ppm)
 of undesirable constituents in the makeup  water and the maximum concen-
 tration k  permitted in the cooling tower.   Then.
          m

               Wm k  = Wb km                                       <31>
 From equations (30)  and (31) ,  the blowdown and makeup are given by

               Wb =  -ri-WL                                     (32)

                        *
and           Wm =  -~— w                                      (33)
                    k  - 1
where         k  = k /k
                    m
                                   102

-------
Now, the annual cost of makeup water can be found simply by multiply-
ing Wffl by the unit cost of water c   ($ per 1000 gal. or $ per m3) .
The cost of water varies widely from region to region in this country.
In the backfit situation, however, it is likely that the water body
used in the open-cycle operation can be relied upon as a readily
available source.  In any case, c  is left as a basic variable, like
                                 W
all other costs, so that its influence on the overall economics can be
evaluated at will.  The cost of treating the blowdown prior to dis-
charge into the environment can be found in a similar manner by
multiplying W, by a unit treatment cost c   ($ per 1000 gal. or $ per
m ) .

The maintenance cost of mechanical-draft cooling towers includes the
annual overhaul labor and parts, and associated overhead.  Both the
fans and pumps are, however, low maintenance items and tower manu-
facturers usually suggest a unit cost, in dollars per year per tower
cell, to account for all tower related maintenance costs.  The main-
tenance cost can be found by using a unit cost of the order of $200
per cell per year  [Ref. 2, p.  568].  In the overall economics of
backfitting, the tower maintenance cost is rather insignificant com-
pared with the other penalties, and  therefore small variations in this
unit cost are unlikely to affect the total cost picture.

The differential operating and maintenance cost of cooling towers can
now be written as
                                              -B1
*!
Q!
k c + c. i
w b (
K*-l (
WL
Q*
                                             Cm  - <%              (34)
where OC_ = differential operation and maintenance cost of cooling
        O
            tower s,  $/year,
                                   103

-------
       Q  = reference heat rejection rate,
       k  = ratio of maximum permissible concentration of undesirable
            constituents in the circulating water to the concentration
            in the makeup water,
       W  = annual water evaporation, m /year
        Xi                                 ~
       c  = unit cost of supply water, $/m ,
        W                                       3
       c, = unit cost of blowdown treatment, $/m ,
        b
       M' = makeup water cost with open-cycle system, $/year,
       B1 = blowdown treatment cost with open-cycle system, $/year,
       C  = annual maintenance cost of cooling towers, $/year,
        m
       C1 = annual maintenance cost of open-cycle system, $/year.
        TTl
 F.  PROCEDURE FOR THE ECONOMIC EVALUATION OF BACKFITTING
 The various  items which must be considered in the evaluation of the
 cost of backfitting an existing power plant or unit with mechanical-
 draft wet cooling towers have been described individually in the pre-
 ceding paragraph.  The manner in which these items are to be combined
 in order to  calculate the total cost of backfitting will be considered
 next, followed by a general description of the computer program that
 has been developed for this purpose.  Subsequently, in part H of this
 section, a hypothetical test case is considered in order to illustrate
 the general  methodology presented below.  In Section V.J, a variation
 in the loading pattern (from "full-throttle") with meteorological
                        /•"
 conditions will be considered.

 As indicated earlier, it is necessary to have available a certain
 amount of information concerning (a) the characteristics of the power
plant and site, (b)  the size of cooling towers which are to be used,
and (c)  the various unit  costs and economic parameters which apply
to the particular plant or utility situation, before a detailed
economic analysis can be undertaken.  In particular, the methodology
suggested here requires that the following quantities be known a priori:
 (a)    Power  plant and site data:
                                  104

-------
      1.  Nameplate capacity, P   (kW);


      2.  Reference heat rejection rate, Q   (kJ/hr); this can be found


          from the reference turbine  heat rate, T   , or from the refer-
                                  *               HR

          ence plant heat rate, P ,  and plant efficiencies n , n  (see
                                  HK                          I   p

          Section IV.A);


      3.  Turbine heat  rate correction curves A[p,T ], as in Figure 1;
                                                    S

      4.  Remaining useful life of the plant or unit  (years);


      5.  Characteristics of the  existing condensers if they are to be


          retained  (limitations of temperature rise and water flow


          rate), or their salvage value C' if new condensers are to be
                                         c

          fitted;


      6.  Salvage value C1  of pumps  and piping associated with the


          open-cycle system, and  the  salvage value  C1 of system com-
                                                    o

          ponents other than pumps, piping and condensers;


      7.  Annual makeup water cost, M', blowdown cost, B1, and mainten-


          ance cost C1  associated with open-cycle cooling;
                     m

      8.  Meteorological data for the site  (as in Table 2).  These can


          be used to determine the design temperatures, T ,  , T,,  , the
                                                         wb,   ab,
                                                        ~  d     d

          extreme 10-hour exceedance  temperatures,  T . , T,, , and the
                                                    wb   db

          frequencies of occurrence of T , , T,, as  explained in Section
                                        wb   db

          IV.B.



  (b)  Cooling Towers:


      1.  The SIZE of cooling towers, EITHER explicitly in terms of the
                                                            *

          length L and  the height H of the evaporative pile,  OR impli-


          citly in terms of the design range, approach and water flow


          rate corresponding to a specified design  wet-bulb temperature;
 It will be recalled that L and H are sufficient to describe the

physical size of the towers since the width of the pile  (W) has been

fixed, and since all detailed calculations are based upon a represent-

ative set of empirical data concerning the heat transfer properties,

and air- and water-loadings in the pile.
                                  105

-------
     2.  Unit cost of towers, c ($/TU);
     3.  Unit maintenance cost, c ($/tower cell or $/fan, per year);
                               *m
     4.  concentration ratio,  k , and unit cost of blowdown treatment,
         cb  ($/m3);
     5.  Capital cost, C_, and downtime, DT, required for hook-up and
                        Jrl
         testing of towers.
 (c)  Economic parameters:
     1.  Fixed charge rate,  FCR (see Section IV.C and Figure 7);
     2.  Unit capital cost of replacement capacity,  c  ($/kW);
     3.  Unit cost of replacement energy, e' ($/kW-hr) during outage
                                           J6
         due to hook-up and testing;
     4.  Unit cost of replacement energy, e  ($/kW-hr) after backfit-
                                           A/
         ting, and
     5.  Unit cost of fuel,  f ($/kW-hr of consumed fuel), water, c
             3               °  2                                 W
         ($/m ) and land, a  ($/m ).

Once this information has been gathered, the calculation of 1:he total
differential cost of backfitting can be carried out either by using
the computer program or by referring to the results presented graphic-
ally in the preceding sections.  Since the latter have been obtained
for a representative number of turbine types and meteorological con-
ditions, and presented in a normalized format, they can be used to
analyze a wide variety of power plants or units.  The general procedure
to be followed is described below:
(a)  Preliminary considerations:  The heat rate correction curves of
     the affected turbine should be examined to determine which one of
     the three model turbines (A, B or C) will best represent the
     affected unit.  Similarly,  the site meteorological data should
     be studied to establish which one of the four model sites  (Chicago,
     Los Angeles, Miami or St. Louis) will best describe the affected
     site.
                                  106

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(b)   Cooling tower data:  The procedure for the economic evaluation of
     backfitting becomes particularly simple when the physical size of
     the tower  is prescribed in the form of the pile length L and the
     pile height H, the pile width W being fixed at the standard value
     of 18 ft (5.49 m), since the various quantities of interest can
     then be determined directly from the example results.   As remarked
     upon earlier, however, cooling tower manufacturers do  not usually
     specify the physical size of the towers.  Instead, the size is
     implied by specifying the range and approach occurring with a
     specified water flow rate at a design wet-bulb temperature.  In
     order to make use of the example results it is then necessary to
     determine the corresponding physical dimensions of the towers of
     the type used in the example calculations.  This can be accom-
     plished either by requesting the relevant information  from the
     manufacturers or by inferring the physical dimensions  from
     Figure 12  (which assumes a fixed width, water loading, air load-
     ing, and thermal performance characteristics).  In the latter case,
     the length, height and the total water flow rate can be determined
     when the range, approach, reference heat rejection rate and design
     wet-bulb are given.

(c)   Capital costs and performance data:  The example results can now
     be used to find capital cost of the cooling towers and associated
     equipment, and also the capacity loss, energy loss, excess fuel
     consumption and water evaporation as follows:
          Given L and H, read Figure 11 to find the number  of tower
                                                                 *
          units, TU.  Alternatively, given the range, approach, Q  and
          T  , read Figure 12 to find L and H, and then read Figure 11
           wb
          to find TU.   (Note that, in this case, the rating factor
          can be found from the manufacturer's charts, such as those
          shown in Figure 10, and TU determined from equation  (21)
          using the specified water flow rate in gpm.  Figure 12 should
          nevertheless be used to find L and H since this information
                                   107

-------
           is required for the subsequent analysis.)
           Determine the capital cost of the towers, C   from equation
                                                     c s
           (22) using the appropriate unit cost c.
           Given L, determine the total water flow rate from Figure 12.
           Hence, read Figure 13 to find the pump and pipe system cost,
           C   .
           PP
           If new condensers are to be used, determine the required sur-
           face area A  from Figure 14 and the cost C  from equation
           (23) using the appropriate unit cost c  .
                                           *     c
           Determine additional land area requirement based on desired
           criterion.  If noise level is important, see Ref., 7  (Vol. I,
           Appendix G).   (Alternatively, use equation  (24) or other
           site-dependent criterion),.,
                 *
           Given Q  and H, read Figure 16 to determine the reference
                  *              '                                  *
           length L  of towers.  Calculate the normalized length L/L .
                  *
           With L/L  and H known, determine the normalized capacity loss
               *                                                   *
           (C /P ) from Figure 25, the normalized energy loss  (E /PE )
            Li                                                  L
           from Figure 26, the normalized excess fuel consumption
                *                                       •        r
           (F_/PE ) from Figure 27 and the normalized water evaporation
            E  *
           (W_/Q ) from Figure 28.  Hence find C , E , F  and W  .
            L                                  , L   L   E      L

 (d)  Final economic evaluation:  The above information, along with the
     quantities specified initially, can now be used in the equation
     given in Appendix I to evaluate the total cost of backfitting the
     power plant with a cooling tower of dimensions L and H.
The procedure outlined here is further demonstrated by taking  a  hypo-
thetical test case in Section V.H.

G.  THE COMPUTER PROGRAM
The computer program which accepts any set of numerical values for the
                                  108

-------
various parameters and performs the calculations outlined in the pre-
vious sections is listed in Appendix III.  The thermodynamic models
used to simulate the performance of cooling towers are basically the
same as those developed by Croley, Patel and Cheng [15] for the wet
portion of dry-wet combination towers, but there are a number of impor-
tant differences in other respects.  In particular, the economic con-
siderations are formulated specifically for the analysis of backfitting
an existing power plant or unit with mechanical-draft wet cooling
towers and cannot be used, without modification, to study the design
of towers for new plant or units.

The computer program consists of the MAIN program and seven subroutines,
namely OPECOS, MODELW, NTUCAL, RATFAT, FAN, FOGSEN, and POWERS.  The
MAIN program reads all inputs, calculates the overall capital and total
costs, and controls the printout of these quantities.  The inputs,
along with the symbols and units used, are listed in Appendix II, and
a typical output is shown at the end of the program listing in Appendix
III.  The primary functions of the various subroutines are as follows:

     OPECOS:  This subroutine evaluates the annual operating costs by
              summing the various costs associated with each set of
              meteorological conditions  (see equations (27) through
                                       •
              (29).
     MODELW:  This subroutine determines the turbine operating point
              (PrQ) on the heat rejection rate characteristics by
              matching the heat rejected from the turbine with the
              cooling capacity of the towers.  These calculations are
              performed for each set of meteorological conditions.
     NTUCAL:  This subroutine contains the basic thermodynamic model of
              evaporative cooling. Given the ambient meteorological
              conditions, the heat transfer coefficients for the pile,
              the air- and water-loading used, the hot-water temper-
              ature, the output is the cold-water temperature and con-
              sequently the rate at which heat is rejected from the
                                  109

-------
              towers.  This calculation is nested in an iterative cycle,
              controlled by MODELW, in which the cooling tower perform-
              ance is matched with the turbine performance.
     RATFAT:  Here the rating factor charts (Figure 10) are used to
              find the rating factor corresponding to a given set of
              range, approach and design wet-bulb temperature.  This
              subroutine is used only once, in the evaluation of the
              capital cost via the tower-unit method.
     FAN:     Here, the specified fan characteristics are used to find
              the fan horsepower corresponding to the given air flow
              rate  (determined by the air-loading and the face area of
              the towers) and a prescribed pressure drop.
     FOGSEN:  This subroutine can be used to calculate the "amount of
              fogging" that may result at each set of meteorological
              conditions.  Three different fog-sensitivity parameters
              are calculated.  This particular feature of the program
              has not been used in the present study but has been re-
              tained in the listing for future reference.  Further
              details are given in the report of Croley, Patel and
              Cheng [15],
     POWERS:  This subroutine calculates the turbine throttle setting
              T  corresponding to the operation point  (p,Q) on the
               O
              turbine heat rejection rate characteristics.  Equation
              (3) is then used in the MAIN program to calculate the
              power P from the heat rejection rate Q and the
              throttle setting T .
                                S

From the program outline given above, it will be clear that the MAIN
program and the subroutines OPECOS, MODELW and POWERS do not contain
any information concerning the type of cooling system that is consid-
ered.  They relate primarily to the economic analysis and the operating
characteristics of the turbine.  The fact that mechanical-draft cooling
                                  110

-------
towers are being analyzed is reflected only in the thermodynamic model
used in subroutine NTUCAL and by the presence of subroutines RATFAT,
FAN and FOGSEN.   (In fact, subroutines NTUCAL and FOGSEN refer only to
a particular crossflow evaporative pile and tower exhaust, respectively,
whether used in mechanical- or natural-draft towers.  Thus, these two
subroutines are used essentially unchanged for natural-draft calcula-
tions also.)  This particular arrangement was developed since it
greatly facilitates the adaptation of the program to study other closed-
cycle cooling systems considered later.  In subsequent sections, there-
fore, only the changes in the basic program will be documented.
H.  A HYPOTHETICAL TEST CASE
            /
1.  Consider a power plant with the following characteristics:
Nameplate capacity, P
Reference heat rejection rate, Q

Turbine type
Remaining life of plant
Existing condensers are to be retained
  so that salvage value of old conden-
  sers  (C1) and cost of new condensers
  (Cc) are both
Salvage value of pumps and pipes
  associated with open-cycle system
  (assumed to be 20% of new pumps
  and pipes), C1
               PP
Salvage value of other open-cycle
  system components, C'
Annual cost of makeup water
  with open-cycle, M1
Annual cost of blowdown treatment
  with open-cycle, B1
Site meteorological data similar to
      Design dry-bulb temperature,  T
                                     db.
                                             = 312.5 MW
                                             = 1.912 x 109 Btu/hr
                                               (2.017 x 10  kJ/hr)
                                             = A
                                             = 20 years
                                             =  0.20 C
                                                     PP
                                              =  0
                                              =  0
                                              =  0
      Design wet-bulb temperature,  Twb
MIAMI
89°F (31.7°C)
78°F (25.6°C)
                                   111

-------
  Extreme wet-bulb temperature, Twb      = 83°F (28.3°C)
  Frequency of occurrence of T, , T ,     = As in Table 3
Assume that this plant is to be backfitted with cooling towers
whose characteristics are:
Pile length, L
Pile height, H
A two-sided pile with
  one-side pile width, W
Water loading, per unit plan
  area of pile
Air loading, per unit face
  area of pile

Total water flow rate,
  GPM (=12.5 x 2 x L xw)

Fan diameter
Distance between fan centers, approx.
Number of cells or fans,
N(= INTEGER [400/32])
Unit cost of towers, c.
Unit maintenance cost, c
                        m
Concentration ratio
  (supply water:  100 ppm;
   maximum permissible:   330 ppm), k
Unit blowdown treatment cost, c.
   Cost of hook-up and testing, C

   Downtime, DT

Alternatively, Range    = 21.4°F
               Approach = 11.4°F
                              HT
             wb
                        = 78°F
                              ( 6.3°C)
                              (25.6°C)
  400 ft (121.9 m)
  45 ft (13.7 m)

  18 ft (5.49m)

  12.5 gpm/ft2   2
  (0.509 m3/min/m )
  1800
  (8790 Kg/hr/m )

  180,000 gpm
  (681.3 m /min)
  28 ft (8.53 m)
  32 ft (9.75 m)

  12
  $7.50/TU
  $200/cell/year
= 3.3
                   *
= $0.05/1000 gal
  ($0.0132/m )
= Assumed to be included
  in cost of towers
= 720 hrs (30 days)
Then, read Figure 12 to
obtain L, H and water flow
rate given above
                             112

-------
3.
It is assumed that the following economic parameters apply to the
affected utility:
Fixed charge rate  (20 years remaining
  life), FCR (from Figure 7)

Unit cost of replacement capacity
  (gas turbines), c
                   J6
Unit cost of replacement energy during
  downtime  (difference between pur-
  chase price and usual production
  costs), e'

Unit cost of replacement energy after
  backfit  (gas turbine; capital,
  operation, maintenance, etc.), e

Unit cost of fuel  (fossil), f
    Unit cost of water, c
                         w
    Unit cost of land, a
4.  Use of example results:

 (a) Use Figure 11 to find the number of
      tower units  (alternatively, given
      range, approach and design wet
      bulb, use Figure 10 to obtain
      the rating factor, multiply by
      GPM to find TO), TU

 (b) Refer to Ref. 7 to find the specific
      land area corresponding to a de-
      sired noise level  (60 dB, say)

    Thus, land area required,
      A, = 0.1 x 312.5
 (c) Read Figure  16 to find L
                                    *
    Determine normalized length, L/L

 (d) Read Figure  25  (turbine A, Miami)
      to find normalized capacity loss,
      CL/P*
    Thus, capacity loss
      CT = 0.0212 x 312.5 x 1000
       L
 (e) Read Figure  26  (turbine A, Miami)
      to find normalized energy loss,
      E./PE*
                                               0.179
                                             = $90/kW
                                         = $0.007/kW-hr



                                         = $0.01/kW-hr

                                         = $0.000751/kW-hr-th

                                         = $0.10/1000,gal
                                           ($0.0264/m )

                                         = $3000/acre
                                           ($7412.9/hectare)
                                         = 0.1770 x 10



                                         = 0.1 acres/MW


                                         = 31.25 acres
                                           (12.65 hectares)

                                         = 485 ft (147.8 m)

                                         = 0.825



                                         = 0.0212


                                         = 6625 kW



                                         = 0.0168
                                  113

-------
    Thus, energy loss,
      E  = 0.0168 x 312.5 x 1000 x 8760
       L
(f) Read Figure 27 (turbine A, Miami)
      to find normalized excess fuel
      consumption, nT F,,/PE
                    X  £>
    Thus, excess fuel,
      Fw= 0 x 312.5 x 1000 x 8760/0.85
       E
(g) Read Figure 28 (turbine A, Miami)
      to find normalized water
      evaporation, W_/Q*
                    L
    Thus, evaporation,
      WT = 8.33 x 1.912 x 10/3.413 x 10
    Also, blowdown, W,  = W  —-
                     b    L  *
    And, makeup,
  = W
                            k  - 1
                            W
                          = 46.00 x 10  kW-hr/year
                          = 0
                          = 0 kW-hr/year
                            8.33 acre-ft/yr/MW-th
                            (1.03 x 10 m /yr/MW-th)
                            4667 acre-ft/year
                            (5.757 x 106 m3/year)

                            2030 acre-ft/year
                            (2.504 x 10  m /year
  6697 acre-ft/year
  (8.261 x io6 mVyear)
5.  Cost determination:

    Capital costs

    Cooling towers,

      C   = TU x e  = 0.1770 x io6 x 7.50
       cs         t
    Pump and pipe system
      (Figure 13 with known GPM),  C
                                   PP
    Pump and pipe system salvage,
      C1  = 0.2 C
       PP        PP
    New condensers,  C
                     c
    Salvage value of old condensers, C'
                                      c
    Salvage value of other open-cycle
      component s, C'
                   o
    Hook-up and testing cost,  C
                               HT
    Additional land, A a  = 31.25 x 3000

    Replacement capacity,
      CCR =
6625 x 90
= $1,327,500


= $1,656,000


= ($ 331,200)

= $    0

= ($   0    )


= ($   0    )

= included  in  tower  cost

= $   93,750


= $  596,250
                                  114

-------
Downtime ,
       - DT x P  x e,

       = 720 x 312.5 x 1000

                   x 0.007               = $1,575,000
      TOTAL ANNUAL OPERATING COST, OC
              TOTAL CAPITAL COST, CC ,    = $4,917,300
Operating costs/year
Excess fuel cost,
  °CEF * Vc
       = 0 x 0.000751                    = $
Replacement energy cost,
      = 46.00 x IQ  x o.Ol               = $  460,000

Supply water cost,
  W c  = 6697 x(3.259 x lo )
   m w

        x 0.1/103                        = $  218,255

Cost of blowdown treatment,
  W.c.  = 2030 x  (3.259 x 10 )
   b a

        x 0.05/103                       = $   33,079

Maintenance of towers,
  C  = N6  = 12 x 200                    = $    2,400
   m     m

Makeup water cost with open-cycle
  system, M1                             = ($   0    )

Blowdown treatment cost with
  open-cycle system, B1                  = ($   0    )

Maintenance cost of open-cycle
  system, C1                             = ($   0    )
           m                                    _
                                         = $  713,734
Total costs
From equation  (20), the total excess unit cost due to

  backfitting, tc, is given by
                               115

-------
            PC + CC x FCR
         ~    8760 x p*
            713,734 +  (4,917,300 x Q.179)
                8760 x 312.5 x 1000
       tc =   0.5822 mills/kW-hr
 The costs  in the above equation are seen to be close to the results
 given by the computer calculations included in Appendix III
 (OC = $714,691/yr, CC = $4,916,361. ;   tc = Q.5825 mills/kW-hr) .

 J.  EXAMPLE OF A VARIABLE LOADING PATTERN
 A general  discussion of the treatment of a variable loading pattern is
 presented  in Section IV.D.  A hypothetical example for the purpose of
 illustrating differences with the idealized full-throttle loading
 pattern is now given.  The mechanical-draft wet cooling tower problem
 of the preceding section was rerun, employing the computer model in
 Appendix III, with a variable loading pattern.  To summarize the
 features of this pattern, the full-throttle was maintained for about
 55% of the meteorological conditions  (when possible) and a 0.7 throttle
 opening was maintained for the rest of the meteorological conditions
 (when possible).  The actual loading pattern considered is given in
 Table 7.   It is not implied that the variable loading pattern is
 practical  or realistic, and it is considered merely for illustration.

 The summary results of these calculations appear in Appendix III,
 following  those corresponding to the example calculations for the
 full-loading pattern.  Several interesting differences in the results
 are worthy of comment here and are summarized in Table 8.  The values
presented  in the table are from the computer calculations.

The excess fuel consumption is nearly zero for the full-throttle case
while definitely nonzero for the reduced loading pattern.  This differ-
ence is due to the change in the open-cycle fuel consumption with the
                                  116

-------
                           Table 7.  VARIABLE LOADING PATTERN FOR MECHANICAL-DRAFT WET



                                              COOLING TOWER EXAMPLE
                      Wet Bulb Temp, Twb °F  (°C)
fraction of full loading

(frequency of occurrence)

20-30
30-40
(t-l.l]-4.4)
40-50
(4.4-10.0)
50-60
(10.0-15.6)
60-70
(15.6-21.1)
70-80
(21.1-26.7)
80-90
(26.7-32.2)
90-100
(32.2-37.8)
100-110
(37.8-43.3)
I Bi
O *- •
ro 1
O rs-
CN i
VD
0.0















«»•••*
•
o 7
o •
ro rH
1
' T.f

0.7
(0.0003)
0.7
(0.0027)











0
0 •
m o
1 H
O 1
«



0.7
(0.0084)
0.7
(0.0200)
0.7
(0.0033)







VD
o in
VO H
ii
in •
o
i-H





0.7
(0.0283)
0.7
(0.0570)
0.7
(0.0146)
0.7
(0.0002)



H
O H
77
O VD
VD •
in
H







0.7
(0,0838)
0.7
(0.1945)
0.7
(0.0333)
0.7
(0.0001)

O VD
OOCN
0 H
CN








'
1.0
(0.2667)
1.0
(0.2632)
1.0
(0.0064)

CN
O CM
tT> CO
1 1
o r-
00 •
VD
CN











1.0
(0.0092)
1.0
(0.0078)

00
o r-'
O ro
H 1
1 CN
O •
Ol CN
ro















0.0
u
o
E?
 M
 Q

-------
  Table 8.  COMPARISON OF SELECTED RESULTS FROM THE MECHANICAL-DRAFT
       WET COOLING TOWER EXAMPLES FOR DIFFERENT LOADING PATTERNS

excess fuel
consumption
energy loss
water
evaporation
blowdown
total capital
cost
total differential
annual
operating cost
total
differential
unit cost
Full -throttle loading
0
46086 MW-hr
4668 acre-ft /yr
(5.758 x lo6 m3/yr)
2030 acre-ft /yr
(2.504 x io6 m3/yr)
$ 4,916,361
$ 714,691 /yr
0.5825 mills/kW-hr
Variable loading (Table 7)
6.829 MW
27388 MW-hr
4230 acre-ft /yr
(5.218 x io6 m3/yr)
1839 acre-ft /yr
(2.268 x 10 6 m3/yr)
$ 4,443,861
$ 549,083 /yr
0.5671 mills/kW-hr
reduced loading, resulting in an increase in the excess fuel consump-
tion.  The energy loss, water evaporation, blowdown,  and total differ-
ential annual operating costs are all greater for the full-throttle
operation than for the reduced loading, as expected.   More power is
produced under full loading, which is expected to generally increase
all of these absolute quantities (as compared to the  relative quantity
of excess fuel consumption).  The decrease in the total capital cost
for the variable loading pattern reflects the difference  in the energy
loss during downtime because of operation at a lower power level.   It
is interesting to note that in this comparative example,  the variable
loading pattern exhibits a 23% decrease in differential operating
                                 118

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costs and a 9.6% decrease in capital costs consequent with lower tur-
bine output.  However, the decrease in the total differential unit
cost is only 2.6% because it is prorated with respect to a larger
annual energy output.

Even though it is not used in the present study, the capacity factor
may be computed from the variable loading pattern given in Table 7.
The capacity factor, CF, which is the ratio of the annual design
power output (power demand) to the maximum possible annual power
production, is computed as the sum of the products of the fraction
of full loading multiplied by the corresponding frequency of occurence
over all meteorological conditions.  For the variable loading pattern
under consideration, CF = 0.834.
                                  119

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                              SECTION VI
                   NATURAL-DRAFT WET COOLING TOWERS

As  is true for the mechanical-draft wet cooling tower, already dis-
cussed in Section V, the amount of cooling obtained with an evapora-
tive, natural-draft cooling tower depends primarily upon the ambient
wet-bulb temperature, the temperature of hot water entering the tower,
and the size and thermodynamic characteristics of the "wet pile" inside
the tower.  Furthermore, since the air flow is generated by the differ-
ence in air densities inside and outside the tower shell, and not by a
fan, the air-flow rate and hence, the tower performance is also depend-
ent on the ambient dry-bulb temperature of the air.  As is true for
mechanical-draft towers, much of the empirical information on the
design and heat transfer properties of natural-draft towers is re-
garded as proprietary by the manufacturers for obvious reasons.  An
attempt is made in the present study to develop a methodology that is
capable of accepting any set of design parameters so that the perform-
ance of towers of different designs can be analyzed.  Detailed example
results are then presented for a particular set of input parameters
which were obtained through the cooperation of a leading manufacturer
of  crossflow cooling towers.  These example results therefore apply
to  CROSSFLOW, NATURAL-DRAFT WET TOWERS.  It is believed, however, that
equipment designs are not so radically different that the applicabil-
ity of the example cost information is limited to the product of a
single manufacturer.

A significant number of comments which are applicable to cooling
towers or to closed-cycle cooling systems in general have already
                                 120

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been listed in Section V.  Therefore, this and the two succeeding
sections will follow the format of Section V closely with reference
to relevant comments made therein.  As is true for the other closed-
cycle cooling systems, the physical size of the natural-draft tower
                                            »
will be different in a backfit situation than for a new plant due to
the economic peculiarities of the backfit situation.  Throughout this
section  (as with other closed-cycle cooling systems), the physical size
of the tower is regarded as a primary variable so that the various
quantities of interest  (as outlined in Section V) can be calculated
for a range of sizes.  These quantities are then to be used in con-
junction with the economic considerations outlined in Section IV, to
identify the project costs.

A typical natural-draft, crossflow, evaporative cooling tower is
shown in Figure 29 where it is seen that the overall tower structure
consists of an annular evaporative pile about the bottom circumference
of a tower shell.  For structural reasons, the shape of the tower shell
is prescribed by the equation of a hyperboloid.  Thus, the physical
size of a tower is specified by the width, W, and height, H, of the
evaporative pile; by the shell height, S; the height of the "throat"
section of the shell, T, and by the diameters of the shell at the
           4
bottom, D , and throat, D  .  These six parameters can be used as
primary indicators of the physical size of the cooling tower.  However,
so many variables make example calculations intractible.  Therefore, a
"standard shell shape" is assumed  (Figure 29) which is used by one
major cooling tower manufacturer and is believed to be representative
of most shell shapes employed in the United States.  The ratios of
the shell dimensions portrayed in Figure 29  (r  = T/S, r2 = D2/Di and
r3 = S/D.,) as actually used in tower construction are proprietary
information.  However, if these ratios are known, the physical size
of a tower can be specified by three variables W, H, and S together
with the equation of the hyperboloid.  These quantities are used as
the primary variables in the example calculations which follow.  It
will be clear that H is the length of the water path and is a measure
                                   121

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WATER
OUTLET
             Figure 29.   Hyperbolic natural-draft crossflow,
                         wet cooling tower
                                 122

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of the pumping height required.  Also, W is a measure of the length
of the air path and therefore will influence the air-flow resistance.
Furthermore, the shell height, S, determines the overall shell di-
mensions and will influence air flow both by determining reference air
density at the top and by its "pipe flow" resistance.  It is important
to remember that the air flow rate is a complex function of shell
geometry and the thermodynamic properties of the evaporative pile.

For a given air-flow rate, water-flow rate, dimensions of the fill,
empirical heat-exchange coefficients of the fill, and hot-water temp-
erature, the basic theory of Merkel [9,10,11,12,13,14,15] can be used
to calculate the temperature of the cold water, the temperature and
humidity of the exit air, and the heat rejection rate from the cooling
water through the pile.  In fact, these calculations exactly parallel
those for the evaporative pile of the mechanical-draft crossflow tower
as already described by Croley, Patel and Cheng [15] for a given air-
flow rate.  Of course, the dimensions and heat exchange coefficients
of the pile are different, but the calculations are the same.  However,
an additional complication arises due to the wide fluctuation in the
air-flow rate with air temperatures, water temperatures, and heat
rejection rate for a given tower design.  In actuality, the air-flow
rate determines the heat rejection rate, cold-water temperature, and
pile and shell flow resistance.  In turn, air-flow rate is determined
by the inside air temperature and humidity, outside air temperature
and humidity, and pile and shell friction losses.  Therefore, the
joint determination of air-flow rate and heat rejection rate are nec-
essary to determine operation characteristics of a given tower design
at specified values of the air dry- and wet-bulb temperatures and
hot-water temperature.  This joint determination is described shortly.
First, several basic models are described which are necessary for the
joint determination.  Then, the basic calculation of heat rejection
rate, cold-water temperature, and air-flow rate for a given tower
design and specified meteorological conditions are described.
                                   123

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 A.  OPERATION MODELS FOR NATURAL-DRAFT, CROSSFLOW, WET COOLING TOWERS
 The operation of the natural-draft cooling tower depends heavily, as
 already mentioned, on the air-flow rate, which in turn depends upon
 ambient dry- and wet-bulb air temperatures, the hot-water temperature
 and the heat rejection rate for a given tower design.  As the air
 passes through the tower, it experiences frictional head losses in
 flowing through the pile and through the shell.  Plots of the pressure
 drop  of the air flow through the pile as a function of the air-flow
 rate  loading are made by manufacturers; see e.g., Figure 30.  Such
 proprietary information establishes the flow resistance through the
 pile.  The hyperbolic shell can be considered approximately as a large
 circular  cylinder of the same height with some mean diameter.  This
 diameter  is calculated as that which yields the same cylindrical
 volume as contained in the hyperbolic shell.  Such expressions have
 been  used elsewhere [18] for simplification of geometries.  Air flow
 through this equivalent cylindrical shell can be approximated as in-
 compressible pipe flow.  Therefore, the Darcy-Weisbach friction factor
 can be found from standard hydraulic charts as a function of the
 Reynolds  number and the relative roughness of the pipe (assumed to be
 zero, representing a smooth pipe since the diameters are large).
 Both  of these frictional head losses can then be combined to give an
 overall head loss coefficient, K as follows:

                    K = (H + I )  ^|                              (35)
                              P   V2

 in  which  K = overall head loss coefficient, & = frictional head loss
 in  the shell (ft of air), H  = frictional head loss in the evaporative
pile  (ft  of air)  and V = average velocity of air in the tower cylinder
 (ft/sec).

The model for calculation of the air-flow rate for given values of the
ambient dry- and wet-bulb temperatures, the hot-water temperature, the
tower resistance coefficient, K, and a given design can be described
                                  124

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                          PILE  CHARACTERISTICS
                              (PROPRIETARY)
                    POINT  A
                                       HOT-WATER
                                       TEMPERATURES
                       INCREASING  K
     AIR FLOW  RATE  LOADING  ON FACE  AREA  OF  PILE

                          (cfm/ft2)
           Figure 30.  Pile characteristics curve and

                    air flow rate calculations
                             125

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as follows:
     1.  Calculate the air pressure at the top and bottom of the shell
         as a function of air temperature, assuming a "standard
         atmo spher e"  [19];
     2.  Calculate the humidity and density of the incoming
         ambient air;
     3.  Assume that  the exit air temperature is equal to the
         ambient dry-bulb temperature as a first approximation;
         assume air-flow rate is zero as a first approximation;
     4.  Calculate the exit air density at the exit air temperature
         assuming saturation;
     5.  Calculate the air-flow rate through the tower using the
         Bernoulli equation for incompressible flow with no energy
         inputs [20]  and K;
     6.  If the air-flow rate of step 5 is sufficiently close to the
         previous value, stop, otherwise proceed;
     7.  Calculate the cold-water temperature and heat rejection
         rate from the pile using this air-flow rate and standard
         thermodynamic models [15];
     8.  Assume that  the exit air temperature is equal to the average
         of'the hot-  and cold-water temperatures [21,22]; and
     9.  Go to step 4.
Although the use of the Bernoulli equation in step 5 and the assumption
of step 8 are simplifications, they were made in the interest of
brevity and have been used elsewhere in design applications [20,21,22].
More complete thermodynamic balances are presently under research.

The procedure just identified above is referred to as subroutine
AIRFLR in the computer model listings in Appendix IV.  The use of this
model can be made for any value of K for a given set of meteorological
conditions, hot-water temperature and a given tower design.  However,
the values of K for different tower designs are not readily available
information.  Thus, a second model for determination of the tower
                                  126

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resistance parameter, K, for given values of dry- and wet-bulb temper-
atures and hot-water temperature can be described as follows:
     1.  Specify dry- and wet-bulb temperatures and hot-water
         temperature;
     2.  Arbitrarily pick a "K" value;
     3.  Solve for air-flow rate using subroutine AIRFLR;
     4.  Calculate corresponding pile losses, I , using K, I  and
                                               P
         the air-flow rate  (see equation 35);
     5.  Plot £  on pile characteristics chart as in Figure 30  and
     6.  Repeat steps 3 through 5 for selected values of "K" until
         a point is found  (in Figure 30) corresponding to the flow
         characteristics of the pile  (point A).
In general, it is found from this procedure that points corresponding
to these calculations have associated K values which are small for
high air-flow rates and large for low air-flow rates.  Thus, the lines
cross the pile characteristics curve somewhere, and the associated K
value indicates the equivalent tower resistance parameter for this
pile and shell.  This calculation can be repeated for other values of
hot-water temperature and air dry- and wet-bulb temperatures; see
Figure 30.  However, in the preliminary studies conducted under this
research, it has been observed that the selected value of K does  ,.
not change greatly.  Thus, the pile characteristics curve in Figure 30
represents a nearly constant K value, as is expected.  Furthermore, K
values of the order of 20 to 30 are observed.  The resulting air-
flow rate, pressure drop, and tower cooling rate fluctuate very narrow-
ly for variations of the K values in this range.  Thus, it is deemed
sufficient to perform the calculations  (in the procedure just pre-
sented) for a few air and water temperatures, selected to cover the
range of the pile characteristics curve in Figure 30, and then take
the average selected K value as the best estimate of the overall tower
resistance parameter for use at any conditions.  This entire procedure
is represented as subroutine BESTK in the computer model listings in
Appendix IV.
                                   127

-------
 In  the operation models for this tower configuration, the subroutine
 BESTK is used to initially find the best "K" value for use in all
 subsequent calculations, for a given tower design.  Then for any
 specific set of meteorologic conditions and hot-water temperature,
 subroutine AIRFLR is used to jointly determine the resulting air-flow
 rate, cold-water temperature and heat rejection rate, using the best
 "K" value.  Other thermodynamic models and calculations are similar to
 those already described [15].  The economics models are also presented
 in  Sections IV and V.

 B.  CAPITAL COST OF TOWERS AND AUXILIARY EQUIPMENT
 As  with the case of mechanical-draft crossflow cooling towers, the
 capital cost of a natural-draft crossflow cooling tower will be deter-
 mined primarily as a function of its size as represented by the para-
 meters H, W, and S.  Again, however, manufacturers of such cooling
 towers recommend sizing and pricing procedures which bear no direct
 relation to the physical size of the tower.  Instead, the cost of a
 tower is linked to the "design" meteorological conditions (here the
 relative humidity is determined from the design values of dry- and
 wet-bulb temperature) and parameters describing the overall performance
 of  the tower at these design conditions, notably the RANGE and APPROACE
 As  mentioned earlier the rating-factor tower-unit method [16] and the
 K-factor method [17] are examples of such procedures for the mechan-
 ical-draft tower.  Also contained in Ref. 16 is a similar procedure
 for natural-draft crossflow towers.  The manufacturer presents charts,
 such  as those in Figure 31, from which a unit cost  (presumably in
 1970 dollars per thousand Btu/hr) can be found for any given range,
 approach and relative humidity.  The total capital cost can then be
 determined by multiplying the unit cost times the heat rejection rate
 of  the turbine (in thousand of Btu/hr).  From an analysis of previous
 experience, Dickey and Gates [16] have found that the scatter associ-
ated with use of the curves may be ±9%.  Recent correspondence with the
manufacturer places this scatter at about ±15%.
                                  128

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l\\\\\ \2\  \   \3 \
 30\26\22\ 18  16  14   12
                                                    25  RANGE
                                                    100 % RH

                                                      80
                      28 24  20
         \
          10
                         APPROACHES
                                                        0
'fMfli^'1 li *'**'*

 \\l\\\ \\ 2
30\ \24\20\  IS \
 28 \  22  18    14
   26
                                       \
                                                                               12

                                                                 10
                             TOWER  COST-DOLLARS PER THOUSAND  BTU/HR
to
      UJ
                                                \
                                                12
                      30\26 \ 22 20  18
                        28  24
    14
16
             25  RANGE
             50 % RH

               80
                                                                APPROACHES
                                            \l\\\\\2\   \   3\       4
                                            50 \26\22\ 18  16   !4    12
                                                24  20
                               \
                                10
                             TOWER COST-DOLLARS  PER THOUSAND BTU/HR


                   Figure 31.  Typical cost-performance curves for budget estimates

                              for the natural-draft crossflow cooling tower (1970
                              dollars)  [16]

-------
 As discussed by the manufacturer [16], these curves were intended
 only  for preliminary budget estimates.  Economic factors related to
 each  geographical location must be considered, including escalations
 for lead time, allowance for wind loading requirements, and special
 site  preparations.  The curves are suggested for relative evaluations,
 but also serve as initial estimates when updated appropriately.

 In order to proceed further and establish a capability for handling
 towers of different designs, it is necessary to return to a more basic
 approach in which the Merkel theory is used to predict the amount of
 cooling delivered by a tower fill of given type and dimensions.  Such
 a procedure is similar to that described in detail in Ref. 15 and will
 not be repeated.  There it is shown that when the dimensions  (W, H,
 and length, L = TT (D, + W)) and heat transfer coefficients of the fill
 are specified, it is possible to calculate the cold-water temperature,
 and therefore the heat rejection rate, range, and approach, for any
 given set of values of the hot-water temperature, air- and water-flow
 rates and ambient wet-bulb temperature.  When the calculations are
 performed, using the models for air-flow rate described in the pre-
 ceding section, for the design dry- and wet-bulb temperatures over a  . '
 range of values of the design heat rejection rates and tower dimensions,
 and use is made of the unit cost procedures already described, it is
 possible to calculate capital costs as a function of the tower dimen-
 sions as shown in Figure 32.

 These results were obtained using a known (proprietary) set of heat
 transfer coefficients, air- and water-loadings on the pile, and pile
 resistance.  A fixed fill width, W = 21 ft = 6.40  m, had to be used
 since the available pile resistance data were restricted to that par-
 ticular value.  It should be emphasized that Figure 32 results from a
large number of calculations performed using a range of values of heat
rejection rate, fill height and fill length, and a number of values of
the design dry- and wet-bulb temperatures.
                                  130

-------
      25
                  50
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   11.0
   10.0
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    SHELL HEIGHT, S (m)

 75         100
-1 -- 1
                                                    125
                                                               150
175
   0.0
        100
                      200           300           40O

                                 SHELL HEIGHT, S (ft)
                                   500
            Figure 32.   Capital cost estimates  for the  natural-

                          draft  crossflow,  wet cooling tower
                                       131

-------
 For  each  set of conditions  (Q, L, H, Tdb , Twb ), the thermodynamic
 model of  the evaporative pile, described in detail in Ref. 15, was
 used to calculate the corresponding range and approach.  These values,
 in turn,  were used to find the corresponding unit costs from the charts
 shown in  Figure 31.  The total heat rejection rate was then used to
I
 find the  cost corresponding to the specified set of input conditions.
 For  each  set of design dry- and wet-bulb temperatures and pile height,
 the  cost  was found to be a function of the pile length (and hence the
 shell height using the shape of Figure 29), irrespective of the heat
 rejection rate.  A small scatter was observed between the results ob-
 tained with different design dry- and wet-bulb temperatures, and this
 is shown  by the shaded area in Figure 32.  While the scatter is some-
 what consistent, insofar as smaller costs correspond to lower design
 temperatures, its origin lies mainly in the fact that a highly complex
 phenomenon is being represented in a relatively simple form.  In any
 case, the scatter is small and well within the accuracy expected from
 the  various assumptions made in the thermodynamic model of evaporative
 cooling.   The most remarkable feature of Figure 32 is that the cost
 of the tower is primarily a function of the dimensions of the fill,
 and  hence the shell height, as was conjectured earlier.  Thus, for the
 estimation of the capital cost of natural-draft cooling towers, either
 Figure 31 or Figure 32 can be used, depending upon the information that
 is known.

 Estimates of the capital cost of the pump and piping system are made as
 a function of the water-flow rate, and Figure 13 is also used for that
calculation.  Comments on the condenser design are similar to the
mechanical-draft discussion, and equation (23) also applies for natural-
draft towers.

The additional land area required for backfitting with a natural-
draft evaporative cooling tower depends mainly upon the plan area of
the tower and possibly upon the consideration of an acceptable noise
level and other site-dependent conditions.  Unlike the criteria for
                                 132

-------
mechanical-draft towers, however, there are no problems of interference
and plume recirculation due to  the height of the natural-draft towers.

The EPA Development Document  [2, p.  631 ] suggests the allowance of a
clear area 100 ft  (30.5 m) wide around the natural-draft tower.  The
required land area, AL/ for a natural -draft wet cooling tower of bottom
diameter D   is therefore
                            = J- (D]L  +  2D)2                          (36)
where D, the width of  the  clear  area around the tower, may be 100 ft
 (30.5 m) according to  the  above  criterion or  some other value.  Other
land requirement  standards for natural-draft  towers given in Ref . 2
 (p. 631) include  the specification of  350 to  400 sq. ft  (32 to 37 sq. m)
per megawatt.

As for the mechanical -draft towers, land requirements for natural-
draft towers based on  acceptable noise levels have also been studied
in Ref. 7  (Vol. I, Appendix G) .   In the hypothetical test case pre-
sented in part H  of this Section, the  land area requirement is computed
on the basis of a noise level limit of 60 dBA; the width of the clear
area around the tower  is thus found to be D = 200 ft (61 m) .  The
additional land area requirement for this example may easily be
found from equation  (36) .
                                        *
C.  REFERENCE SIZE OF  COOLING TOWERS,  S
A number of quantities which characterize the operation of an existing
power plant or unit using  open-cycle cooling  was defined in Section IV
and part B of Section  V.   As in  Section V.B,  it is convenient to
define a reference size of the natural-draft  cooling towers for the
purpose of nondimensionalization.  For any given pile height, H,
                                                   *
and pile width, W, the reference size  of a tower, S  , can be defined
                                        *
as the shell height required to  reject Q  while maintaining the back
                               *
pressure at p  and delivering P   at some reference ambient dry- and
wet-bulb temperatures.  The reference  dry- and wet-bulb temperatures
                                  133

-------
 and p'  can be  selected arbitrarily without loss of generality.  In the
 example calculations, the pile width, W, is held constant at 21 ft
 (6.40 m), p'=l in. Hg abs  (2.54 cm Hg abs) and the reference dry- and
 wet-bulb temperatures are set equal to 78°F and 68°F  (25.6°C, 20.0°C)
 respectively.   It should be noted that these reference conditions are
 not necessarily the same as those adopted in defining the reference
 sizes of the other closed-cycle cooling systems; see e.g., Section V.B.
                                            *   *   *      *
 The reference  size of each cooling system (L , S , A  , or N ) is used
 only for nondimensionalizing the cooling system size, and, therefore,
 as long as the reference size is known (Figures 16, 33, 54, and 63),
 the proper economic assessment of the prototype cooling system can be
 made.   The reason for employing different sets of reference meteorolog-
 ical conditions is related to the peculiarities of each cooling system.
 For example, practical experience with the operating characteristics of
 natural-draft  cooling towers suggests the use of more extreme reference
 meteorological conditions.

                  *                                              *
 It is clear that S  can be found for any given set of values of Q
 and H using the theory of Merkel in conjunction with the known heat
 transfer properties of the condenser and the evaporative pile, and
 the water-loadings recommended by the tower manufacturers.  The com-
 putation construction outlined in Section V.B was also used with the
                                                               *
 natural-draft  models to calculate the reference shell height, S .
                                 2                   32
 With a water loading of 18 gpm/ft -plan area (0.733 m /min/m -plan
 area), and appropriate information concerning the heat transfer proper-
                                     *     it
 ties of  the fill, the dependence of S  on Q  and H is shown in Figure
 33.  It will be seen that the reference shell height is a nonlinear
             *                                                 *
 function of Q   and decreases with increasing H for a constant Q .
As in mechanical-draft towers, an attempt was made to use the refer-
                    *                                 '
ence shell height, S , to normalize the tower size so that the examjple
results could be employed to assess the performance of power plants
or units with different nameplate capacities and heat rejection
rates.   It is again important to emphasize that the foregoing consid-
erations apply regardless of the type of turbine that is employed
                                   134

-------
u>
U1
                     600
                                REFERENCE HEAT  REJECTION  RATE, Q* (I09 KJ/hr)

                                  1.0       2.0       3.0       4.0       5.0      6.0
                  £  500
                  X


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                  UJ
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                  UJ
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                     300
                  UJ
                  tr
                  UJ

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                  cc
                      100
                                  1.0        2.0       3.0       4.0        5.0       6.0

                                 REFERENCE  HEAT  REJECTION  RATE, Q* (10* Btu/hr)
                                                                                         175
                                                                                         150  -
125  o
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     X
100
75
                                                                                         50
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                                  Figure 33.  Determination of reference  shell height

-------
                                        «
 since the definition and evaluation of S  is independent of the
           *
 source of Q  .
D.  OPERATION OF A TOWER OF GIVEN SIZE (S,H)
When the width of the pile, W, is fixed,  the physical size of the
cooling tower is characterized by only two parameters, namely the shell
height, S, and the pile height, H.  In turn, all other dimensions
may be determined from these two, using the simplifications presented
at the beginning of this section.  For the example calculations
illustrating natural-draft towers, representative values recommended
by leading manufacturers will be used for the various quantities.
Following the procedure outlined in Section V.C and described in Ref.
15  (see Sections III.B, E, and F), the detailed operation of a turbine-
condenser cooling system may be found for any and all meteorological
conditions.  As with the mechanical-draft cooling tower, these models
were used with the natural-draft cooling tower to evaluate maximum
capacity loss, C , annual energy loss, ET, annual fuel "penalty", F ,
                L                       L                          E
and annual evaporative water loss, W , as described in Section V.C.
                                    L

E.  PARAMETRIC STUDIES
Detailed calculations of the type mentioned above were performed for
a range of values of the tower shell height and pile height.  The
results were nondimensionalized by again employing suitable scaling
parameters.  The tower shell height, S, was normalized with respect to
                             *
the reference shell height, S ; the capacity loss was normalized with
respect to the nameplate capacity; the energy loss and excess fuel
consumption were normalized using the maximum energy that can be
                      *
produced in a year, PE , and the water evaporation was normalized with
                                               *
respect to the reference heat rejection rate, Q .  Figures 34 through
37 show the variations of the normalized maximum capacity loss, the
normalized annual energy loss, the normalized annual fuel penalty, and
the normalized annual evaporative water loss with normalized tower
size for the particular case of turbine A (i.e., P  = 411 MW,
                                  136

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   0.8
   0.7
   0.6
    0.5
0.4
     822 MW
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    O.I
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                          I       I        I


                            LOS  ANGELES

                                TURBINE  A

                                 36%  EFF.


                      PILE HEIGHT, H   822 MW

                      42 ft ,12.80m


                      49ft, 14.93m
                      56 ft, 17.07 m


                      63 ft, 19.20 m
             o


             A


             a
                  0.8
1.2
1.6
2.0
            411 MW

              •


              A


              a


              g   •
2.4
                NORMALIZED SHELL HEIGHT, S/S



               Figure 34.  Normalized capacity loss
                                 137

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                                                2.4
                                  138

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                                   139

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                  140

-------
 *                                          *             Q
p  = 1.00 in. Hg abs = 2.54 cm Hg abs, and Q  =2.545 x 10  Btu/hr =
          9
2.686 x 10  kJ/hr for fossil-fuel operation, see Table 1) for the
meteorological conditions at Los Angeles  (Tables 4 and 5) .  Also shown
in these figures are the same results for a hypothetical turbine whose
nameplate capacity and reference heat rejection rate are twice those
of turbine A  (i.e., P  = 822 MW, Q  = 5.090 x lo9 Btu/hr =  5.372x 1Q9
kJ/hr) but whose basic heat rate characteristics are the same as those
of turbine A  (Figure 4) .  The observations presented in Section V.D
as comments  (a) through  (e) can also be made for Figures 34 through 37
regarding natural-draft evaporative cooling towers.  Furthermore, the
following two comments are also in order.
 (a)  The annual energy loss, E  , increases at a slightly higher rate
                              L
     than the maximum capacity  loss, C  , as compared to the mechanical-
                                      L
     draft results  (Figures 21  and 22) .  This difference is mainly due
     to the wide fluctuation of the air-flow rate in the natural-draft
     tower as compared to the constant air-flow rate of the mechanical-
     draft tower.  At extreme meteorological conditions, energy losses
     might be realized with the large natural-draft towers which may
     not occur with the large mechanical-draft towers.

 (b)  The nondimensionalizing process did not result in a complete
     collapse of all results into single curves (for both the 411 MW
     and 822 MW outputs) as they did for the mechanical-draft calcula-
     tions.  Furthermore, the problem cannot be resolved by redefining
                          *
     the reference size, S , used in nondimensionalizing the shell
     height, S.  All that can be accomplished with a redefinition of
     the reference size is to stretch and/or move the sets of curves in
     the horizontal sense only.  There would still be similar differ-
     ences between the two sets of curves in the vertical direction.
     The major implication of this difference is that for natural-
     draft cooling towers, there is an "economy of scale" operating.
     It is clear that the costs of capacity loss, energy loss, excess
                                  141

-------
      fuel consumption, and water loss are directly related to these
      quantities, and, therefore, the vertical axes of Figures 34
      through  37 may be interpreted as costs.  It is seen from the
      figures  that the unit costs decrease as the turbine size increases.
      Since  the unit costs are dependent upon the reference heat reject-
      ion rate, one would not observe a collapse in the results for
                                                   *                *
      calculations repeated with the same value of P  but different Q
      reflecting type Of unit  (fossil or nuclear) as with the mechanical-
      draft  towers  (see Section V.D).  Thus, the operating characteris-
      tic curves for natural-draft crossflow evaporative towers are
      dependent upon the turbine efficiency at reference conditions
        *   *   *
      (P , Q , P )•

 In view of  the discrepancies encountered in the calculations for nat-
 ural-draft  towers, as compared to mechanical-draft towers,, the follow-
 ing two departures from procedures established with the mechanical-
 draft example presentations are made.  The first procedural deviation
 is that all operating characteristics plots are based upon a dimen-
 sional tower  size.  There is no advantage to be gained in nondimen-
 sionalizing tower size as just discussed.  The second deviation is
 that all calculations are repeated for a second base turbine efficiency,
 HT = 28% (in addition to the assumed 36%) .  The example results can then
 be used by  applying two corrections, described in detail in Sections
 VI.F and VI.H.  Briefly, the corrections involve making coarse adjust-
 ments by means of interpolation or extrapolation to graphical presenta-
 tions of capacity loss, energy loss, fuel penalty, and water loss, with
 regard  to observed deviations due to differences in nameplate capacity
 and  turbine efficiency.  Because of the shape of these curves, a log-
 arithmic-linear interpolation/extrapolation procedure is employed.

 In order to build up a representative library of the operating char-
acteristics of natural-draft cooling towers, a parametric study was
conducted using the following information:
                                  142

-------
         Heat rate characteristics of turbines A, B, C
         (Figures 4, 5, 6);
         Meteorological data at Chicago, Los Angeles, Miami, and
         St. Louis;
         Base turbine ef f iciences, n  = 36% and 28%;
         Power levels of 822 MW and 411 MW for turbine A at Los Angeles,
As indicated in Sections IV and V, and above, these conditions are
expected to represent a majority of the situations which will be en-
countered in the consideration of backfitting across this country.
The final results are presented in Figures 38 through 53.

Comments on the operating  costs associated with the natural-draft
cooling towers are the same as in Section V.E with the exclusion of
items pertaining to the fans and fan requirements.  Also, the unit
maintenance costs for natural-draft towers are of the order of $1,000
to $3,000 per tower per year.  This figure was estimated by the
writers from considerations of mechanical-draft maintenance costs.
The actual figure will depend upon the particular tower design and
its size.  Maintenance costs found in the literature [23] appear to
be too large and probably  include other items such as pump operating
costs.

F.  PROCEDURE FOR THE ECONOMIC EVALUATION OF BACKFITTING
The various items which must be considered in the evaluation of the
cost of backfitting an existing power plant or unit with natural-draft
wet cooling towers have been described individually in the preceding
sections.  The manner in which these items are to be combined in order
to calculate the total cost of backfitting is presented in this part
followed by a brief description of the computer program that has been
developed for this purpose.  A hypothetical test case is presented
in part H to illustrate the general methodology and use of the graph-
ical results.  Reference will be made to related portions of the
preceding Sections where indicated.
                                  143

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   SHELL  HEIGHT, S (ft)
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           Figure 38.  Variation of normalized capacity
                       loss with shell height and plant
                       capacity, 36% turbine efficiency
                            144

-------
            SHELL HEIGHT, S (m)
                    100          150
                      LOS  ANGELES
                          TURBINE A
                          36%  EFF.
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   100
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Figure  39.  Variation of normalized energy
           loss with shell height and plant
           capacity, 36% turbine efficiency
                         145

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           Figure 40.  Variation of normalized excess fuel

                      consumption with shell height and

                      plant capacity,  36%  turbine efficiency
                              146

-------
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                              148

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                                   149

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                                   151

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                                           152

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                                        154

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                                         155

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                                          160

-------
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 -0.14
    -0.16
    -O.I 8
   -0.20
   -0.22
   -0.24
       100
            50
            —IT-
                              SHELL HEIGHT, S(m)


                        100 (TURBINE A)
                     50
                                    100
                               r/S  f

                               if/    I

                              II   I
                             III
63

56'

49'

42'
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                                                   150
                                                                 200 (TURBINE B,C)
                         200
             200  (TURBINE  A)
                                                          MIAMI

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                         '63 ft, 19.20 m


                         '56ft, 17.07m

                         . 49 fl, 14.93m


                         .42 ft, 12.80m
                                           1
                                        400
                                  SHELL  HEIGHT, S (ft)
                                   600 (TURBINE B,C)
             Figure  48(c).   Normalized excess fuel  consumption,

                               36%  turbine efficiency, Miami
                                           162

-------
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  -0.04
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                        200
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                                          63 ft, 19.20 m
                                          56ft, 17.07m
                                          49ft, 14.93m
                                          42 ft, 12.80m
                                                                 200 (TURBINE B,C)
                                                        ST. LOUIS
                                                          36% EFF.
                                       400
                                 SHELL  HEIGHT, S (ft)
                                                            _L
600  (TURBINE B,C)
            Figure 48(d).  Normalized excess fuel consumption,
                             36% turbine efficiency, St.  Louis
                                         163

-------
                                                            o
                      50
                                SHELL  HEIGHT, S (m)


                                    100           ISO
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                                          J_
                         200              400


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                                                                  m

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                                                            10,000
                                                            8000
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                   Figure 49(a).  Normalized evaporation,  36%

                                    turbine efficiency, Chicago
                                          164

-------
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                            SHELL  HEIGHT, S (m)

                                100           ISO
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                                   LOS  ANGELES
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                                                        12,000
                                                        10,000
                                                       8000
                                                       6000
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                                                              10,000
                                                             8000
                                                             6000
                                                       4000
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                      200             400

                               SHELL HEIGHT , S (ft)
                                                     600
              Figure 49(b).
                              Normalized  evaporation, 36%

                              turbine efficiency, Los Angeles
                                     165

-------
                   50
                             SHELL HEIGHT, S (m)


                                 100           150
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                     200             400


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                                                        10,000
                                                       8000
                                                       6000
                                                              12,000
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           Figure 49(c).  Normalized  evaporation, 36%

                            turbine efficiency,  Miami
                                       166

-------
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                             SHELL  HEIGHT, S (mi

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          63 ft, 19.20m

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          49 f t, 14.93 n>—,
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                                                           12,000
                                                           10,000
                                                           8000
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                       200              400


                                 SHELL HEIGHT, S (ft)
                                                         600
              Figure  49(d).
                                Normalized  evaporation,  36%

                                turbine efficiency, St.  Louis
                                         167

-------
0.24
                50
                           SHELL HEIGHT, S (m)

                             100           150
                             200
                  200
          Figure 50(a).
        400
SHELL HEIGHT, S (ft)
600
Normalized  capacity loss,  28%
turbine  efficiency, Chicago
                                  168

-------
   0.24
                     50
SHELL  HEIGHT, S (m)

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                                                    o
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                                                        49'
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               Figure 50(b).
                        42ft, 12.80 m


                       [V49 ft, 14.93 m


                        S6 ft, 17.07 m

                       S63ft, 19.20 m
                           ,42'
                           -49'

                           -56'

                           '63'
         400

SHELL HEIGHT, S (ft)
                                                          600
Normalized capacity loss, 28%
turbine efficiency, Los Angeles
                                      169

-------
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                         63 ft, 19.20 m
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              Figure 50(c)
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SHELL  HEIGHT, S (ft)
                                                          600
Normalized  capacity loss,  28%
turbine efficiency, Miami
                                        170

-------
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                               SHELL HEIGHT, S (m)

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                                                    63ft,19.20m
                                     _L
                       200
                                    400

                            SHELL  HEIGHT, S (ft)
                                                        600
          Figure 50(d).
                              Normalized capacity  loss, 28%

                              turbine  efficiency,  St.  Louis
                                   171

-------
                                 SHELL HEIGHT, S (m)
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                           SHELL HEIGHT, S (m)
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                             100
                                           150
                                     200
                                              TOTAL (INCL.  PUMP)
                                                  56 f t, 17.07 m
                                                  63ft, I9.£0m
                                                  42'
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                                    400

                            SHELL HEIGHT , S (ft)
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              Figure 51(c).   Normalized  energy loss,  28%
                              turbine efficiency, Miami
                                 174

-------
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 0.18
 0.16
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                                                       	1	


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                                                         28% EFF.
                                              TOTAL (INCL. PUMP)
                                                       — 42 ft, 12.80 m

                                                         49ft, 14.93 m
                                                         56 ft, 17.07 m
                                                         63 ft, 19.20 m

                                                         42'

                                                         49'
                                                         56'
                                                         63
                    200               400

                              SHELL HEIGHT, S (ft)
                                                           600
            Figure 51(d)
                                Normalized  energy  loss, 28%

                                turbine efficiency,  St. Louis
                                         175

-------
                             SHELL HEIGHT, S 
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                           100 (TURBINE A)

                                   100
                                                 ISO
                       200
               200  (TURBINE A)
63ft, 19.20m
56 ft, 17.07m
49ft, 14.93m
42 ft, 12.80m
                  200 (TURBINE B,C)
                                                    LOS   ANGELES
                                                        28%  EFF.
                                        400
                                  SHELL HEIGHT, S (ft)
             600 (TURBINE B,C)
            Figure 52(b).   Normalized excess fuel consumption,
                             28% turbine efficiency, Los Angeles
                                          177

-------
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                                  SHELL  HEIGHT, S (m)


                            100  (TURBINE A)
                      50
                                    100
                                                   ISO
200 (TURBINE B,C)
                         200
               200  (TURBINE A)
                                                          63ft, 19.20 m


                                                          56 ft, 17.07m


                                                          49f«, 14.93m


                                                          42 ft, 12.80m
                                                                 MIAMI

                                                                28 % EFF.
                                          400
                                  SHELL HEIGHT, S (ft)
                                                             600 (TURBINE B,C)
            Figure 52(c).   Normalized excess fuel  consumption,

                             28%  turbine efficiency, Miami
                                            178

-------
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                              SHELL HEIGHT, S (m)

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                     50
                                100
                                                  ISO
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                                                                 T
                                                            ST.  LOUIS
                                                             28%  EFF.
                                                    63 ft, 19.20m

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                                                    49ft, 14.93m

                                                    42 ft, 12.80m
                                                            JL
                        200
            200 (TURBINE A)
                                      400
                                 SHELL HEIGHT, S (ft)
                                                           600  (TURBINE B,C)
          Figure  52(d).   Normalized excess  fuel consumption,
                            28% turbine  efficiency, St.  Louis
                                           179

-------
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Figure 53(b).
Normalized evaporation,  28%

turbine efficiency, Los  Angeles
                          181

-------
           50
SHELL HEIGHT, S (m)

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56 II, 17.07m

49 ft, 14.93 m
                                                       UJ
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                                    SHELL HEIGHT.S (ft)


                                    Normalized evaporation,  28%

                                    turbine  efficiency,  St.  Louis
                                             183

-------
 The  economic  evaluation of backfitting with natural-draft evaporative
 towers  is very  similar to the procedure already identified in Section
 V.F  for mechanical-draft towers.  In particular, the quantities which
 must be identified prior to the evaluation are the same as those listed
 in that section, except for items b-1,2.  Instead the following quant-
 ities must  be identified for natural-draft towers:

 (b)   Cooling  Tower
      1.  The  size of the cooling tower in terms of the shell height,
                                                      *
         S, and the height, H, of the evaporative pile ;
      2.  The  capital cost of the natural-draft tower, C  , from
                                                       C 5
         Figure 32.

 Once this information has been gathered, the calculation of the total
 differential  cost of backfitting can be carried out either by using
 the  computer  program or by referring to the results presented graphic-
 ally, if applicable.  The general procedure to be followed is similar
 to that already identified with mechanical-draft towers in Section V.F,
 and  it  is further illustrated with the example presented in Section
 VI.H.

 G.   THE COMPUTER PROGRAM
 The  computer  program which accepts any set of numerical values for the
 various parameters and performs the calculations outlined in the pre-
 vious sections  is listed in Appendix IV.  The thermodynamic models used
 to simulate the performance of cooling towers are basically the same
 as those developed by Croley, Patel and Cheng [15] for the wet portion
 of dry-wet combination towers, but there are a number of important
 It will be recalled that S and H are sufficient to describe  the physi-
cal size of the towers since the width of the pile  (W) and  the  shape of
the hyperbolic shell have been fixed, and since all detailed  calcula-
tions are based upon a representative set of empirical data concerning
the heat transfer properties, and water-loading in the pile.
                                  184

-------
differences in other respects,   in particular, the economic consider-
ations are formulated  specifically for the analysis of backfitting an
existing power plant or unit with natural-draft wet cooling towers and
cannot be used, without modification, to study the design of towers
for new plants or units.

The computer program consists of the MAIN program and eight subroutines,
namely OPECOS, MODELW, NTUCAL, AIRFLR, BESTK, CAPCO, FOGSEN, and
POWERS.  The MAIN program reads  all inputs, calculates the overall
capital and total  costs,  and controls the printout of these quantitiea
The inputs, along with the symbols and units used, are listed in
Appendix II.  The primary functions of the various subroutines not
previously identified  are as follows:

     AIRFLR:  This  subroutine is described in Section VI.A.  It
              calculates,  through iteration, the proper air flow rate
              and evaporative cooling.  This subroutine calculates the
              buoyant  air flow rise and outlet water temperature,
              given ambient dry- and wet-bulb temperatures, height of
              tower, tower friction factor, water temperature, and
              flow  rate.
     BESTK:   This  subroutine is also described in Section VI.A.  It
              calculates,  through iteration, the value of the tower
              friction factor which is appropriate for air flow rate
              calculations for a given tower specification.
     CAPCO:   Computation of the capital cost of the natural-draft
              cooling  tower is made in this subroutine.  Capital
              cost  is  determined as a function of the wet-bulb temp-
              erature, relative  humidity, cooling range, approach, and
              heat  rejection  rate [16].

The overall program logic  is similar to that already described for the
mechanical-draft economic  calculations.  Minor changes have been made
                                  185

-------
 in the other subroutines and the main program to accommodate the dif-
 ferent cooling model.  These changes are included in the program
 listing in Appendix IV.

 H.  A HYPOTHETICAL TEST CASE
 1.  Consider a power plant with the characteristics identified in
    Section V.H.I, which also implies that the extreme dry-bulb
                  XV
    temperature,  T   =  97.0°F (36.1°C) for Miami.
                  db

 2.  Assume that this plant is to be backfitted with a natural-draft
    cooling tower whose characteristics are:
    Shell Height, S                         = 400 ft (121.9 m)
    Base Diameter, D^                       = 305 ft (93.1 m)
    Pile Height,  H                          =  49 ft (14.9 m)
    Pile Width, W                          =  21 ft ( 6.4 m)
                                                        2
    Water Loading, per unit plan            =  18 gpm/ft
      area of pile                             (0.733 m3/min/m2)
    Total water flow rate,                  = 387,132 gpm
       GPM(= 18 x TT^ + W)x W)               (1465.3 m3/min)
    Concentration ratio, k                  =3.3
    Unit blowdown treatment cost, c         = $0.05/1000 gal.
                                              ($0.0132/m3)
    Cost of hook-up and testing, C          = included in cost
                                  HT           _ .
                                              of towers
    Maintenance cost, C                     = $2,000/yr
                       m
    Downtime, DT                            = 720 hrs (30 days)

3.  Assume that the various economic parameters are as identified in
    Section V.H.3.
4.   Use of example results:
(a)  Use Figure 32 to find the capital
      cost of the natural-draft evapo-
      rative cooling tower                  = $5,160,000
                                  186

-------
(b)  Refer to Ref.  7 to find the clearance
      width around tower corresponding
      to a desired noise level (e.g. 60dB)   = 200 ft (61.0 m)

    Thus, land area required, A  from        = 390,000 sq ft
      equation 36 is                         =9 acres
                                               (3.6 hectares)
(c)  Calculate the base efficiency of
      the turbine
                                                   i

    _  _   cP            3.413 xlQ6x312.5       -v
                                                 _ o.36
           t   t
         cP +Q    3.413x10  x 312. 5 XL 912x10

(d)  Read Figure 38 to find the normal-
      ized maximum capacity loss (for
      Los Angeles) for 411 MW, 36% effi-
      ciency (A), and 822 MW, 36%  (B) .     A = 0.020
      Read Figure 42 to find the norm-     B = 0.040
      alized maximum capacity loss for     C = 0.026
      411 MW,  28% (C) , and 822 MW, 28%  (D) D = 0.336

(e)  Interpolate  (log) "economy of scale"
      correction factor for 312.5 MW
      unit for normalized maximum
      capacity loss, i.e.
               (n -0.36)

    E *
    correction factor =
              (0.28-0.36)


               (D  -0.36)

              (0.28-0.36)

                            _ T?                          ~*3
                            ~
                        822 - 411
(f)  Read Figure 46(c) and 50(c)
      (Turbine A, Miami) to find the
      normalized maximum capacity loss,
      C /P* for efficiencies of 36% (G),   G = 0.021
      and 28% (H), respectively            H =0.032
(g)  Calculate the normalized maximum
      capacity loss corresponding to
      the given efficiency (I)

                (nT-o.36)
               (0.28-0.36)
                                 187

-------
(h)  Correct the normalized maximum
      capacity loss for economy of scale:


    exp[lnl + correction factor x (P*-411)]   = 0.01779


    Thus, the maximum capacity loss,
      C  = 0.01779x312.5x1000              = 5560 kW
       L

(i)  Repeat steps (d)  through (h)  using
      Figures 39, 43, 47 (c), and 51(c)
      respectively, to determine the
      corrected value of the normalized
      energy loss,  E /PE*
                    L
      A                                      = 0.015
      B                                      = 0.011
      C                                      = 0.017
      D                                      =0.029

      E = In (0.015)  + (°'3n~o2'36)  [In (0.017 -In (0.015)] =-4.1997
                       "U • 08
      F = ln(0.011) +   '~'    [ln(0.029)  -ln(O.Oll) ] =-4.5099
                       ~U . Uo

      correction factor
      G                                      = 0.018
      H                                      = 0.022
      Inl = ln(0.018) +   '"o    [ln(0.022 )  -In (0.018)]  =-4.0174
                          — u . uo

      exp[lnl + correct ion factor x (p  -411)] = 0.01939


      Thus,  the energy loss,

      ET =0.01939 x 312.5 x 1000 x 8760         = 53.1 x 1Q6 kW-hr/yr
       Ij
(j)  Repeat  steps (d)  through (h)  using
      Figures 40, 44,  48 (c), and 52 (c)
      respectively,  to determine the
      corrected value of the normalized
      excess fuel consumption, TI  F /PE*
      (use absolute  values for log -linear
      interpolations)

      A                                      =0
      B                                      =0
                                  188

-------
     c                                       =0
     D                                       = -0.01

     but interpolation does not really
     apply since A,  B, C,  D, E, and
     F <^0;  therefore set correction
     factor                                 = o

     G                                       =0
     H                                       =0

     and using simple linear interpolation:

                 -.
                              *
     I + correction factor  x (p  -411)         = 0

     Thus,  the excess fuel consumption

       F=0x 312.5 x 1000  x 8760/0. 85        = 0 kW-hr/yr
         E

(k)  Repeat steps (d)  through (h) using
     Figures 41, 45, 49 (c), and 53 (c)
     respectively, to determine the
     corrected value of the normalized
     water evaporation, W /Q*
                          Lt
     A                                       = 7.83
     B                                       = 7.79
     C                                       = 7.83
     D                                       =7.04
      E = ln(7.83) +   '"       [In (7. 83) -In (7. 83)] =2.0580
                       ~U • Uo
      F = ln(7.79) +   'n"no    [in (7. 04) -In (7. 79)] =2.0528
                       — U. Do

                 _   fc     2.0528 -2.0580     _             -5
      correction factor = - 822 -411 -     ~ ~1-2652   10

      G                                      = 8.40
      H                                      = 8.35
         = ln(8.40+   '":    [ln(8.35) -In (8. 40)] =2.1282
                        — U. Ut>

      expflnl + correct ion factor x (p*-411)] = 8.4102

      Thus,  the water evaporation,

       W =8.4102 x 1.912 x l09/3- 413 x 106    = 4711 acre-ft/vr
         L                                      (5.811X10  m3/yr)
                                 189

-------
    Also, blowdown, W, = W
                     b    I
        and makeup, W  = WT  —
                     ~    L
                              = W  +W
                 m
                        k  -1
  2048 acre-ft/yr
  (2.526 x 10  m /yr)

  6759 acre-ft/yr)
  (8.337 x 10  m /yr)
                                  PP
5.  Cost Determination

    Capital Costs
    Cooling tower,  C
                    cs
    Pump and pipe system (Figure 13
      with total water flow rate
      = 387,132 gpm (1465.3 m3/min),  C
    Pump and pipe system salvage,
      C1  = 0.2 C
       PP        PP
    New condensers, C
Salvage value of old condensers, C'
                                  c
Salvage value of other open-cycle
  components, C'
               o
Hook-up and testing cost, C
                           HT
Additional land, A a  = 9 x 3000
                  L x/
Replacement capacity,
  CC  = C c  = 5560 x 90
    x\    .Li A,
Downtime,
  CC   = DT x p* x e'
    DT            a
       = 720 x 312.5 x1000 x 0.007
         TOTAL CAPITAL COST, CC
= $5,160,000



= $2,950,000


= ($590,000)

      0

= (   0    )


= (   0    )

= included in tower cost

= $   27,000


= $  500,400



= $1,575,000
                                               $9,622,400
Operating Costs/year
    Excess fuel cost,
      OC,,^ = F f  = 0
        EF    EC

    Replacement energy cost,
    EF = FEfc = ° X °-000751
      OCR =  E
             = 53.1 x 10  x o.Ol
Supply water cost,
  W c  = 6759 x  (3.259 x 10 ) x 0.1/10
   m w
      0


  $  531,000


  $  220,276
                              190

-------
    Cost of blowdown treatment,
      Wbcb = 2o48x (3.259X1Q5)  xQ.05/103     =$  33,372
    Maintenance of towers, C                 = $    2 000
    Makeup water cost with
      open-cycle system, M1
    Blowdown treatment cost with
      open-cycle system, B1
    Maintenance cost of open-cycle
      system, C1
               m
         TOTAL ANNUAL OPERATING COST,  OC     = $  786,648
    Total costs
    From equation (20),  the toal excess unit cost  due  to
      backfitting, tc,  is given by
           _ OC + CC x FCR
               8760 x P*
             786,648 + (9,622,400  x Q.179)
                 312.5 x  1000 * 8760
        tc =0,9165 mills/kW-hr
The effectiveness of the logarithmic-linear interpolation/extrapolation
scheme to correct the graphical results for economy of scale can be
noted by comparing this solution with the results of the computer cal-
culations.  The total capital cost, annual operating cost, and excess
unit cost given by the computer program are respectively:  CC =
$ 9,974,271, OC = $ 892,084, and tc = 0.9781 mills/kW-hr.  The differ-
ence between the graphical result and the computer result for the total
excess unit cost is seen to be approximately 6.4%.  This small differ-
ence indicates that the graphical method with logarithmic-linear
interpolation/extrapolation yields a good approximation for the given
problem.
                                  191

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                              SECTION VII
                             COOLING PONDS

Man-made  cooling ponds are a possible heat rejection
method for backfitting needs.  The economics of.a cooling pond are
dependent on topography, available land, and the ease of construction
at a given site.  The physical factors which determine the cooling
capacity  of these ponds have long been of fundamental interest in the
fields of oceanography, limnology, hydrology, and meteorology.  Various
compendiums of information [24,25,26] have presented thermodynamic and
economic  methods and data for cooling ponds.  Heat is rejected from
cooling ponds by natural effects of conduction, evaporation, convection,
and long-wave radiation.  Ponds also absorb heat through solar and
atmospheric radiation, plus waste heat from the power plant.

In most areas, the required size of a cooling pond is about 1 or 2
acres/MW  (0.4 or 0.8 hectares/MW) [25], but some very efficient ponds
require as little as 0.75 acres/MW (0.3 hectares/MW).  At 4 acres/MW
(1.6 hectare/MW) it is often possible,to obtain cooling water temper-
atures within 5 degrees F (2.8 degrees  C) of the equilibrium temper-
atures of open cycle cooling [24].  Generally, the overall water
consumption is about 1 to 3% of the flow rate, comparable to cooling
tower operations.

The economics of cooling ponds are strongly site dependent since they
require large land areas and basins of low permeability.  Like other
evaporative systems, there may be problems of evaporative water loss,
fogging,  icing, and blowdown.  Advantages of cooling ponds are
                                  192

-------
simplicity of operation, low maintenance costs, low power requirements,
aid in settlement of suspended solids, high thermal inertia, and they
may also serve recreational purposes.

The thermodynamics of cooling ponds is also strongly site dependent
due to meteorological and topographical variables.  Analytical models
have been developed to include transient effects, vertical temperature
gradients, complex boundaries, and lateral and longitudinal temperature
gradients [24,25,27,28,29],  Evaluation of these models and of various
components of the heat balance equation are current topics of study
[30,31,32,33].  The completely mixed, steady state, shallow cooling
pond model is used in this report in an effort to make general economic
evaluations of backfitting with a minimum of input parameters.  The
thermodynamics of this model are well known and restated in the follow-
ing paragraphs.

A.  OPERATION MODEL FOR THE FULLY-MIXED POND
To mesh with models describing condenser and power plant behavior, the
cooling pond model was formulated to accept input parameters of two
categories.  One set of input data consists of parameters assumed to
be fixed for a specified geographical location.  For example, these
parameters include atmospheric pressure, wind velocity, month of the
year, fluid and thermal properties of water, cloudiness ratio, clear
sky solar radiation values, and reflection percentages.  The second
set of input data consists of variables needed in the operation of the
MODELW subroutine which performs the economic analyses.  These
variables are the temperature of the hot water entering the pond, the
water flow rate, the area of the cooling pond, the dry-bulb air temp-
erature, and the wet-bulb air temperature.  The outputs of the model
are:  1.  the cold-water temperature (for a fully-mixed pond model,
this temperature is the surface temperature of the pond), and 2.  water
loss due to evaporation from the pond.
                                   193

-------
 In this  section, the symbols for the input variables of the cooling
 pond model are:
          T    = temperature of hot water entering the cooling
                 system
          GPM  = water flow rate
          A    = area of cooling pond
          T,  = dry-bulb temperature of air
           db
          T  ,  = wet-bulb temperature of air
           wb
 The symbols  for the output variables of the model are:
         T ,TS  = cold water temperature, surface temperature of pond
           W  = water loss due to evaporation from the cooling pond
             L
 The outputs  of the model are a result of solving the heat balance
 equation which is described next.  The technique used is an iterative
 procedure which seeks out the surface pond temperature that satisfies
 the heat balance equation.
 Significant terms in the heat balance equation are now reviewed.
 Complete discussions [24,25,33] are available in the literature.  The
 general heat balance equation can be written:
                        QP + QR = QW + QE + QC                    (37)
 where      QP  = heat supplied to pond from power plant
           QR  = heat supplied to pond due to solar radiation and
                 atmospheric radiation

 The terms on the right-hand side of equation  (37) are heat loss terms
 defined as
           QW  = long-wave radiation from pond
           QE  = evaporative heat loss
           QC  = conductive heat loss
The dimensions of these terms are heat/unit area/unit time.  All  of
the terms in equation (37) except QR, depend on the surface water
                                  194

-------
temperature of the pond.  The purpose of the model  is to calculate
the surface temperature TS, by a  simple iterative procedure.

The residual of equation (37), RES, is defined as the difference between
the heat input and the heat loss  terms, i.e.,
                  RES = QP + QR - (QW + QE + QC)                  (38)
where RES is calculated for different estimates of  the surface temp-
erature.  When RES = 0, the heat  balance, equation (37) is satisfied.
The iterative method is initiated by arbitrarily choosing two temper-
atures which span TS, and it advances by sequentially bisecting the
temperature interval and correcting the limits of the temperature
span as RES->0.  When RES becomes  sufficiently small, equation (37) is
assumed to be satisfied.

In order to calculate the residual defined in equation (38) each of the
heat transfer terms must be computed independently.  The complete
description of these heat transfer terms is found in the work by
Ryan and Stolzenbach [34].  In the following equations, all of the
                                                      2
heat transfer terms are daily averages given in Btu/ft /day.  QR is
the total radiative heat transfer expressed as
                       QR = QA -  QAR + QS - QSR                   (39)
where          QA = atmospheric radiation to water  surface
              QAR = reflected atmospheric radiation from surface
               QS = solar radiation to surface
              QSR = reflected solar radiation from  surface
An approximation [34, p.. 1-23] to the atmospheric radiation term is
                     QA - QAR = 800 + 28T                         (40)
This linear equation is applicable for 40 lTdb £90°F.  The solar
radiation is approximated [34] by
                       QS = QSCU.O - 0.65 R2)                    (41)
                                            c
                                   195

-------
where QSC = the clear sky solar radiation, and R  is the cloudiness
                                                c
ratio.  The QSC depends on time of year and the latitude [24, p. 12,
Fig. 4],  The worst condition  (i.e., when solar radiation to a pond
will be greatest) can be approximated as:
                    QSC = 2800 Btu/ft2/day                        (42)
This value is used in the present calculations, and an average value
of R  = 0.5 is also used.
    c

The long-wave radiation from the water surface is usually the largest
item in the heat balance equation, and it is expressed as [34, p. 1-23]
                  QW = 4.10 x 1Q~8  (TS + 460)4                    (43)
The evaporative heat loss term is still subject to considerable
research.  For evaporation from a heated surface the MIT formula,
based on field data, [34, p. 1-34, Eq. 44] is used.
              QE = [22.4  (Aey)1/3 + 14.0V2](eg-eA)               (44)
where         V  = wind speed  (mph) at a height of 2m
              e  = air saturation vapor pressure at water surface
               O
                   temperature (mm Hg)
              ea = air vapor pressure at T_,  (mm Hg)
               A                          OLD
             A6  = virtual temperature difference
       where TS  = TS/(1.0 - 0.378e /p )
             ^-T^/d.O-O.aTSe^)
              p  = atmospheric pressure = 760 mm Hg
               f\

Some further comment is necessary for the evaporative heat  loss  term.
If the wind speed is given at some height other than 2 m, then the
logarithmic velocity profile can be used to approximate V  .
                               ln(2.0/z )
                       V2 = VZ ln(2/Z )°                          <45>
                                  196

-------
where     z  = 0.005 m
           o
           z = arbitrary height
          V  = wind speed at height z.
           Z
For all the calculations, an average wind  speed  is chosen particular
to the geographic  location of the cooling  pond.  As noted in Ref. 34
 (p. 1-44), equation(44) is only valid when  e  > e  , or when the evapor-
                                           ItD   *\
ative heat loss is out  of water.  In each  iteration, the evaporative
heat loss, QE, is  calculated by equation(44) with A6  replaced by  |A9  I
if TS>T   , and if TS < T_, , QE is set equal to zero.
      — db              db
The conductive heat  loss  term  is discussed  in Ref. 34  (p. 1-42).  The
relationship given there  is written as
                                rpo ^ rp
                                    db  [22.4(A9)1/3 + 14.0VJ    (46)
                                SS-eA
                                               V          —2"
where   c  =  0.255 mm Hg/°F

It should be  noted that  QC can be negative.  The water loss term
which is closely related to  the  evaporative heat loss is discussed
next.

The water loss by evaporation  can be calculated after the evaporative
heat loss is  known.   The latent  heat of vaporization is given by
[35, p. 60]
                   H  =  1087 - 0.54(TS)  (Btu/lb)

The evaporative water loss per unit area  is then

                         w^  =  QE/yHv  (ft3/ft2/day)                (47)
where               Y =  62.4 lb/ft3

B. CAPITAL COSTS OF COOLING  PONDS
The capital costs given  below  should be accepted as rough estimates
                                   197

-------
 based on the  source information which is stated.  In particular, the
 date bases for the costs are approximated from the vague source
 material which is available.  Because of the large land area require-
                                              I
 ments,  land cost is the most important economic factor for cooling
 ponds.  The additional land necessary for backfitting with a cooling
 pond, A , is  split into two categories, viz., A, the land required
        L
 for the cooling pond itself and, A  , additional land needed for access
                                  3.
 roads,  placement of service facilities, landscaping, and other mis-
 cellaneous uses.   (A  = A + A )  Land costs are highly variable and
                    Xj        a
 typical values given in the literature range from $500 to $5,000 per
 acre  ($1235 to $12,355 per hectare).  In the hypothetical example
 presented in  Section VII.G, unit cost for the pond itself, c , includ-
 ing land, pond preparation and construction is taken as $5,000/acre
 ($12,355/hectare), and the cost of the access land, c , is taken as
                                                     a
 $3000/acre  ($7,413/hectare).  The amount of land needed for access
 roads,  etc. is estimated as ten percent of the pond area; i.e.,
 A = 0.1 x A, and the total capital cost of the cooling pond and
  cl
 access  land is given by the sum, c A + c A .
                                  p     a a

 The capital cost for pumps and pipe systems is taken from the report
 by Jedlicka [26].  In the nomographs of Ref. 26  (p. N-43), the pump
 and pipe system costs are shown (assumed to be in 1970 dollars) as
 functions of water flow rate (gpm) and total head  (ft).  In the
 example which follows, a water flow rate of 0.54*10  gpm (2.04*10
m /min) and an assumed head of  40 ft  (12.2 m) results in a total
                /•                   •                       «
cost of $0.80*10 .  This is approximately $1.50/gpm  ($396/m /min)
which is considerably higher than the figure of $0.50/gpm  ($132/m3/min)
stated  in an earlier work [24, p. 8lJ.  Of course, total head is
strongly site dependent and contributes significantly when the pond
is located a large distance from the plant.  Usually, an advantage
of cooling ponds, is that maintenance costs for the pond itself are
              *-•
low.   For the present example, $2.00/acre/year  ($4.94/hectare/year)
[24,  p.  84]  (1970 dollars, assumed) is used for maintenace costs.
                                  198

-------
C.  REFERENCE AREA OF COOLING POND, A*
As discussed in  Section V.B., P*  is the rated or nameplate capacity
obtained at the  reference back pressure, p*, which occurs when the
excess turbine heat rate, A, is zero.  The corresponding heat rejection
rate is Q*.  Then, for any given  water loading, the reference area
of the pond, A*,  can be defined as the area required for the reference
heat rejection rate, Q*, while maintaining the turbine back pressure
at a specified value, p1, at the  reference meteorological conditions.
As explained in  Sections V and VI, all of the reference values chosen
for computing A* may be selected  arbitrarily.  For this study, the
reference dry-bulb temperature is set at 70°F (21.1°C), and the refer-
ence wet-bulb temperature at 60°F (15.6°C).  The reference wind speed
is set at 8 mph  (3.57 m/sec) and  the clear sky solar radiation to the
                            2             42
pond is taken as 2800 Btu/ft /day (3.18xio  kJ/m /day).

The reference area A*, can be found by considering the heat transfer
characteristics  of the condenser  and the performance of the cooling
pond at the reference meteorological conditions.  The reference area
then depends on  the values of Q*, water loading, the specified turbine
back pressure, and the fixed meteorological conditions.  The details
for calculating  A* are the same as for calculating the reference
length of the mechanical-draft cooling tower, Section V.B.  The
results are shown in Figure 54 for a specified turbine back pressure
of 2.0 in. Hg  (5.08 cm Hg).  The  reference area, A*, is a nearly
linear function  of the reference  heat rejection rate, Q*, and A*
increases with increasing values  of water loading.  The reference
area found from  Figure 54 is used to nondimensionalize the pond area.

D-  PARAMETRIC STUDIES
Detailed calculations can be made using the cooling pond as the closed-
cycle cooling system to be backfitted to an existing power plant or
unit.  The calculations are made  for a range of values of pond surface
area and water loading.  The pond area is normalized with respect to
                                  199

-------
N)
O
o
                1600
               o
               o


              *<
  12OO
UJ
a:
                 800
2

UJ
o
z
UJ
o:
UJ
u.
UJ
cr
                 400
                            1.0
                       REFERENCE HEAT REJECTION  RATE, Q*  (109 KJ/hr)

                      2.0      3.0      4.0     5.0      60      7.0      8.0
p'»2.0 in. Hg abs (5.08  cm Hg abs)


Tdb " 70°F <21-10 c>

Twb*« 60° F ( 15.6-C)

Vg * 8 mph {3.57 m/sec)


QSC= 2800 Btu/ft2/day(3.?8 xlO4 KJ/m2/day)
WATER LOADING, gpm/ft  (


              0.075 (3.06 xlO'3)



              0.0625 (2.55x10-')

              0.050 ( 2.04 x 10"3)
              0.0375 (1.53 xlO-3)


             V025 (1.02 x 10'3)
                                                                                                        600 o
                                                                                                             u
                                                                                          500
                                                                                                         400 <
                                                                                                            UJ
                                                                                                            a:
                                                                                                        300
                                                                                    z
                                                                                    o
                                                                                                         200
                                                                                                         100
                            1.0       2.0      3.0      4.0      5.0       6.0      7.0      8.0

                                     REFERENCE HEAT REJECTION  RATE, Q*(109 Btu/hr)
                                                                                    O
                                                                                    z

                                                                                    a
                                                                                    UJ
                                                                                    u_
                                                                                    UJ
                                                                                    cc
                                  Figure 54.   Reference  area of  cooling  ponds

-------
the reference area, A*; the maximum capacity loss, annual energy loss,
annual excess fuel consumption, and annual evaporative water loss are
all normalized as in  Sections V and VI.  Meteorological conditions are
chosen as representative of four geographical locations:  Chicago,
Los Angeles, Miami, and St. Louis, as discussed in part B of Section
III.  In addition to  the meteorological parameters of the ambient dry-
and wet-bulb temperatures, the wind speed, clear sky solar radiation,
and cloud cover must  be considered in the study of cooling ponds.
Values of the last three are chosen as fixed for all geographical
locations in this parametric study.  Because of the thermal inertia of
cooling ponds, the use of average values for these parameters is
probably more realistic than for the other cooling systems considered
in this report.

As for the other cooling systems, it is necessary to carry out studies
of the 411 MW and the 822 MW power plants, under identical meteorolog-
ical conditions, in order to check for scale effects on the computed
results.  Variations  of the normalized quantities (maximum capacity
loss, annual energy loss, annual excess fuel consumption, and annual
water loss due to evaporation) with the normalized pond area for the
                                       9                   9
411 MW plant  (turbine A, Q* = 2.545x10  Btu/hr = 2.686x10  kJ/hr)
and the 822 MW plant  (turbine A, Q* = 5.090xio9 Btu/hr = 5.372xio
kJ/hr) for meteorological conditions at Los Angeles (Table 4 and 5)
                                   2           -332
and one water loading (0.025 gpm/ft  = 1.02xio   m /min/m ) are shown
in Figures 55 through 58.  Since the curves shown in these figures do
not completely collapse, it is seen that an economy of scale exists
for the fully-mixed cooling pond  (similar to the natural-draft cooling
tower, as discussed in Section VI.E.).

Parametric studies of variations of the normalized quantities mentioned
above with normalized pond area for the four geographical locations
are shown in Figures  59 through 62. ' Since the study on scale effects,
Figures 55 through 58, indicates differences in the normalized
                                  201

-------
   0.20
   0.18
*
Q.
X.

o
V)
tO
o
O
o
o
    0.16
    0.14
   0.12
   0.10
   0.08
   0.06
   0.04
   0,02
—T	-I	1	


 LOS ANGELES


   TURBINE A

 •  p* = 411  MW

 o  p* *822 MW



 WATER  LOADING

 0.025 gpm/fl2

 (1.02 x10-3m3/min/m2)
             0.2     0.4     0.6     0.8    1.0     1.2

                 NORMALIZED  POND  AREA, A/A*


           Figure 55.  Normalized capacity loss
                      1.4
                          202

-------
   0.20
   0.16
   0.16
ui
o.
UJ
   O.14
CO
O 0.12
O
UJ
   0.10
§0.08
              LOS ANGELES
                TURBINE A
              •  P* * 411  MW
              o  p* *822 MW

              WATER LOADING
              0.025 gpm/ft2
              (1.02x 10"3m3/min/m2)
(E
  0.06
  O.04
  O.02 -
            0.2
0.4
0.6
0.8
1.0
1.2
                NORMALIZED POND  AREA, A/A
             Figure 56.  Normalized  energy loss
1.4
                              203

-------
  -0.02

K

 UJ
U.

 I—0.04
  -0.06

GL
ID
co

o
o
CO
CO
X
UJ
-0.08
   -0.10
   -0.12
   -0.14
g  -0.16
Z
   -0.18
  -0.20
                               LOS ANGELES

                                  TURBINE  A
• p* = 411 MW

o P* « 822 MW



 WATER LOADING

 0.025 gpm/ft2

 (1.02 x 10'3m3/min/m2)
        i     0.2    0.4    0.6     0.8     1.0     1.2
               NORMALIZED POND AREA, A/A*


         Figure  57.  Normalized  excess fuel consumption
                         204

-------
 o
 E
 «
 £  9.0
 i
o  8.0
    7.0
 u
 o
O  6.0

    5.0
OL
g  4.0
UJ
£  3.0

I
S
N
O
   1.0
                                 LOS ANGELES

                                   TURBINE A
                            • P
                            o p
                                  411 MW

                                  822 MW
                           WATER LOADING
                           0.025 gpm/ft2
                           (1.02 xKT3m3/min/m2)
            0.2    0.4     0.6    0.8    1.0
               NORMALIZED  POND AREA, A/A*
                                              1.2
                                                     13
                                                    12 o
                                                       E
 11
                                                       9)
                                                     10 ^
                                                        o
                                                        0)
   10
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8  *— •
   *
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   0.22
   0.20
   0.16
   0.16
a  O.H
•x.
y
to  O.12
to
3
t  o.io
sr
a
ui
   0'09
   0.06
tr
o
  0.04
   0.02
WATER LOADING
	0.025 gpm/f»2  1.02x 10'3 m3/min/m2
—— 0.050 gpm/ft2, 2.04 x 10~3m3/min /m2
	0.075 gpm/ft2, 3.06 x 10'3 m3/min/m2
             0.2     0.4     0.6     0.8     1.O     1.2     1.4
                       NORMALIZED POND AREA, A/A*

              Figure 59(a).  Normalized capacity  loss,
                               Chicago
                                   1.6
1.8
                                        206

-------
0.22
0.20 -
     WATER LOADING
         0.025 gpm/ft2, 1.02x10'3 n>3/min/m2
     	-0.05O gpm/ft2, 2.04xKT3m3/min/m2
     	0.075 gpm/ft2, 3.06xKT3m3/min/m2
          I	1	I	1	1
                       0.6    0.8     1.0    1.2    1.4
                     NORMALIZED POND AREA,  A/A*
                Figure  59(b).  Normalized  capacity  loss,
                                Los Angeles
                                       207

-------
0.22
0.20 -
         WATER LOADING
              0.025 gpm/ft2, 1.02 m3/min/m2
         	0.050 gpm/ft2, 2.04 m3/min/m2
         	0.075 gpm/ft2, 3.06 m3/min/m2
                 I	1	1
                O.4    0.6     0.8     1.0    1.2
                    NORMALIZED POND AREA,  A/A*
                Figure 59(c).
Normalized capacity
Miami
loss,
                                        208

-------
0.22
0.2O
          WATER LOADING
          	0.025 gpm/ft2, 1.02 x 10-3m3/min/m
          	0.050 gpm/ft2, 2.04 x 10'3 m3/min/m2
          	0.075 gpm/ft2, 3.06 x 10"3 m'/min/m2
                  0.4    0.6    0,8    1.0     1.2     1.4
                       NORMALIZED  POND AREA, A/A*

                   Figure  59(d).  Normalized capacity  loss,
                                    St.  Louis
                                        209

-------
   0.22
   0.20
   0.18
   0.16
   0.14
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el-
's.
 _l
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Z
  0.02
                                                         CHICAGO
                                           WATER LOADING
                                               0.025 gpm/ft*.

                                                1.02 x 10'3m3/min/m2


                                             	O.Q50 gpm/ft2,

                                               2.04 x 10-3m3/min/m2
                                                3.O6 x 10-3m3/min/m2
                    ENERGY LOSS
                                                JL
             a2     0.4     0.6     0.8     l.O     1.2

                           NORMALIZED POND  AREA,
                                                        1.4

                                                     A/A*
1.6
1.8
                       Figure 60 (a).
                                        Normalized  energy  loss,

                                        Chicago
                                         210

-------
   0.22
   0.20
    0.18
   0.16
    0.14
IU
a.
x

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 »
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    0.12
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                                                 i	1	1	r


                                                     LOS  ANGELES
                                            WATER LOADING

                                                0.025 gpm/ft2,

                                                1.02 x 10"3m3/min/m2



                                           --- 0.050 gpm/ft2,

                                                2.04 * 10-3m3/min/m2
                                                3.06 x 10-3m3/min/m2
         PUMP

         ENERGY

         LOSS
             0.2
                 0.4
0.6
                                  0.8
                                      1.0
                     1.2
1.4
                                                              1.6
                         NORMALIZED  POND AREA, A/A
                     Figure 60(b).   Normalized energy loss,

                                      Los Angeles
1.8
                                          211

-------
   O.22
   0.20
   O.18
   0.16
   0.14
*
iu
Q.
UJ
V)
vt
O.12
   O.10
   O.08

-------
0.22
0.20 -
                                             I	,	,	,


                                                    SI  LOUIS
                                                O.O25 gpm/fr.
                                                1.O2 x lCT3m3/min/m2
                                           	0.050 gpm/ft2,
                                                2.04 x 10-3m3/min/m2
                                           	0.075 gpm/ft2,

                                                3.06xlO-3m3/min/m2
      PUMP
      ENERGY LOSS
                       0.6     0.8     1.0     1.2     1.4

                      NORMALIZED  POND AREA,  A/A*
                 Figure  60(d).  Normalized  energy loss,
                                 St.  Louis
                                     213

-------
*, -0.02
O.
\
P-"

* -0.04
_

* -0.06
z
g
i-
   -O.O8
(A
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    -0.12
UJ  -0.14
    -0.16
    -0.18
   -0.20
   -0.22
                                                           CHICAGO
WATER LOADING

     0.025 gpm/ft2,
     1.02 x KT3m3/min/m2


	0.050 gpm/ft2,
     2.04 x 10'3m3/min/m2


	0.075 gpm/ft2,

     3.06 x 10"3m3/min/m2
              0.2    0.4    0.6      0.8     1.O     1.2     1.4

                           NORMALIZED  POND AREA, A/A*
               1.6
1.8
                  Figure  61(a).   Normalized excess fuel.
                                    consumption,  Chicago
                                         214

-------
-0.22
                                    WATER LOADING
                                         O.O25 gpm/ft2, l.O2xlO-3m3/min/m2
                                    	0.050 gpm/ft2, 2.04 xlO-3m3/min/m2
                                    	0.075 gpm/fl2, 3.06 x 10-3m3/min/m2
0.2     O.4    0.6     0.8     1.0     1.2     1.4
            NORMALIZED  POND AREA, A/A *
                                                            1.6
1.8
                  Figure  61(b).  Normalized excess  fuel
                                   consumption, Los Angeles
                                     215

-------
                                             WATER  LOADING
                                                  0.025 gpm/ft?
                                                  1.02x 10-3m3/min/m2
                                             	0.050 gpm/ftf
                                                 2.O4xlO-3m3/min/m2
                                              	0.075  gpm/ft2
                                                  3.06xlO-3m3/min/m2
-0.22
           0.2
  0.6     0.8     1.0     1.2      1.4
NORMALIZED  POND AREA, A/A"
                  Figure 61(c).   Normalized excess fuel
                                   consumption, Miami
                                      216

-------
                                             WATER LOADING
                                                  0.025 gpm/ft2,
                                                  1.02 x 10-3m3/min/m2
                                                  2.04 x 10-3m3/min/m2
-0.22
           0.2
0.4
  0.6     0.8     1.O    1.2     1.4
NORMALIZED  POND AREA, A/A *
1.6
1.8
                 Figure  61(d).
                Normalized excess  fuel
                consumption, St. Louis
                                   217

-------
   22
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    18
 S 16
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   12
O 10
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                                                    -1	1—

                                                     CHICAGO
            WATER LOADING

            	0.025 gpm/ft2, 1.02 x 10'3 m3/min/m2
            	0.050 gpm/ft2, 2.04 x 10'3 m3/min/m2

            	0.075 gpm/ft2, 3.06 x 10'3 m3/min/m2
           0.2
                         _L
                                      _L
                                                                       26
     24 o
        E
     22
                                                                       20
                                                                         10
                                                                          O
                                                                       16 3
                        0.6     0.8     1.O    1.2      1.4

                       NORMALIZED POND AREA,  A/A*
                                                           1.6
1.8
                                                                         *
                                                                         O
                                                                       14
                                                                        12 O
                                                                         cc.
                                                                       lo
                                                                         UJ
                                                                       8 tr
                                                                         UJ

                                                                       ..s
                                                                         Q
                                                                         UJ
                                                                         N
                                                                       4 13


                                                                       .1
                 Figure  62(a).
                                 Normalized evaporation,
                                 Chicago
                                      218

-------
  22,
                                                   LOS  ANGELES
-20|


£

a>
£


J  18|


5
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V.
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   141
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           0.2    0.4    0.6    0.8    l.O     1.2     1.4

                       NORMALIZED POND AREA, A/A*
                                                1.6
1.8
                   Figure 62(c).
                         Normalized evaporation,

                         Miami
                                        220

-------
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                                                        ST. LOUIS
          WATER LOADING

          	O.O25 gpm/ft2,  1.02 x 10"3 m3/min/m2

          	0.050 gpm/ft2,  2.04 x 10"3m3/min/m2

          	0.075 gpm/ft2,  3.06 x 10'3 m3/min/m2
         TURBINE
           0.2    0.4    0.6    0.8     1.0     1.2     1.4

                        NORMALIZED POND  AREA,  A/A*
                                                            1.6
1.8
      26





      24 o

         E
         w
         V
         £

      22 7
                                                                         ,20
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                                                                          0
                   Figure 62(d).   Normalized  evaporation,

                                    St.  Louis
                                       221

-------
 quantities with power plant size, the final results for the cooling
 pond,  Figures  59 through  62 are valid for a 411 MW plant only.  There-
 fore,  if  the graphical results are to be used for other size plants
 or units, the  interpolation technique described for the natural-draft
 towers (Sections VI.E and VI.H) should be employed.  However, the
 differences in the results for the 411 MW and the 822 MW plants
 (Figures  55 through 58) are seen to be .quite small.

 In the sample  calculations presented in Section VII.G for a 312.5 MW
 plant,  the curves are read directly, assuming that any errors which
 are introduced are small.  This assumption is checked by comparing the
 results from the graphical computation with results obtained using the
 computer  program.  The comparison is quite acceptable as seen at the
 close  of  Section VII.G.   It must be emphasized that if the size of
 the power plant being studied varies greatly from 411 MW, the computer
 program must be used to obtain accurate results.

 E.   PROCEDURE  FOR THE ECONOMIC EVALUATION OF BACKFITTING
 Particular items which must be considered in the economic evaluation
 of  backfitting with a cooling pond have been previously described.
 Any specific differences  in the technique for computing the total
 cost of backfitting with  a cooling pond are presented next, followed
 by  a brief description of the computer program that has been developed.
 A hypothetical test case  is presented in part G to illustrate the use
 of  the  graphical results.

 The  procedure  for the economic evaluation of backfitting with a cooling
 pond is very similar to that already presented for the mechanical-
 draft cooling  tower (Section V.F) and the natural-draft cooling tower
 (Section VI.F) with the following exceptions.  In items  (b) and  (c) of
 those Sections, the following quantities must be identified for cooling
ponds:
                                  222

-------
 (b)  Cooling pond
     1.  The size of the cooling pond in terms of its
         area, A;
     2.  Unit, cost of the cooling pond including land, pond
         preparation and construction, c  ($/acre or $/hectare);
 (c)  Economic parameters:
     6.  Unit cost of pump and pipe system  [26], c
                                                   PP

Once this information has been gathered, the total differential cost
of backfitting with a cooling pond can be calculated by the computer
program or estimated by the graphical results presented in Section
VII.D.  Use of the graphical results is subject to the limitation
discussed at the end of Section VII.D.  Illustration of the use of the
graphical results is presented in Section VII.G.

F.  THE COMPUTER PROGRAM
The computer program which accepts any set of numerical values for the
various parameters and performs the calculations previously described
is listed in Appendix V.

The computer program consists of the MAIN program and five subroutines,
namely OPECOS, MODELW, COOL, MIX, and POWERS.  The main program reads
all inputs, calculates the overall capital and total costs, and
controls the printout of these quantities.  The inputs along with the
symbols and units used are listed in Appendix II.  The primary func-
tions of the various subroutines not previously defined are as follows:
     COOL:  This subroutine contains the iterative method for computing
            the cold-water (surface) temperature of the cooling pond
            from the heat balance, eguation (37).  The subroutine is
            independent of the particular mathematical model which is
            employed to predict the cooling performance of the pond,
            and it accepts information which is transferred from sub-
            routine, FIX.
                                 223

-------
     FIX:  The thermodynamic (mathematical) model of the cooling pond
           is found in this subroutine.  In the present study, the
           completely mixed, steady state, shallow cooling pond model
           is used, as described in Section VILA.

The overall program logic is similar to that already explained for the
cooling tower economic calculations.  Minor changes have been made in
the main program and subroutines to accomodate the cooling pond model.
These changes are shown in the program listing included in Appendix V.

G.  A HYPOTHETICAL TEST CASE
1.  Consider a power plant with the characteristics identified in
Section V.H.I, which also implies that the extreme dry-bulb tempera-
      /\
ture, T,.  = 97.0°F (36.1°C) for Miami.
       db

2.  Assume that this plant is to be backfitted with a cooling pond
whose characteristics are:
    Pond area, A                            = 250 Acres
                                              (101.2 hectares)
                                                         2
    Water loading, per pond area            = 0.05 gpm/ft
                                              (0.002 m3/min/m2)
    Wind speed, V                           =8.0 mph
                                              (3.57 m/sec)
                                                         o
    Solar Radiation,  QSC                    = 2800 Btu/ft /day
                                              (3.8 xio4 kJ/m2/day)
    Total water flow rate,
       GPM (=0.05x250x43560)               = 544,500 gpm
                                              (2061 m3/min)
    Unit cost of cooling pond
       (including land cost),  c             = $5000/acre
                                              ($12,355/hectare)
                                  224

-------
    Unit maintenance cost, c
                            m
    Concentration ratio, k*
    Unit blowdown treatment cost, c
                                   b
    Cost of hook-up and testing, C
                                  HT
    Downtime, DT
    Unit cost of pump and pipe system,
       c
        PP
= $2.00/acre/year
  ($4.94/hectare/year)
= 3.3
= $0.00
~ included in cost of pond
= 720 hrs (30 days)

= $1.50/gpm
  ($396./m /min)
3.  It is assumed that the following economic parameters apply to the
affected utility.  All other characteristics are the same as in Section
V.H.3.
    Unit cost of water, c
                         w
    Unit cost of access land, c
= $0.00
= $3000/acre
  ($7413/hectare)
4.  Use of example results:
     (a) Read Figure 54 to find A*
          Determine normalized area
          A/A* =250/260
     (b) Read Figure 59(c)  (turbine A,
          Miami) to find normalized
          capacity loss, C /P*
                          it
        Thus, capacity loss
          C  =0.0402x312.5x1000
           Ll
     (c) Read Figure 60(c)  (turbine A,
          Miami) to find normalized
          energy loss, E/PE*
                        Lt
        Thus, energy loss,
          E  =0.0360x312.5x1000x8760
           L
     (d) Read Figure 61(c)  (turbine A,
          Miami) to find normalized
          excess fuel consumption,
          nz FE/PE*
= 260 acres (105.2 hectares)
= 0.961


= 0.0402

= 12562 kW


= 0.0360

= 98.55 xio6 kW-hr/year
= 0.0
                                  225

-------
        Thus, excess fuel

          P  =0x312.5x1000x8760/0.85
           H


    (e) Read Figure 62(c) (turbine A,

          Miami) to find normalized

          water evaporation, W /Q*
                              L
        Thu s,  evaporat ion,


          W =11.55 x 1.912  x 109/3.413 x 1Q6
        Also, blowdown, W = W.
                         b   L k*-l
        and makeup,


          W = W  -~- = W. + WT
           m   L k*-l    b   L
= 0 kW-hr/year
= 11.55 acre-ft/yr/MW-th


  (1.42 xio4 m /yr/MW-th)
= 6470 acre-ft/year


  (7.98 x10  m /year)



= 2813 acre-ft/year


  (3.47 xio  m /year)
= 9283 acre-ft/year


  (11.45 xio6 m /year)
5.  Cost determination



    Capital costs
    Pond cost, C  = A x c = 250 x 5000
                cs      p


    Access land cost = A  x c = 25 x 3000
                       a   a


    Pump & pipe system cost,

      c   x GPM = 1.50 x 544,500
       PP


    Pump & pipe system salvage,

      C'  =0.2 C
       PP       PP


    New condensers,  C
    Salvage value of old condensers,  C1
                                      c
    Salvage value of other open-cycle

      components, C'
                   o


    Hook-up and  testing cost,  c
                               HT
   Replacement capacity,

     CC_ =CC0 =12562 x 90
       K,    L  Jo
= $1,250,000



= $75,000





= $816,750





= ($163,350)



= $    0



= ($   0   )





= ($   0   )



= included in pond cost





= $1,130,580
                                  226

-------
Downtime, CC   = DT x p* x e{
               = 720 x 312.5 x1000 x 0.007 = $1,575,000

             TOTAL CAPITAL COST, CC     = $4,683,980
Operating costs/year

Excess fuel cost, OC   =F  f            = $   o
                    Er   ]E  C
Replacement energy cost,
  OCR = ELeJl = 98.55 x io6x o.Ol           = $985,500

Supply water cost,
  We  =9283 x 3.259 x 10  x o             =$   0

Cost of blowdown treatment,
  Wfccb = 2813 x 3.259 x 105 x o             =     0

Maintenance of ponds,
  C  =c  XA = 2.0X250                   = $500
   m   m

Makeup water cost with open-cycle
  system, M1                            = ($  0   )

Blowdown treatment cost with open-
  cycle system, B'                      = ($•  0   )

Maintenance cost of open-cycle
  system, C1                            = ($  0   )
           m
     TOTAL ANNUAL OPERATING COST, OC    = $986,000
Total costs

From equation  (20), the total excess unit cost due to backfitting,
  tc, is given by

     OC + CC x FCR
tC ~   8760 x P*

   _ 986,000 + (4,683,980 x Q.179)
   ~     312.5 x 1000 x 8760
tc =0.6665 mil 1 s/kW-hr
                              227

-------
To check the assumption made at the end of Section VII.D, i.e., that
the errors introduced by reading Figures 59 through 62 directly for the
312.5 MW plant are small, this example was also analyzed using the
computer program.  The computer results are CC = $4,583,027 ;   OC =
$927,333/yr; tc = 0.6384 mills/kW-hr.  The difference between the
graphical result and the computer result for the total excess unit
cost is seen to be approximately 4.4%, indicating that the graphical
method does indeed yield a good approximation for the given problem.
                                 228

-------
                              SECTION VIII
                         SPRAY CANALS AND PONDS

For applications where cooling towers are not desired and where land
is not available for  cooling  ponds,  another alternative which could be
considered  for  a closed-cycle cooling system is the use of spray cool-
ing.  Such  a  system,  simply described, consists of an" array of nozzles
or other devices which spray  the  cooling water directly into the air
where both  evaporative and  sensible  heat transfer take place.  The
cooled water  is then  collected for recirculation through the power
plant condensing system.

The use of  spray cooling may  increase the heat transfer per unit sur-
face area by  twenty times that of a  cooling pond resulting in a sig-
nificant decrease in  the land requirement [39].  The low profile of
a spray cooling system generally  presents little or no aesthetic
disadvantages.

Spray cooling systems are usually arranged in one of several different
ways.  One  method which has been  employed for several years is referred
                          Or
to as "conventional"  spray  cooling [12, 23, 26, 32, 40, 4l].  Such a
system consists of a  fixed  array  of  pipes and spray nozzles located
in a small  pond which serves  mainly'as a collecting basin.  The hot
water is taken  directly from  the  condenser, sprayed once, and the
cooler pond water is  returned to  the  condenser.  Conventional spray
ponds have  been employed for  relatively small scale applications, and
they are usually designed for a 10°-15°F (5.6°-8.3°C) cooling range
and for about 10°F  (5.6°C)  approach  to the wet bulb temperature [12],
                                 229

-------
 A second technique, employing what may be referred to as a "parallel
 pass"  concept,  is also in current use [32, 42, 43].  In this type of
 cooling system, the water is sprayed from a hot-water delivery canal
 to a cold-water receiving canal.  Such a system may also be designed
 for multiple parallel passes by including one or more intermediate
 canals between  the hot-water and the cold-water canals [39].  For
 this type of cooling system, devices other than spray nozzles are often
 used to propel  the water.  One manufacturer supplies a spray cooling
 system which utilizes a series of rotating discs mounted on a common
 shaft  to spray  the water [43].

 A third possibility for spray cooling is the use of the "series
 concept" in which spray devices are arranged along a canal [39, 42, 44,
 45, 46].  The condenser discharges hot water into the canal, and the
 canal  water is  sprayed into the air many times as it moves through the
 canal.  The amount of heat which is dissipated to the atmosphere
 depends upon the number of times the water is sprayed, and the length
 of the canal.   This technique has the capability of yielding a closer
 approach to the ambient wet-bulb temperature than the other methods
 [42].

 Spray  canals utilizing the series concept appear to be the most popular
 method of spray cooling in new installations and particularly for
 large  power plants [39, 42].  A recent innovation in spray cooling is
 the floating (powered) spray module [46, 47, 48].  Spray modules
 usually consist of from one to twelve nozzles arranged as a floating,
 self-contained  system with a pump.  Dependent upon the particular
 design, the pump power may range from 20 hp  (14.9 kW) to 100 hp
 (74.6 kW), and the pump discharge may vary from 2600 gpm  (9.84 m /min)
 to 12000 gpm (45.4 m /min)  [42, 47, 48, 49].  Each module is serviced
 by its own pump and is independently deployed along the canal, being
moored and electrically connected to shore.
                                  230

-------
The floating  spray modules  take  in water  from just below the float
level to a depth of  approximately 3  ft  (0.91 m) , and the spray pattern
produced may  vary from 20 to  50  ft  (6.1 to 15.2 m) in diameter and
from 10 to 20 ft  (3.05. to 6.1 m) high.  These ranges are, again,
dependent upon the particular design of the module [47, 48, 49].

One set of module characteristics is chosen for the present analysis.
This set of characteristics reflects units commonly in use and con-
ditions most  likely  to be faced  in  backfitting  applications.  The
three major manufacturers of  powered spray modules can each supply
units matching the size which is considered in this study [47, 48, 49].

A.  OPERATION MODELS OF SPRAY COOLING
The thermodynamic analysis  of a  spray canal for a particular applica-
tion includes many site-dependent variables.  It is not possible to
include all of these variables in the present study, and certain fea-
tures of the  spray cooling  system are held fixed with the resultant
limitations on the analysis.  The particular spray modules chosen for
the current investigation utilize a  75 hp (55.9 kW) pump and have a
                                   3
discharge rate of 10000 gpm (37.8 m  /min) .  In all cases, the spray
canal is assumed to  be straight  and  oriented perpendicularly to the
direction of  the prevailing summer wind.  The canal cross-section is
trapezoidal with side slopes  of  3-horizontal to 1-vertical, and the
depth is 10 ft (3.05 m) .  The canal  top-width depends upon the number
of rows of spray modules mounted across the canal, i.e., the number
of modules per group.   Likewise, the length of the canal depends upon
the number of module groups deployed along it.  The depth of water
flowing in the canal is held  constant at  8 ft (2.44 m) .

The spacing between  adjacent  modules in both the streamwise and trans-
verse directions is  held constant according to the following plan.  The
modules are considered to be  arranged along the canal on lines which
are parallel  to the  canal sides.  The centerline of the first module
                                  231

-------
 is  located at a distance of 100 ft  (30.5 m) from the upstream end of
 the canal.  Adjacent modules along the canal are separated by a dis-
 tance of  100 ft  (30.5 m), center-to-center, and the downstream end of
 the canal is also 100 ft  (30.5 m) from the center of the last module.
 For modules arranged in multiple rows across the canal, the center-to-
 center distance between rows is 75 ft  (22.9 m), and the canal shoreline
 on  either side of the modules is located at a distance of 50 ft (15.2m)
 from the  center of the outboard rows.  The rows of modules are along
 lines which are perpendicular to the canal.

 As  mentioned, the canal geometry and the module layout are fixed for
 the present analysis.  However,  there is enough built-in flexibility
 for this  set-up to handle many different module arrangements.  See,
 for example [47, 48 J.  It should be mentioned that the canal geometry
 and module spacing as described determine, mainly, land requirements
 and canal construction costs which are considered in detail in Section
 VIII.B.

 With the  spray module characteristics and the canal geometry chosen,
 the thermodynamic analysis of spray canal cooling depends upon the
 mathematical simulation which is employed.  There are three basic types
 of  models for predicting the thermal performance of spray cooling
 systems.  These models are listed by Ryan [39] as the manufacturer's
 model, the NTU model, and the cellular model.

 The manufacturer's models are usually based on the measured performance
 of  a single nozzle.  Various performance curves and correction factors,
 all proprietary information, have been developed and are used by the
manufacturers to size and fit given cooling applications.  The infor-
mation on system performance which is available to the public may be
useful for simplified performance checks [47, 48].

The cellular model, which assumes that the spray field is made up of
                                  232

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a number of identical droplets each surrounded by a cell of air, was
originally developed for the analysis of conventional spray cooling
[50].  This model may not be useful for modular spray cooling due to
large droplet size in the sprays, but certain variations of the basic
model are being considered  [39].

The NTU  (number of transfer units) model is similar to the theory based
on the Merkel equation which is commonly used to describe the heat
transfer occurring in evaporative cooling towers [44, 46].  The basis
of this model is carefully  explained by Chen [5l] and summarized by
Porter [52] and Porter and  Chen [53].  The NTU method is used in the
current  investigation following their presentation.

The Merkel equation may be  written as

                      TH
                       H    dT
                                 =  (K  AVmJt,                  (48)
                         h(T)-h     ' c  d' d  d
                       C       a
in which 5 is the  specific heat of  liquid water at constant pressure;
T  and T  are the  temperatures of the cold and hot water, respectively;
 C      H
h(T) and h  are the total heats  (sigma functions) of the water at
          cl
temperature T, and of the air-vapor mixture, respectively; KC is the
effective droplet  convective heat transfer coefficient; A, is the
droplet surface area; m, is the mass of the droplet, and t, is the
time of flight of  the water droplets.  The overbar indicates average
values over the time of flight of the spray which integrates the
complex dynamical  effect into a single parameter called the number of
transfer units  (NTU) [52].

If it is assumed that h  may be approximated by its average value
                       cl
(constant) at the  local wet-bulb temperature, Twb£, and that dh/dT=b
is constant over the integration, NTU may be replaced by an average
value, NTU, which may be approximated by
                                 233

-------
                         NTF~~  (E/bJ  In -2-^                 (49)
 Herein,  b   is  the  constant, b,  evaluated  at the  film temperature, Tf,
 which is estimated as  the average of the  hot-water temperature and
 the  local  wet-bulb temperature  [52j; i.e.,
                             Tf °  (TH * Twb£)/2                   (50)

 Equation  (49) may be  inverted to yield a relationship for the cooling
 range  of  a  single module,
              T-T  =  (T-T    )  '(1-expt-NTU (b_/£)])               (51)
                H  C     ri WJDX/              r

 For  a  known  hot-water  temperature entering a module, the temperature of
 the  cold water  being returned  to the canal can be computed  from  this
 equation if  the local  wet-bulb temperature, T , „, the constant,  b^,
                                             wb*-                  l
 and  the average number of transfer units, NTU, are known.   The deter-
 mination of  these quantities is discussed in the following  paragraphs.

 For  the proper  assessment of spray cooling, it is quite  important to
 consider the effects of the sprays upon  the local psychrometric  con-
 ditions.  The presence of hot-water sprays will increase the  air temp-
 erature and  humidity in their  vicinity.  Therefore,  if spray  modules
 are  placed close together, these interference effects upon  the down-
 wind units which cause a  decrease in cooling performance must be
 considered.   Since the wet-bulb temperature of the air is driven toward
 the  local canal temperature, Porter [52] and Porter  and  Chen  [53]
 suggest a correction in the local wet-bulb temperature of the form
                          T    = T   -F  (T-T  )                   (52)
                           wb&    wb w  H   wb

where T ,  is the ambient wet-bulb temperature and F  is the wet-bulb
       wb                                           w
                                  234

-------
correction factor.  The correction factor, which varies from zero to
one, is an experimentally determined function of distance downwind
from the center of individual  spray modules.  A set of average values
of F  is given by Porter [52]  for different numbers of rows of modules
    Vv
across the canal and for various row separation distances.  These
values were determined from  field measurements of two types of
modules operating at different flow rates and module configurations.
It is noted by Porter  [52] that these correction factors should be
regarded as tentative due to the limited amount of verification.  The
maximum row separation distance reported in Porter's table is 60 ft
(18.3 m) , and those values of  the wet-bulb correction factor are used
in the present study for a row separation distance of 75 ft  (22.9 m)
resulting in a slightly conservative correction.  The local wet-bulb
temperature needed in  equation (51) is  then computed from equation  (52)
using the wet-bulb correction  factor from Porter's table [52].

The constant, b_, which is used in equation  (51) is the rate of change
of the total heat of the air-vapor mixture with respect to wet-bulb
temperature evaluated  at the film temperature, Tf.  The dependence of
the total heat  (sigma  function) of air-water vapor mixtures upon wet-
bulb temperature  is given by Berry  [54] as
                        h  = 0.240 T,.+w (h -T  +32)              (53)
                         a          db  s  v  wb

where w   is  the  specific humidity, and h^, the enthalpy of  the vapor
is expressed in  terms of the dry-bulb temperature as

                             h  = 1061.8+ 0.44T,,                  (54)
                              v                db

Equations  (53) and  (54)  may be combined yielding

                 h  =  (0.240 + 0.44w )T_ +w (1093.8-T)           (55)
                                   S  Cl-D  S          W£5
                                   235

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The  specific humidity, w  , is given in terms of the atmosphereic
                        s
pressure, p  , and the vapor pressure of the air, e , by [54]
           A                                      A

                      w  = e /1.608(p -e )                        (56)
                       s    A        A  A

and  the vapor pressure is expressed in terms of its saturation value,
e  ,  by [15]
 S

           e  = e  -0.000367 p [T-T J[l+ (T   -32)/157l]      (57)
            As            A  db   wb       wb

The  saturation value of the vapor pressure is taken from the saturation
curve as discussed in [15].

The  total heat of the air-vapor mixture at different values of wet-
bulb temperature can be computed from equation  (55), and b  can be
found from a finite-difference approximation of its definition; i.e.,
                                                                  (58)
 in which the ratio is evaluated at the film temperature.

 The average number of transfer units, NTU, is also needed in equation
 (51) to compute the cooling range of a single module.  It is generally
accepted that NTU depends primarily upon wind speed [46, 47, 52, 53]
although this concept is subject to some controversy [39].  Porter
[52] and Porter and Chen [53] have presented an approximate correla-
tion of module NTU with wind speed.  The values of NTU were determined
from tests of entire canals by matching their observed performance to
the theory [53],  However, Porter  [55] has reported that this curve
results in values of NTU which are too high.  In his discussion of
the relationship between wind speed and NTU, Ryan  [39] compares  the
curve of Porter and Chen  (as it first appeared  in  a technical  report
prior to the publication of [53J) with one constructed from  some
                                  236

-------
unpublished data  of  Hoffman.   Hoffman's curve  is  somewhat  lower than
that of Porter  and Chen.   Another curve of NTu" vs_. wind  speed presented
by a spray module manufacturer [47]  is  also  lower than Porter and
Chen's curve.   Therefore,  for  the present study,  a relationship between
NTU and wind  speed was  constructed by considering the average of the
two curves presented by Ryan  [39].   The equation  of this straight line
is

                            NTU = 0.036  V2 +0.156                  (59)

where V   is the wind speed in  mph.   This curve is useful for approx-
imating values  of NTU to be used in  equation (51); however, a better
estimate  of NTU would be necessary for  a more  accurate assessment of
a given situation.

Equation  (51) and the material just  presented  allow the thermodynamic
analysis  of a single module.   This information for a typical module
must be included  with the  flow properties of the  canal water in order
to investigate  the cooling performance  of the  entire spray canal
system.   Assuming complete mixing of the canal water with the spray
water between passes of modules .along the canal,  Porter  [52] gives
the equation  to determine  the  canal  cooling  performance which is used
in the present  study, viz.,
       f/£]) >   <60>

In this equation, N     is  the  total number of modules in the canal, and
r  is the ratio of the  flow rate per module to the total canal flow
 F
rate.  It should be noted  that N    = N  x m where N is the number of
                                tot
module groups deployed  along the canal,  and m is the number of modules
per group.  As mentioned earlier, each module may contain from one to
twelve nozzles.  The number of nozzles is not important in the present
study, and it should not be confused with N or m.
                                   237

-------
The amount of spray water evaporated must also be calculated to deter-
mine make-up water requirements for the spray cooling system.  The
fraction of canal flow evaporated is directly proportional to the
cooling range and is approximated by Porter [52] as
                                                                  (61)
where H   is the latent heat of vaporization of water  (at constant
pressure) and B   is the so-called Bowen ratio, which is the ratio of
               o
the  sensible to the evaporative heat transfer.  In the present study,
the  latent heat of vaporization is computed by [35j
                      HV = 1087-0.54T   (Btu/lb)                   (62)

and the Bowen ratio is assumed to be zero, resulting in a conservative
estimate of the water evaporated.  The total evaporative water loss,
W  , is given by the product of r  x GPM.
 L                             E

The thermodynamic model described in the preceding paragraphs of this
Section is employed to estimate the cooling effectiveness and water
evaporation rate of different size spray canal systems.  The opera-
tional aspects of this model as it is applied to the backfit situation
are described next.

The input variables for the spray canal model include the meteorolog-
ical conditions, spray module layout, and hot-water flow conditions.
The meteorological conditions include the dry-bulb temperature, T   ,
                                                                 db
wet-bulb temperature, T , , atmospheric pressure, p , and wind speed,
                       Vfi)                         £\
V  .  The spray module layout is described in terms of the number of
module groups (or passes) along the canal, N, the number of modules
per group (or the number of rows of modules) across the canal, m,  and
the spacing between adjacent modules.  The input variables related
to the hot water at the canal inlet are the hot-water temperature,  T ,
                                                                     H
                                  238

-------
and the total canal  flow  rate, GPM.   it  should be noted that the
canal flow rate  is specified by  the  reference heat rejection rate,
Q*, if a particular  design  cooling range is predetermined; i.e.,

                            GPM = c3Q*/£RC                        (63)

where GPM is the canal  flow rate in  gpm;  Q* is the reference heat
rejection rate in Btu/hr, £ is the specific heat at constant pressure
in Btu/lb-°F, and RC is the cooling  range in degree F.  The constant
c3 = 7.481/(60x62) is the numerical  factor converting Ib/hr to gal/min.

The wet-bulb correction factor is chosen,  based on the geometric
information, and it  is  used together with the hot-water and ambient
wet-bulb temperatures to  compute the local wet-bulb temperature by
equation  (52) .   Next, the wind speed is  used in equation  (59) to
estimate NTU.   The  psychrometric variables are then combined according
to equation  (55)  through equation  (58)  to obtain the value of b_,
and the cold-water  temperature  can be computed from equation (60) for
the known ratio of  module flow  rate to  canal flow rate for any number
of modules.  With the  cold-water temperature thus computed, the
fraction of  water lost due to evaporation is found from equation  (61) ,
and the total  evaporative water loss can be calculated.

The outputs  from  the spray cooling model are the temperature of the
cold water being  returned to the condenser and the total water loss
due to evaporation.  This information is utilized together with the
condenser and  other power plant parameters in performing the economic
analysis.

B.  CAPITAL  COSTS OF SPRAY CANALS
The most significant components of the  capital costs for a spray  canal
are the costs  of  the modules, the  cost  of the canal construction
(excavation  and canal  lining) ,  and the  cost of the pump and piping
                                  239

-------
 system related to transporting the hot water from the condenser to
 the canal and returning the cold water to the condenser.

 Capital  costs of spray modules are, of course, dependent upon the
 particular model design and manufacturer which supplies the units.
 Unit prices may be quoted in terms of $/hp or directly in $/unit.  On
 the basis of private communication with two manufacturers [56, 57]
 and a published cost estimate [49], a unit cost figure which lies
 between  the highest and lowest cost estimates has been chosen.  It is,
 however, not entirely clear what these costs include regarding auxil-
 iary equipment; therefore, for the present study, a unit capital cost,
 c  = $22,500  per module  (1974 estimate) including mooring and
 electrical equipment is used.

 The cost of canal construction is another major component of the capi-
 tal costs.  The major items contributing to the cost of canal construct-
 ion are  the excavation and lining costs as well as the cost of the
 land itself.  The length and top-width of the canal are based upon the
 number,  layout, and spacing of the modules as described in the previous
 Section.  The required land area is taken as 2.5 times the plan area
 of the canal.  The additional land area is necessary for access roads,
 electrical service facilities, and mooring facilities.

 The cost of land varies over a wide range, as mentioned earlier, and
 for this study, it is taken as a  = $3000 / acre  ($7413/hectare).  The
                                Xj
 cost of  canal excavation is determined from the volume of earth
 removed  in building the canal.  In the present study a unit excavation
 cost, c  = $2.50/yd  ($3.27/m ) is used.  The cross-sectional shape of
       ij
 the canal is held fixed as described in Section VIII.A, and the canal
volume is easily computed when the length and top-width are known.

Canal lining costs depend upon the type of lining being used and vary
over a wide range.   Minimum lining costs are obviously incurred  for an
                                  240

-------
unlined canal, and  the most  expensive  canal lining in common use is
concrete  [47].  There are  several other possibilities for canal linings
which offer a choice between higher  capital cost and a decreased
durability.  The  canal lining for the  present  study is taken as
concrete,  6 in.  (0.15 m) thick.  The lining cost is based upon a unit
concrete  cost of  $50/yd   ($65.40/m3) which includes the canal construc-
tion costs.  For  a  canal lining  of constant thickness, unit costs are
usually expressed in terms of the lining area.  Expressing the concrete
lining cost for the given  cross-sectional shape in terms of the lining
area results in a unit lining cost,  c  = $0.93/ft  ($10/m ) .  These
                                     L
1974 estimates for  excavation and concrete were obtained from local
contractors, and  it is assumed that  the total  estimate of canal
construction costs  is representative of actual charges.

The capital cost  of the pump and piping system which circulates the
condenser cooling water is based upon  the canal flow rate and the total
pumping head.  This cost may be  determined from the chart or formula
given by  Jedlicka [26, p.  N-43 or Eq.  (30), p. 64].  Assuming a pumping
head of 40 ft  (12.2 m) , the  unit cost  of the pump and piping system,
c  ,  (including installation)  is seen  to be approximately $1.50/gpm
 PP    3
 ($396/m /min) based on 1970  estimates.  Annual maintenance cost for the
spray canal system  is taken  as 1% of the pump  and module operating cost

C.  REFERENCE SIZE  OF SPRAY  CANALS,  N*
The reference size  for a spray canal,  N*, is defined as the number of
groups of modules along the  canal, N,  required to reject Q* while
maintaining the-turbine back pressure  at p1 and delivering P* at the
reference  meteorological conditions  which may  be arbitrarily selected.
In the present study, spray  canals are investigated with either one
or four modules per group; therefore,  for each value of Q*, two refer-
ence sizes are needed.  The  reference  meteorological conditions for
the spray  canal study are:   wet-bulb temperature, 68°F  (20.0°C);
dry-bulb temperature, 78°F (25.6°C), and wind  speed, 8 mph (3.57 m/sec).
                                 241

-------
 The reference  spray canal size corresponding to a particular heat
 rejection rate (Figure 63) is found by first computing and plotting
 the turbine back pressure, p, versus N, for a range of heat rejection
 rates,  Q, at the reference meteorological conditions.  These computa-
 tions are carried out for various values of m, the number of modules
 per group.  The canal flow rate is determined from equation (63)
 (for each value of Q), and the thermodynamic model for spray cooling
 is combined with the turbine heat rejection rate characteristics to
 obtain  the desired information, p vs. N.

 Data for Figure 63  (Q vs. N) are read from these curves at the value
 of turbine back pressure selected for defining the reference size of
 the cooling system, viz., p' = 2.0 in. Hg (5.08 cm Hg).  One curve
 is drawn for each of the two cases m = 1 and m = 4.  It is seen that
 the curves are linear over the entire range which is considered.
 Figure  63 defines the reference spray canal size, N*, corresponding
 to the  heat rejection rate, Q*, which is used to nondimensionalize
 the size of the spray canal.

 D.  PARAMETRIC STUDIES
 A series of detailed parametric studies are made for the spray cooling
 system  in a manner paralleling the studies of the other cooling systems
 presented in this report.  The calculations are carried out for a wide
 range of canal sizes, defined by N, for the two cases, m = 1 and m = 4
 module  rows across the canal.  The size of the spray cooling system
 depends only on N and m because the spray module size and capacity
 is held fixed  as described in the introduction to this Section.
Results of detailed calculations of maximum capacity  loss, C  , annual
                                                            Ij
energy loss, E  , annual excess fuel consumption, F  ,  and annual water
              lj                                   E
loss by evaporation, W , are presented for a large range of canal
                      L
sizes.  The canal size is normalized by N* as described in Section
VIII.C, and the other variables are normalized with the same  reference
                                 242

-------
to

-------
quantities as the three cooling systems described previously.  Four
sets of meteorological conditions are chosen as representative of
four geographical locations in this country, viz., Chicago, Los Angeles,
Miami, and St. Louis.  All the studies of spray cooling are carried out
for a wind speed of 8 mph  (3.57 m/sec), and the other meteorological
conditions at each location are described in Section IV.B.

Figures 64 through 67 are plots of normalized capacity loss, normalized
energy loss, normalized excess fuel consumption, and normalized water
loss by evaporation vs. normalized canal size for the particular
case of turbine A  (411 MW), at Los Angeles with m = 1 and m = 4.  Also
shown in  these figures are the results for a hypothetical turbine
which has a nameplate capacity and reference heat rejection rate
twice those of turbine A, but whose basic heat rate characteristics
are the same as those of turbine A.   (See Section V.D or VI.E for
details.)  As for the natural-draft cooling tower and the cooling pond,
the normalized results for the two turbine sizes did not collapse
indicating a certain scale effect as discussed in Section VI.E.

Detailed  studies of the dependence of the quantities listed above
upon spray canal size for turbines A, B, and C  (see Figures 4, 5, and
6 and Table 1 ) at each of the four geographical locations are
presented in Figures 68 through 71.  The turbine designs represent a
wide range of practical applications for which the plotted results
may be applied.  But, because of the scale effects, the final results
are valid for a 411 MW unit only.  If the graphical results are to be
used for  other sizes of turbines, the interpolation technique described
for the natural-draft towers  (Sections VI.E and VI.H) should be
employed.  However, over most of the range of practical application,
the differences in the results for the 411 MW and the 822 MW units
(Figure 64 through 67) are seen to be small.

In the sample calculations presented in Section VIII.G for a 312.5 MW
unit,  the curves are read directly, assuming that any errors which are
                                   244

-------
                LOS ANGELES
                  TURBINE A
                   op* =822MW
                   • P* = 411 MW
             m= NUMBER OF MODULES
                   PER GROUP
  0.2    0.4     0.6    0.8    1.0

    NORMALIZED CANAL SIZE, N/N*
Figure 64.  Normalized capacity loss
              245

-------
 LU
LU
 c/)
 o
 a:
 LU
 Q
 LU
 N
   0,08
<  0.06



O


   0.04






   0.02
     0 -
                            LOS ANGELES

                              TURBINE A



                             op*= 822MW

                             ,p*= 411 MW
             m = NUMBER OF MODULES PER GROUP
               m=l
                            rrr-1
             0.2    0.4     0.6     0.8    1.0    1.2


               NORMALIZED CANAL SIZE, N/N*




             Figure 65.  Normalized  energy loss
                           246

-------
u
D.
 Ul
u.
O

a.
O
O
UJ

u.
UJ
O
X
UJ
Q

UJ
N
     0.0
   -0.02
   -0.04
   -0.06

-------
 o
 e

 <5
 x:
                         LOS ANGELES
                           TURBINE A
           o
           e
                              o P* = 822 MW

                              • P* =411 MW
 o
 O)
 0)
 tk
 o

•2 12.0
   10.0
CC  8.0

O
O.
UJ

a:
UJ


I

o
LU
N
oc
o
6.0
4.0
   2.0
          m= NUMBER OF MODULES PER GROUP
                                               12OOO T
                                                         _l
                                                   10000
                                                         o:
                                                   8000  9
                                                     UJ


                                                6000 uj
     4000  UJ
           N
                                                2000  g
     0
            _L
                      _L
                                    -L
_L
            0.2    0.4    0.6    0.8    1.0     1.2

                NORMALIZED CANAL SIZE, N/N*
               Figure 67.  Normalized evaporation
                           248

-------
0.18  -
           0.2     0.4     0.6     0.8     1.0     1.2     1.4
               NORMALIZED CANAL SIZE, N/N*
         Figure 68(a).  Normalized  capacity loss, Chicago
                             249

-------
o

 en
   0.18
   0.16
   0.14
   0.12
                                  LOS ANGELES
 % 0.10
 Q.
 <
 O


 2 0.08
 N
   0.06
   0.04
   o.oa
             0.2    0.4     0.6     0.8     1.0     1.2     1.4

                 NORMALIZED CANAL SIZE, N/N*



         Figure 68(b).  Normalized capacity loss, Los Angeles
                              250

-------
   0.2     0.4     0.6     0.8     1.0     1.2
       NORMALIZED CANAL SIZE, N/N*
Figure 68 (c).  Normalized capacity loss, Miami
                  -251

-------
 0.18 -
0.02 -
           0.2     0.4     0.6     0.8     1.0     1.2
               NORMALIZED CANAL SIZE, N/N*
1.4
       Figure 68(d).   Normalized capacity loss, St. Louis
                             252

-------
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  z

  CO
            I-     H
    0.12-1 0.16-1 0.18
    0.10-
   O.O8 -
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 CO
 O
   0.04 -
 a:
 UJ
 -z.
 UJ
 0 0.02 -
 N
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 0.14-
 0.12-
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                  O
                                 i	r
                                                  CHICAGO
                                       TOTAL (INCL. PUMP  LOSS)
                                PUMP ENERGY  LOSS TURBINE A, B, C
                                        I	i	i       i	
                         0.2    0.4    0.6    O.8    1.0     1.2

                             NORMALIZED  CANAL SIZE, N/N*
                                                          1.4
              Figure 69(a).   Normalized energy loss, Chicago
                                           253

-------
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    0J
.012-
        .010-
0.08-
        0.06-
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        0.02-
            0.16 -
       0.14  -
            0.12 -
          O J O.04 -
             0.02 -
                               TOTAL (INCL. PUMP LOSS)
                    PUMP ENERGY LOSS

                    TURBINE A, B, C
      0.10  -
            0.08 -
      0.06 -
                        0.2     0.4     0.6     0.8     1.0    1.2     1.4

                         NORMALIZED CANAL SIZE.N/N*
           Figure 69(c).   Normalized  energy  loss, Miami
                                   255

-------
      CO
      cc
  03

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  z
  m
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                                 n       I
                                                   ST.  LOUIS
                                          TOTAL (INCL. PUMP LOSS)
                                             PUMP ENERGY LOSS
                                             TURBINE  A, B, C
                                                       i       i
                         0.2    0.4     0.6     0.8     1.0     1.2

                             NORMALIZED CANAL SIZE, N/N*
                                                          1.4
          Figure 69(d).   Normalized energy loss, St.  Louis
                                    256

-------
 0.2     0.4     0.6     0.8     1.0      1.2
                               (TURBINE  A,B)
0.2
0.4
                           0.6      0.8      1.0
                                  (TURBINE  C)

   NORMALIZED CANAL  SIZE, N/N*

Figure 70(a).  Normalized excess fuel
              consumption, Chicago
             257

-------
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              0.2    0.4     0.6     0.8     1.0     1.2
                                            (TURBINE  A,B)
                   I	i	i       i	|	|
                   0      0.2    0.4     0.6     0.8     1.0
                                              (TURBINE C)

                NORMALIZED CANAL SIZE, N/N*


             Figure 70(b).  Normalized excess fuel
                          consumption,  Los Angeles
                            258

-------
                              .0     1.2
                             (TURBINE  A,B)
           0.2
    0.4     0.6
 0.8      1.0
(TURBINE C)
  NORMALIZED  CANAL SIZE, N/N
Figure  70(c).
Normalized excess fuel
consumption, Miami
             259

-------
Ul
       0
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                                                 (TURBINE C)


                 NORMALIZED  CANAL  SIZE, N/N*


               Figure 70(d).  Normalized excess  fuel

                              consumption,  St. Louis
                            260

-------
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                     NORMALIZED  CANAL SIZE, N/N*
                                                         - 12000
                                                         - 10000
                                                         - 8000
                                                         -  6000
                                                         - 4000
                                                         - 200O
1.4
                                                                 m

                                                                 UJ
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                                                                             o
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         10000
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             Figure 71(a).  Normalized  evaporation, Chicago
                                         261

-------
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         NORMALIZED CANAL SIZE, N/N*






Figure 71(b).  Normalized  evaporation,  Los Angeles
                           262

-------
    0.2    0.4     0.6    0.8    1.0
      NORMALIZED CANAL SIZE,  N/N*
                                             12000
                                           - 10000
                                           - 8000
                                           - 6000
                                           - 4000
                                           - 2000
1.4
                                                   03
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Figure 71 (c).   Normalized evaporation, Miami
                              263

-------
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              Figure 71(d).   Normalized  evaporation, St.  Louis
                                           264

-------
introduced are small.  This assumption is checked by comparing the
results from the graphical computation with results obtained using
the computer program.  The comparison is quite acceptable as seen
at the close of Section VIII.G. It must be emphasized that if the
size of the unit being studied varies greatly from 411 MW, the computer
program must be used to obtain accurate results.

E.  PROCEDURE FOR THE ECONOMIC EVALUATION OF BACKFITTING
The various items which must be considered in the evaluation of the
cost of backfitting an existing power plant or unit with a spray
canal cooling system have been previously described.  The manner in
which these items are to be combined in order to calculate the total
cost of backfitting is considered in this section which is followed
by a brief description of the computer program that has been developed
for this purpose.

The technique for the economic evaluation of backfitting with a spray
canal cooling system is very similar to the procedure already dis-
cussed for the other cooling systems (Sections V.F, VI.F,  and VII.E)
with the following exceptions.  In items  (b) and (c) of those Sections,
the following quantities must be substituted for the study of spray
canals:

(b)  Spray canals
     1.  The size of the spray cooling system in terms of the number
         of module groups along the canal, N, and the number of modules
         per group (rows) across the canal, m;
     2.  Unit cost of spray modules, c   ($ /module), unit canal con-
                                      s
         struction costs (excavation, c  , and lining, c ), and physical
                                       r>               J-i
         dimensions of the canal (length, L , top-width, W, depth,
                                           C              C
         D , water depth, D  , and cross-sectional  shape).
          c                cw
                                  265

-------
 (c)  Economic parameters:
     6.  Unit cost of pump and pipe system [26], c

 Once this information has been gathered, the total differential cost
 of backfitting with a spray canal can be calculated by the computer
 program or estimated by the graphical results presented in Section
 VIII.D. Use of the graphical results is subject to the limitation
 discussed at the end of that Section.  Illustration of the application
 of the graphical results is presented in Section VIII.G,

 F.  THE COMPUTER PROGRAM
 The computer program which accepts any set of numerical values for the
 various parameters  (except those which have been held fixed for the
 present study) and performs the calculations outlined in the previous
 sections is listed in Appendix VI.  The thermodynamic model used to
 simulate the performance of spray canals is basically the same as that
 developed by Porter [52] and Porter and Chen [53], but there are a
 number of important differences in other respects.  In particular,
 the economic considerations are formulated specifically for the
 analysis of backfitting in existing power plant or unit with a spray
                                                            \
 canal cooling system and cannot be used, without modification, to
 study the design of spray canals for new plants or units.

 The computer program consists of the MAIN program and four sub-
 routines, namely OPECOS, MODELW, SPRCOL, and POWERS.  The MAIN program
 reads all inputs, calculates the overall capital and total costs, and
 controls the printout of these quantities.  The inputs, along with
 the symbols and units used, are listed in Appendix II.  The primary
 functions of the various subroutines not previously identified are
as follows.

SPRCOL:   This subroutine which computes the cold-water temperature
                                  266

-------
         and the water loss due to evaporation contains the thermo-
         dynamic model described in Section VIII.A.

The overall program logic is similar to that already described for the
other cooling system  calculations.  Minor changes have been made in
the main program and subroutines to accomodate the spray canal cooling
model.  These changes are included in the program listing in Appendix
VI.

G.  A HYPOTHETICAL TEST CASE
1.  Consider a power plant with the characteristics identified in
    Section V.H.I, which also  implies that the extreme dry-bulb
                 ^
    temperature, T,. = 97.0°F  (36.1°C) for Miami.
                  db
2.  Assume that this plant is  to be backfitted with a spray canal
    system whose 'characteristics are:
    Number of module groups,  N
    Number of modules/group,  m
    Module size,
    Module pump flow rate
    Canal cross-section

    Canal length, L
    Canal depth, D
    Water depth, D
                  cw
    Canal top-width, W
    Wind speed, V

    Total water flow rate,
             1.912 x lo9' ..  7.481
        GPM
                  20        60><62'
            equation  63)
= 80
= 1
= 75 hp pump (55.9 kW)
= 10,000 gpm (37.8 m /min)
= Trapezoidal (3-horizontal
  to 1-vertical side slope)
= 8100 ft (2470 m)
= 10 ft (3-05 m)
= 8 ft (2.44 m)
= 100 ft (30.5 m)
= 8 mph
   (3.57 m/sec)
= 192,254 gpm
  (727.7 m3/min)
                                  267

-------
    Unit module cost, c
                       s
    Unit cost of pump and pipe
       system, c
                PP
    Unit canal excavation cost, c
    Unit canal lining cost, c
    Concentration ratio, k*
    Unit blowdown treatment cost, c.
    Cost of hook-up and testing, C,
                                  HT
    Maintenance cost, C
                       m
    Downtime, DT
                                  =  $22,500/module

                                  =  $1.50/gpm
                                    ($396  /m3/min)
                                  =  $2.50/yd3
                                    (3.27/m3)

                                            2
(Concrete,  6 in.  (0.15 m)  thick    =  $0.93/ft
                                    ($10/m2)
                                  =  3.3
                                  = $0.05/1000 gal
                                    ($0.0132/m3)
                                  = included  in unit module cost
                                  = 1% of  pump and  module
                                    operating cost
                                  =720 hrs (30 days)
3.  Assume that the various economic parameters are as identified in
    Section V.H.3.
4.  Use of example results:
    (a)   Land Area required
         A  = 2.5 XL  x w
          L         c   c
                                  =  46.5  acres
                                    (18.8 hectares)
    (b)   Excavation required,
         excavation volume =
         = 8100(10)(100-30)/27
 excavation volume  =  L D  (W -3D  )
                      c c   c  c
    (c)   Lining required
         lining area = L (W-6D +2/Io" D )
                        c     c       c
         = 8100 x (lOO-60+20/Io")
                                  = 210,000 yd
                                    (160,566 m3)
                                  = 836,290 ft
                                    (77,691 m2)
                                  268

-------
(d)   Read Figure 63 to find N*
     Determine normalized canal
       size, N/N*                  '  =1.18
(e)   Read Figure 68(c) (turbine A,
       Miami)  to find normalized
       capacity loss, C/P*          = 0.024
                       LI
     Thus, capacity loss
       C  = 0.024x312.5*1000       = 7500 kW
(f)   Read Figure 69(c) (turbine A,
       Miami) to find normalized
       energy loss, E /PE*
                     L
     Thus, energy loss,
       E  =0.02x312.5x1000x8760
                                = 0.02
                                = 54.75x10 kW-hr/year
(g)  Read Figure 70(c) (turbine A,
       Miami) to find normalized
       excess fuel consumption,
       ni VPE*
     Thus, excess fuel,
                                = 0
       F  = 0 x 312.5 x 1000 x 8760/0.85 = 0 kW-hr/year
        E
(h)  Read Figure 71(c) (turbine A,
       Miami) to find normalized
       water evaporation, W /Q*
                           Lt
Thus, evaporation
  W  =10.7 x 1.912 xl09/3.413
      x 106
                                = 10.7 acre-ft/yr-MW(th)
                                  (1.32 xio4 m3/yr-MW(th)
                                     = 5994 acre-ft/year
                                   (7.39x
                                                  m/year)
                             269

-------
    Also, blowdown, W, = W  .  . .    = 2606 acre-ft/year
                     b    L k  -1                fi  3
                                      (3.21 x iofa m /year)
    And, makeup,
                k*
      W  = W  . •   n = W,  + W         = 8600 acre-ft/year
       m    L k*-l    b    L                    _  _
                                      (1.06 x 10  m /year)
 (i) Read Figure 69(c) (turbine A,
      Miami) to find normalized
      pump and module energy loss,
      E /PE* =                      = 0.019
       L
    Thus, pump and module energy
      loss,
      ET (pump) = 0.019 x 312.5 x1000
                                                6
                x 8760              = 52.01 x io  kW-hr/year
•5.  Cost determination:

    Capital costs
    Spray module cost,
         N(m)c  =80x1x22,500      = $1,800,000
              s
    Excavation cost,
         (excavation volume)xc_
                              E
           = 210,000x2.50          = $  525,000
    Lining cost,
         (lining area) x c
                         L
            = 836,290X0.93         = $  777,750
    Pump and pipe system cost,
         c   xGPM = 1.50x192,254   = $  288,380
    Pump and pipe system salvage,
         C1  = 0.2 C                = ($ 57,680)
          PP        PP
    New Condensers, C               =0
                     c
                            270

-------
Salvage value of old condensers,


     Cc                         = (    0   )


Salvage value of other open-


     cycle components, C1       = (    0   )
                        o


Hook-up and testing cost, c _   = included in module cost
                           HT

Additional Land,


     A a  = 46.5x3000          = $139,500



Replacement capacity,


     CC  =Cc  = 7500x90        =$675,000
       K   Li X/


Downtime,



       DT          ea

     = 720x312.5x1000x0.007  = $1,575,000
      TOTAL CAPITAL COST, CC    = $5,722,950




Operating costs/year



Excess fuel cost,





          = Ox 0.000751         =     0



Replacement energy cost,
         = 54.75 x I06x 0.01     =$547,500
Supply water cost,


     W c  =8600x (3.259x10 )
      m w          .,

           x 0.1/10'            = $280,274
Cost of blowdown treatment


     W c  =2606x (3.259X 10 )
      b D           o
           x 0.05/10            = $42,465
                         271

-------
         Maintenance cost,
              C  =0.01 x  (52.01 x io6)
               ro
                  x 0.01                 = $5,201
         Makeup water cost with open-
              cycle system, M'           = (   0  )
         Slowdown treatment cost with
              open-cycle system, B'      = (   0  )
         Maintenance cost of open-
              cycle system, C1           = (   0  )
                             M
         TOTAL ANNUAL OPERATING COST, OC = $875,440

         Total costs
         From equation  (20), the total excess unit cost due to
              backfitting, tc, is given by
                         OC + CC x FCR
                     ° ~   8760 x p*
                       = 875,440 + (5,722,950 x .179)
                             312.5 x 1000 x 8760
                         tc = 0.6940 mills/kW-hr
To check the assumption made at the end of Section VIII.D, i.e., that
the errors introduced by reading Figures 68 through 71 directly for
the 312.5 MW unit are small, this example was also analyzed using the
computer program.  The computer results are CC = $5,703,772; OC =
$907,214/yr; tc = 0.7044 mills/kW-hr.  The difference between the
graphical result and the computer result for the total excess unit
cost is seen to be approximately 1.5%, indicating that the graphical
method does indeed yield a good approximation for the given problem.
                                 272

-------
                              SECTION  IX

                              REFERENCES
1.  Development Document  for  Proposed Effluent Limitations Guidelines
    and New Performance Standards  for the Steam Electric Power
    Generating Point  Source Category. U.S. Environmental Protection
    Agency. September 1973.

2.  Development Document  for  Effluent Limitations Guidelines and
    New Source Performance  Standards for the Steam Electric Power
    Generating Point  Source Category. U.S. Environmental Protection
    Agency. Washington, D.C.  Report No. EPA 440/1-74 029-a. October
    1974.  770 p.

3.  Proposed Criteria for Water Quality. U.S. Environmental Protect-
    ion Agency. Vol.  I and  II. October 1973.

4.  Development Document  for  Effluent Limitations Guidelines and
    Standards of Performance, Steam Electric Power Plants. Burns &
    Roe, Inc., for U.S.Environmental Protection Agency under contract
    No. 68.01.1512. June  1973, draft.

5.  EPA, Utilities Draw Closer on  Thermal Discharges. Industrial
    Developments, Electrical  World, p. 25-26, November 1974.

6.  Steam  Electric Power  Generating Point Source Category:  Effluent
    Guidelines and Standards. Federal Register. 39_ (196): 36200-
    36201. U.S. Environmental Protection Agency. October 1974.

7.  Comments on EPA's Proposed §304 Guidelines and §306 Standards of
    Performance for Steam Electric Powerplants. Edison Electric
    Institute - Utility Water Act Group. Vols. I, II and III. U.S.
    Environmental Protection Agency. June 1974.

8.  Climatography of  the  United States, No. 82, Decentennial Census
    of United States  Climate, Summary of Hourly Observations, U.S.
    Weather Bureau.

9.  Merkel, F. Verdunskungskuhlung. VDI Forschungsarbeiten  (Berlin).
    275:  1-48, 1925.
                                 273

-------
10.  Nottage, H.B., Merkel's Cooling Diagram as a Performance Correla-
     tion for Air-Water Evaporative Cooling Systems. ASHVE Trans-
     actions. 47_: 429-448, 1941.

11.  Baker, D.R. and L.T. Mart. Cooling Tower Characteristics as
     Determined by the Unit-Volume Coefficient. Refrigerating Engin-
     eering, p. 965-971, September 1952.

12.  Cooling Towers and Spray Ponds. Chapter 21, In: ASHRAE Guide and
     Data Book, New York, ASHRAE, 1969. p. 255-268.

13.  Baker, D.R. and H.A. Shryock. A Comprehensive Approach to the
     Analysis of Cooling Tower Performance. Journal of Heat Transfer,
     ASME. 83: 339-350, August 1961.

14.  Park, J.E. and J.M. Vance. Computer Model of Crossflow Towers.
     In: Cooling Towers. Editors of Chemical Engineering Progress.
     New York, AICHE, 1972. p. 122-124.

15.  Croley, T.E.II, V.C. Patel, and M.S. Cheng. The Water and Total
     Optimizations of Wet and Dry-Wet Cooling Towers for Electric
     Power Plants. Iowa Institute of Hydraulic Research, Iowa City,
     Iowa. IIHR Report No. 163. Office of Water Resources Technology,
     January 1975. 290 p.

16.  Dickey, J.B., Jr., and R.E. Gates. Managing Waste Heat with the
     Water Cooling Tower. 2nd Edition. Mission, Kansas, The Marley
     Company, 1973- 19 p.

17.  Cooling Towers-Special Report. Industrial Water Engineering. 7_:
     22-54, May 1970.                                             "~

18.  Farell, C. and F.E. Maisch. External Roughness Effects on the
     Mean Wind Pressure Distribution on Hyperbolic Cooling Towers.
     Iowa Institute of Hydraulic Research, Iowa City, Iowa.IIHR Report
     No. 164. National Science Foundation and Marley Company. August
     1974. 51 p.

19.  Threlkeld, J.L. Thermal Environmental Engineering. Englewood
     Cliffs, New Jersey, Prentice-Hall, 1970. 166 p.

20.  Kennedy, J.F. Wet Cooling Towers. In: Engineering Aspects of Heat
     Disposal from Power Generation, Vol. II, Harleman, D.R.F.  (ed.).
     Cambridge, Massachusetts, Massachusetts Institute of Technology,
     June 1972. p. 13-1 - 13-67.

21.  Overcamp, T.J. and D.P. Hoult. Precipitation from Cooling Towers
     in Cold Climates. Fluid Mechanics Laboratory, Department of
     Mechanical Engineering, Massachusetts Institute of Technology,
     Cambridge, Massachusetts. Report No. 70-7. May 1970. 30 p.
                                  274

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22.  Crenshaw, C.J. Investigation  into The Variations of Performance
     of Natural Draught Cooling Towers. Proc. Inst. Mech. Eng. 178,
     part 1  (35): 927-948, 1963-1964.                          	

23.  A Survey of Alternate Methods for Cooling Condenser Discharge
     Water. Dynatech R/D Company,  Report No. 16130DHS08/70. Environ-
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24.  Hogan, W.T., A.A. Liepins, and F.E. Reed. An Engineering Economic
     Study of Cooling Pond Performance. Littleton Research and Engin-
     eering Corporation. Littleton, Massachusetts. Report No.
     16130DFX05/70. Environmental  Protection Agency. May 1970. 172 p.

25.  Ryan. P.J. Cooling Ponds: Mathematical Models for Temperature
     Prediction and Design.  In: Engineering Aspects of Heat Disposal
     front Power Generation, Vol. II, Harleman, D.R.F. (ed.). Cambridge,
     Massachusetts, Massachusetts  Institute of Technology, July 1971.
     p. 12-1 - 12-57.

26.  Jedlicka, C.L. Nomographs for Thermal Pollution Control Systems.
     Hittman Associates, Inc. Columbia, Maryland. EPA-660/2-73-004.
     U.S. Environmental Protection Agency. September 1973. 171 p.

27.  Edinger, J.E. Shape Factors for Cooling Lakes. Journal of the
     Power Division, ASCE. 97_ (P04) : 861-867, December, 1971.

28.  Loziuk, L.A., J.C. Anderson,  and T. Belytschko, Finite Element
     Approach to Transient Hydrothermal Analysis of Small Lakes.
     Sargent and Lundy Engineers.  Chicago. Report No. SAD-067.
     August 1972. 32 p.

29.  Loziuk, L.A., J.C. Anderson and T. Belytschko, Hydrothermal
     Analysis by Finite Element Method. Journal of the Hydraulic
     Division. ASCE. 98JHY11) : 1983-1998, November 1972.

30.  Gibbons, J.H. and F.P.  Pike.  A Study of Selected Cooling Pond
     Design Techniques, College of Engineering, University of South
     Carolina. Columbia, South Carolina, Report No. SRO-701-1, UC-12.
     Division of Reactor Research  and Development, USAEC. June 1973.
     74 p.

31.  Ryan, P.J., D.R.F. Harleman,  and K.D. Stolzenbach. Surface Heat
     Loss From Cooling Ponds. Water Resources Research. 10(5);
     930-938, October 1974.

32.  Sonnichsen, J.C., Jr.,  S.L. Eingtrom, D.C. Kolesar, and G.C.
     Bailey. Cooling Ponds - A Survey of the State of the Art,
     Hanford Engineering Development Laboratory. Richland, Washington.
     Report No. HEDL-TME 72-01. USAEC. September 1972. 99 p.
                                  275

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33.  Edinger, J.E. and J.C. Geyer. Heat Exchange in the Environment.
     The Johns Hopkins University. Baltimore, Maryland. Report No.
     EEI 65-902. Edison Electric Institute. June 1971. 259 p.

34.  Ryan, P.J. and K.D. Stolzenbach. Environmental Heat Transfer.
     In: Engineering Aspects of Heat Disposal from Power Generation,
     Vol. I, Harleman, D.R.F.  (ed.). Cambridge, Massachusetts, Mass-
     achusetts Institute of Technology, June 1972. p. 1-1 - 1-75.

35.  Paily, P.P., E.G. Macagno, and J.F. Kennedy. Winter-Regime Heat
     Loss from Heated Streams. Iowa Institute of Hydraulic Research.
     Iowa City, Iowa. IIHR Report No. 155. Iowa State Water Resources
     Institute and National Science Foundation. March 1974. 137 p.

36.  Tichenor, B.A. and A.G. Christiansen. Cooling Pond Temperature
     versus Size and Water Loss. Journal of the Power Division, ASCE.
     97_ (PO3): 589-596, July 1971.

37.  Harbeck, G.E., Jr. Estimating Forced Evaporation from Cooling
     Ponds. Journal of the Power Division, ASCE. 90 (PO3): 1-9,
     October 1964.

38.  Sefchovich, E. Condenser Cooling and Pumped-Storage Reservoirs.
     Journal of the Power Division, ASCE. 9^7_ (P03) : 611-621, July
     1971.

39.  Ryan, P.J. Spray Cooling. In: Proceedings of a Conference on
     Thermal Pollution Analysis, Blacksburg, Virginia, Virginia
     Polytechnic Institute & State University, May 1974. p. 19-32.

40.  Hori, S., U.A. Patchett, and L.M.K. Boelter. Design of Spray
     Cooling Ponds. Heating, Piping and Air Conditioning, ASHVE
     Journal Section, p. 624-626, October 1942.

41.  Malkin, S. Converting to Spray Pond Cooling. Power Engineering.
     p. 48-49, January 1972.

42.  Rainwater, F.H. Report to the Committee on Electric Power on
     Environmental Consequences of Spray Cooling Systems. Seminar
     on Environmental Aspects of the Cooling Systems of Thermal
     Power Stations, Zurich, Switzerland, May 1974. 10 p.

43.  Nelson, B.D. Final Test Report of the Cherne Fixed Thermal Rotor
     Demonstration Conducted at the Northern States Power Company
     Allen L. King Plant, September 1973. Cherne Industrial,  Inc.,
     1973.  74 p.

44.  Kelley, R.B. Large-Scale Spray Cooling. Industrial Water Engin-
     eering, p. 18-20, August/September 1971.
                                  276

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45.  Frohwerk, P.A. Spray Modules Cool Plant Discharge Water. Power.
     p. 52-53, September 1971.

46.  Hoffman, D.P. Spray Cooling for Power Plants. In: Proceedings of
     the American Power Conference, Chicago, Illinois, 35: 702-712,
     1973.                                             —

47.  Kool-Flow, Spray Cooling Modules. Richards of Rockford, Inc.
     Rockford, Illinois, August 1974.

48.  Floating Spray Cooler Equipment and Design Specifications.
     Ashbrook Corporation. Houston, Texas. 1974.

49.  Ryan, P.J. Temperature Prediction and Design of Cooling Ponds.
     In: Engineering Aspects of Heat Disposal from Power Generation,
     Vol. II, Harleman, D.R.F.  (ed.). Cambridge, Massachusetts,
     Massachusetts Institute of Technology, June 1972. p. 11-1 - 11-74.

50.  Elgawhary, A.M. and A.M. Rowe. Spray Pond Mathematical Model for
     Cooling Fresh Water and Brine. In: Environmental and Geophysical
     Heat Transfer, Cremers, C.J., Kreith, F., and Clark, J.A. (eds.).
     New York, ASME, November 1971. p. 1-8.

51.  Chen, K.H. Thermal Analysis of Spray Canal Design. M.S. Thesis,
     Department of Mechanical & Aerospace Engineering, Illinois
     Institute of Technology, Chicago, Illinois. May 1973. 80 p.

52.  Porter, R.W. Analytical Solution for Spray-Canal Heat and Mass
     Transfer. AIAA/ASME 1974 Thermophysics and Heat Transfer Confer-
     ence, Boston, Massachusetts, July 1974.

53.  Porter, R.W. and K.H. Chen. Heat and Mass Transfer of Spray
     Canals. Journal of Heat Transfer, ASME. 96: 286-291, August 1974.

54.  Berry, C.H. Mixtures of Gases and Vapors. In: Mechanical Engin-
     eer's Handbook. Marks, L-S.  (ed.), Fifth Edition, 1951. p. 354-
     363.

55.  Porter, R.W. Illinois Institute of Technology. Chicago, Illinois.
     private communication. October 1974.

56.  Wendt, R.C. Ashbrook Corporation. Houston, Texas, private commun-
     ication. August 1974.

57.  McArt. S. Richards of Rockford, Inc. Rockford, Illinois, private
     communication. November 1974.
                                 277

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                               SECTION X



                          GLOSSARY OF SYMBOLS
A         cooling pond area


A*        reference cooling pond area


A         cooling pond access land area
 a

A         condenser surface area
 c

A         water droplet surface area
 d

A         required land area
 L

a.        unit land cost
 JO

B         tower breadth


B1        blowdown cost with open-cycle system


B         Bowen ratio
 o

bf        dh/dT evaluated at T


C         capital cost of new condenser
 c

C'        salvage value of old condenser
 c

C         capital cost of closed-cycle cooling system
 cs

C         cost of hook-up and testing
 HT

C         maximum capacity loss
 L

C         annual maintenance cost of closed-cycle system


C1        annual maintenance cost of open-cycle system
 m

C1        salvage value of old system components other than pumps,

          piping and condensers


C         capital cost of new pump and pipe system
 PP

C1         salvage value of old pumps and piping
 PP

CC        total differential capital cost


CC        differential cost of unit downtime during changeover to

          closed-cycle cooling
                                  278

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CCR        capital cost of replacement capacity
ccs        differential capital cost of closed-cycle cooling system
CF         plant capacity factor
c, c ,c ,c  numerical conversion factors
c          unit cost of cooling pond access land
 a.
c,          unit cost of water treatment
 b
c          unit cost of new condenser
 c
c_         unit excavation cost for spray canal
 Ei
c          unit canal lining cost
 L
c.         unit capital cost of replacement capacity
c          unit maintenance cost
 m
c          unit cost of cooling pond
c          unit cost of pump and pipe system
c          unit cost of spray modules
c          unit cost of cooling towers
c          unit cost of water
 w
D          width of clearance around cooling tower
D,         bottom diameter of hyperbolic shell
D          throat diameter of hyperbolic shell
 £*
D          top diameter of hyperbolic shell
D          spray canal depth
 c
D          water depth in spray canal
 cw
DT         downtime during hook-up
E          annual energy loss
 Li
EA         actual net energy output for one year
ER         rated net energy output for one year
e          vapor pressure of air at T
 A                                   ajo
e          unit cost of replacement energy
 x/
e«         unit differential cost of replacement energy during downtime
  x>
e
           saturation vapor pressure of air at
F          annual  excess  fuel consumption
 E
F          wet -bulb correction  factor
 w
FCR        fixed charge rate
                                  279

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f          frequency function
f          unit cost of fuel
 c
G          total air flow rate through cooling tower
GPM        water flow rate
H          fill  (pile) height
H          latent heat of vaporization
h(T)       total heat of water at temperature T
h          total heat of air-vapor mixture
 3.
h          enthalpy of water vapor
K          overall head loss coefficient
K          effective droplet convective heat transfer coefficient
 c
k          concentration of contaminants
k*         concentration ratio
k          maximum allowable concentration of contaminants
 m
L          fill  (pile) length
L*         reference length of mechanical-draft cooling tower
L          spray canal length
 C
£          frictional head loss in hyperbolic shell
£          frictional head loss in evaporative pile
 P
M1         makeup water cost with open-cycle system
m          number of spray modules per group
m,         water'droplet mass
 d
N          number of module groups (passes) along spray canal
N*         reference size of spray canal
N          N*m, total number of spray modules in canal
 tot
NTU        number of transfer units
NTU        average number of transfer units
OC         differential operating cost
OC         cost of excess fuel consumption
  EF
OC         operating and maintenance cost of replacement capacity
  R
OC,,        differential operating and maintenace cost of closed-cycle
           cooling system
P          power output
                                  280

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P*         nameplate power output
Pcs        power to operate closed-cycle cooling system
P          power demand
?„„        plant heat rate
 H.K
Pmin       gross power output at extreme temperature
PE*        nameplate energy
p          turbine back pressure
P*         reference turbine back pressure
P1         turbine back pressure for calculation of reference cooling
           system size
p.         atmospheric pressure
 r\
p          maximum allowable turbine back pressure
 max                   '                   e
Q          heat rejection rate
Q*         reference heat rejection rate
Q          in-plant and stack heat losses
Q          rate of heat input  (heat equivalent of fuel consumption)
QA         atmospheric radiation to water surface
QAR        reflected atmospheric radiation from water surface
QC         conductive heat loss
QE         evaporative heat loss
QP         heat input to cooling system from plant
QR         heat input by solar and atmospheric radiation
QS         solar radiation to water surface
QSC        clear sky solar radiation
QSR        reflected solar radiation from water surface
QW         heat loss by long-wave radiation
R          nominal natural-draft tower radius
R          cloudiness ratio
 c
RC         cooling range
RES        residual in iterative solution
r ,r ,r    ratios of hyperbolic shell dimensions
r          fraction of total spray canal flow rate lost by evaporation
 e
r          ratio of flow rate per module to total canal flow rate
 F
                                   281

-------
 S          shell height of natural-draft cooling tower
 S*         reference shell height
 T          throat height of hyperbolic  shell
 T          extreme temperature,  equalled or exceeded  by  10  hours/year
 T          cold-water temperature
 T          design temperature
 T,.         dry-bulb temperature
  OLD
 T          film temperature
 T          hot-water temperature
  H
 T          turbine heat rate
  HH
 T*         reference turbine heat  rate
 T          throttle setting
 T ,         wet-bulb temperature
  wb
 T ,         design wet-bulb temperature
    d
 T          local wet-bulb temperature
 TC         total differential cost
 TS         cooling pond water surface temperature
 TU         tower units
 t,         time of flight of water droplets
 tc         unit excess cost of energy production
 U          heat transfer coefficient
  c
 V2         wind speed at height  of 2m
 v          average velocity
 W          fill (pile)  width
 W,          blowdown water volume
  b
 W          spray canal top-width
  C
 W          annual water loss due to evaporation
  LJ
 W         makeup water volume
 m
 w           absolute humidity of  air
w           evaporative water loss  per unit area
 Xf
w           specific  humidity
 5
z          height above cooling  pond
z          reference height above  cooling pond
                                  282

-------
Y          specific weight of water
A          heat rate correction
At         time duration
A6         virtual temperature difference
n          in-plant efficiency
T}          plant  efficiency
 P
n          turbine base efficiency
£          specific heat  of  liquid water at constant pressure
                                    283

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                              SECTION XI

                              APPENDICES


Appendix                                                         Page

     I.  Summary of Economic Analysis                             285

    II.  List of Inputs to Computer Programs                      289

   III.  FORTRAN Listing
         Mechanical-draft wet cooling tower                       295

         Example results
         Mechanical-draft wet cooling tower
         Full loading pattern                                     314

         Example results
         Mechanical-draft wet cooling tower
         Variable loading pattern                                 317

    IV.  FORTRAN Listing
         Natural-draft wet cooling tower                          32Q

     V.  FORTRAN Listing
         Cooling pond                                             339

    VI.  FORTRAN Listing
         Spray canal                                              354

   VII.  Range of Values of Various Economic
           and Other Parameters
                                 284

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         APPENDIX I





SUMMARY OF ECONOMIC ANALYSIS
            285

-------
Differential Capital Costs
          CC = CCg + CCDT + CCR ,     $                           (15)
             = Y (C  -C'+C   -C1   + C   - C1  + A a  + C  )
               'p  c    c    pp    pP    cs    o     L x.    HT
              + Y (DT * P* * e')
where     CC = total differential capital cost,  $


         CC  = differential capital cost of closed-cycle system,  $
           O

        CC   = cost due to outage at hook-up,  $


         CC  = capital cost of replacement capacity,  $
           R

          Y  = price escalation factor for materials  and labor
           P

          C  = capital cost of new condenser (=  A c ), $
           c                                     c c

          A  = surface area of new condenser
           c

          c  = unit cost of new condenser, $/surface  area
           c

          C' = salvage value of old condenser,  $
           c

         C   = capital cost of new pumps and piping,  $
          PP

         C1  = salvage value of old pumps and piping, $


         C   = capital cost of closed-cycle cooling system (less
          c s

               condenser, pumps and piping), $


          C' = salvage value of old cooling system components,
           o

               excluding condensers, pumps and piping, $


          A  = additional land requirement


          a  = unit cost of additional land , $/unit area


         CTIm = hook-up and testing costs for new system, $
          HT

          DT = downtime during hook-up, hours


          P* = nameplate capacity, kW


          e' = unit cost of replacement energy during hook-up at


               $/kW-hr (difference between purchase price and usual


               production cost with the affected unit)
                                 286

-------
           CL - maximum capacity loss  (10-hr exceedance) , kW
           CS, = unit capital cost of replacement capacity, $/kW

Differential Operating Costs
OC = OCS + OCR + OCEp    ,      $/year                             (16)
          *
         k
                                         - B- + cm - c;
       EL
                                     C  - C1 + PE* < -—- e  + —A f
                                                     PE       PE   °)

where      OC = total differential operating and maintenance cost
                corresponding to maximum power output, $/year
          OC  = differential operating and maintenance cost of new
            O
                closed-cycle system, $/year
          OC  = operating and maintenance cost of replacement energy,
                $/year
         OC,^ = cost of excess fuel consumption, $/year
           EF
           Q* = reference heat rejection rate, kJ/hr
           k* = ratio of maximum permissible concentration of contam-
                inants in the circulating water or blowdown to the
                concentration in the make-up water
           W  = total annual evaporation from the new system, m /year
            L                                 3
           c  = unit cost of supply water, $/m
            w                                       3
           c  = unit cost of blowdown treatment, $/m  (alternatively,
            b
                unit cost of damage to the environment due to blowdown
                release)
           M1  = make-up water cost of open-cycle system, $/year
           B1  = blowdown cost or damage for open-cycle system, $/year
                                   287

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           C  = annual maintenance cost of closed-cycle system, $/year
            m

           C1 = annual maintenance cost of open-cycle system, $/year
            m

          PE* = nameplate energy = P*(kW) x 8760 (hrs/year), kW-hr/year


           E_ = annual energy loss due to backfit,  kW-hr/year
            LI

           e. = unit cost of replacement energy, $/kW-hr
            A/

           F_ = annual excess fuel consumption, kW-hr-th/year
            E

           f  = unit cost of fuel, $/kW-hr-th
            c




Differential Total Costs




              TC = OC + CC x FOR,    $/year                       (17)




                   TT
              tc = ^~                                            (20)

                   PE




where      TC = levelized annual differential cost  of backfitting,


                $/year


          FCR = fixed charge rate


           tc = unit excess cost of energy production resulting from


                backfit, $/kW-hr or mills/kW-hr
                                  288

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            APPENDIX II





LIST OF INPUTS TO COMPUTER PROGRAMS
                 289

-------
POWER PLANT CHARACTERISTICS
 (1)  Turbine Characteristics
                                              9
      (a)   HR, Heat rejection rate matrix  (10  Btu/hr)
      (b)   IHR and IPMAX, Number of rows of heat  rejection rate matrix
      (c)   NPL, Number of columns of heat  rejection  rate matrix
      (d)   TBP, Design turbine back pressure  (in. Hg abs)
      (e)   TPMAX, Maximum turbine back pressure (in.  Hg  abs)
      (f)   TLOW, Lowest turbine temperature in  heat  rejection rate
           matrix  (°F)
      (g)   FINC, Increment of temperature  in  heat rejection rate
           matrix,  (°F)
      (h)   EF, Base turbine efficiency for HR matrix
      (i)   EN, Alternative base turbine efficiency
 (2)  Plant Capacity
      (a)   PLMAX, Maximum plant capacity  (MW)
      (b)   DPL, Power interval  (=1/10 maximum plant  capacity  (MW)
      (c)   PLMIN, Minimum plant capacity  (MW)
      (d)   LP, Power level
      (e)   TTDD, Design terminal temperature  difference  (°F)
      (f)   IPLI, Initial power level index
      (g)   IPLF, Final power level index
      (h)   MM, Interval of power level index
      (i)   CF, Fraction of full load
      (j)   EFI, in-plant efficiency
      (k)   NYEAR, Remaining life of plant  (years)

SITE CHARACTERISTICS
(1)  TDBD, Design Dry-Bulb Temperature (°F)
(2)  TWBD, Design Wet-Bulb Temperature (°F)
(3)  TDB10, Extreme Dry-Bulb Temperature  (°F)
(4)  TWBlO, Extreme Wet-Bulb Temperature  (°F)
(5)  PERCEN,  Temperature Distribution  (Fraction)
                                  290

-------
 (6)    ITWBI,  Initial Wet-Bulb Temperature  (°F)
 (7)    ITWBF,  Final Wet-Bulb Temperature (°F)
 (8)    ITDBF,  Final Dry-Bulb Temperature (°F)
 (9)    ITBD, Temperature Interval  (°F)
 (10)   TWBREF, Reference Wet-Bulb Temperature  (°F)
•(11)   FOGL, Upper Limit of Medium Fogging  (°F-lb H 0/lb air)
 (12)   FOGM, Upper Limit of Medium Fogging  (°F-lb H 0/lb air)

 ECONOMIC PARAMETERS
 (1)   Unit Costs
      (a)   UNCOND, Condenser ($/ft2)
      (b)   FC, Fuel  ($/kW-hr)
      (c)   WC, Water  ($/1000 gal)
      (d)   WW, Waste water treatment  ($/1000 gal)
      (e)   UCAPAB, Capability (capacity) loss  ($/MW)
      (f)   UENER, Replacement energy loss ($/MW-hr)
      (g)   ULAND, Land ($/acre)
      (h)   UDOWN, Downtime cost  ($/kW-hr)
 (2)   PAPCOS,  Pump and Pipe System Cost  ('$)
 (3)   DAYS, Downtime  (days)
 (4)   FCR, Fixed Charge Rate Array
 (5)   CCO, Salvage Value of Old Condenser ($)
 (6)   COO, Salvage Value of Other Open-Cycle System Components ($)
 (7)   CHT, Hook-up and Testing Cost ($)
 (8)   CWATEO,  Makeup Water Cost with Open-Cycle System ($)
 (9)   CBLOWO,-Slowdown Treatment Cost with Open-Cycle System ($)
 (10)  CMAINO,  Maintenance Cost of Open-Cycle System ($)

BASIC THERMODYNAMIC AND OTHER INPUTS
 (1)   Psychrometric Data
      (a)   PSA,  Saturated Vapor  Pressure (psia)
      (b)   DAIR,  Density of Dry  Air dbm/ft )
      (c)   QHSUM,  Cumulative area under saturation curve
                                  291

-------
           (°F-lb H 0/lb air)
                                           3
      (d)  REFSV, Specific volume of air  (ft /lb)
      (e)  PATM, Atmosphere pressure  (psia)
      (f)  CA, Specific heat of air  (Btu/lb /°F)
      (g)  CW, Specific heat of water  (Btu/lb /°F)
2.  Other Information and Program Control Parameters  .
      (a)  CCNO, Concentration of solids  in makeup water  (ppm)
      (b)  CCN1, Maximum allowable limit  of concentration of  solids (ppm)
      (c)  LOCATI, LOCATF, Geographical location parameters
      (d)  IWRITE, Parameter controlling  printout of information
      (e)  IPUNCH, Parameter controlling  output on cards
      (f)  ITPMAX, Flag for maximum turbine back pressure limitation
           (=0,  no; = 1, yes)
      (g)  IEXTRA, Flag for cooling system cost of  backfit or new plant
           (=0, new; = 1, backfit)
      (h)  INUCAL, Parameter controlling  base turbine efficiency
           (=0, base turbine eff. = EF; = 1, base turbine eff. =  EN)
      (i)  NEWCON, Flag for use of new condenser
           (=0, no; = 1, yes)

COOLING SYSTEM DATA
(1)  Mechanical-Draft Cooling Tower
      (a)  NNOTSI, NNOTS, Parameter for different tower heights
      (b)  NOWTSI, NOWTS, Parameter for different tower lengths
      (c)  RFT, Rating factor matrix
      (d)  DTWB, Wet-bulb temperature interval in rating  factor matrix
          (°F)
      (e)  NOITT, Number of iterations in NTU calculations
      (f)  Tower size
            (i)  ELENG, Total tower length  (ft)
           (ii)  FT, Tower height  (ft)
          (iii)  WIDTHW, Tower width  (ft)
           (iv)  DIAM, Fan diameter  (ft)
                                   292

-------
            (v)   DMIN, Distance between adjacent fans (ft)
     (g)   Tower parameters
            (i)   AW, Proprietary pile coefficient
           (ii)   BW, Proprietary pile coefficient
     (h)   EFFICW, Water pump efficiency
     (i)   HEIGHT, Pumping height (ft)
     (j)   HW,  Tower operation parameter (ft)
          (=0, tower not operating; = HEIGHT, tower operating)
     (k)   AFRL, Air flow rate loading (Ib/hr/ft2-face area)
                                               2
     (1)   WFRL, Water flow rate loading (gpm/ft -plan area)
     (m)   SLANDA, Specific land area (acres/MW)
     (n)   FANPOW, Fan power (hp)
     (o)   WPDRO, Static pressure drop across pile  (proprietary),
          (in. HO abs)
                                                          2,oT
     (p)   UO, Overall heat transfer coefficient (Btu/hr/ft /°F)
     (q)   WTCOS, Unit cost of wet tower  ($/tower unit)
     (r)   AMANT, Tower maintenance cost  ($/tower cell)
(2)   Natural-Draft Cooling Tower
     (a)   NNOTSI, NNOTS, Parameters for different shell heights
     (b)   NOWTSI, NOWTS, Parameter for different pile heights
     (c)   UC, Unit cost matrix ($/1000 Btu)
     (d)   DRH, Relative humidity in unit cost matrix
     (e)   NOITT, Number of iterations in NTU calculations
     (f)   FRIFAC, Smooth pipe curve from Moody chart
     (g)   Tower size
            (i)  WIDTHW, Pile width (ft)
           (ii)  BASEDI, Base diameter  (ft)
          (iii)  HTND, Total tower height  (ft)
           (iv)  FILLHT, Pile .height (ft)
     (h)   ELEV, Elevation of site from sea level  (ft)
     (i)   Tower parameters
            (i)  AW, Proprietary pile coefficient
           (ii)  BW, Proprietary pile coefficient
                                 293

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     (j)   EFFICW,  Water pump efficiency
     (k)   HEIGHT,  Pumping height (ft)
                                               2
     (1)   AFRL, Air flow rate loading (Ib/hr/ft -face area)
                                               2
     (m)   WFRL, Water flow rate loading (gpm/ft -plan area)
     (n)   SLANDA,  Specific land area (acres/MW)
                                                          2
     (o)   UO, Overall heat transfer coefficient (Btu/hr/ft /°F)
(3)   Cooling Ponds
     (a)   NNOTSI,  NNOTS, Parameter for different water loadings
     (b)   NOWTSI,  NOWTS, Parameter for different pond areas
     (c)   RHO, Specific weight  of water  (Ib/ft )
     (d)   C, Specific heat of water
     (e)   MONTH, Index for month of year
     (f)   W2, Wind speed at 2 meters above ground  (miles/hr)
     (g)   QSC, Clear sky solar radiation (Btu/ft /day)
     (h)   AMR, Average monthly reflection (fraction)
     (i)   UPOND, Unit cost of pond ($/acre)
     (j)   UPUMP, Unit cost of pump and pipe system  ($/gpm)
     (k)   UMAINT,  Maintenance cost ($/acre/year)
     (1)   CLD, Cloud cover ratio
     (m)   AREAL, Specific pond area  (acre/MW)
                                                 2
     (n)   GPMLOD,  Water flow rate loading (gpm/ft )
(4)   Spray Canals
     (a)   UTCOS.T,  Unit cost of modules ($/module)
     (b)   F, Interference matrix for modules
     (c)   RP, Design cooling range for water flow rate calculations (°F)
                                  294

-------
           APPENDIX III





          FORTRAN LISTING





MECHANICAL-DRAFT WET COOLING TOWER
                295

-------
c
C * MECHANICAL DRAFT WE r COOLING TOwER
c

*

      OIMtNSION HR(50,14),IHR(14),ARHT<10).PSA(250)
     l,PAPCOS(24),FT(10>,HTCOSTUO),AU(10>,8H<1JI,FCRRI5I
      DIMENSION EL ENGl10), KlOTHMlO),NYEAK<5),FCR(111
      COHMON/DENSIT/ DAIR125C)
      COMMON/INPU/ PERCEN(l2,lb,2),HWUO),EF(
      COMMON/INPUT4/ WPDRO!13),FILLHT(10 I,POROP,HICTH.FANPOW!20,131
      COMMON/CMWCT2/ RFT(10,2C,6),DTWa(9»
      COMMON/TURBIN/ HR,I MR,TLOW.FINC
      COMMON/TOWERS/ ARWT,AW.BW,GPM,CONST,NOITTfAFR
     IfAIJK.BIJK,RLG,ENTU,N,FNTUiEGPM,GPMW
      COMMON/AIRF/ AFRl,FANW2.PUMCP1
      COMMON/NOT/ NUMTOWfELENGT.AMANT
      CQMMON/CONSTA/ CONST 1.OCNST
      COMMON/TURB/ POWER,TTCO,TET,TTD.TTOKO,TTDO
      COMMON/NCALA/ PSA.TPS,TS>TWBAL.OHl,CH2,HA
      COMMON/TOWERC/ NQTS(1C),hTCOST
      COMMON/TEMP/ ITHBI,ITWBF,ITBO,ITDBF
      COMMON/ECONO/ NYEAR,FC.V«C,KM,DR,CCNO,CCN1 .ANPOHE.HEIGHT,EFFICW
     ..COMMON/POWERC/ IPLltIPLF,» ((HR(ItJ),J'l,NPL).I'l,IPMAXI
  110 FORMAT!10F8.5)
      REAOIS.lOl) (PSA(I),1=1,250)
  101 FORMATI10F8.5)
      READ(5,101) (OAIRd ),!>!,250)
      REAOI5.101) IOHSUMI11,1*1,210)
      READ(5,102) (IHRd),!'!,NPL)
  102 FORMAT! 1-VI3)
      READ!5,501) («RFT.I'1,24)
  106 FORMAT!10F8.0)
      READ!5,103) ((FANPOW1 I,J),J = 1,13),1=1,20)
  103 FORMAT!13F6.1)
      READ(5,IOA) (WPOR0111,1-1,13)
  104 FORMAT!13F6.4)
      READI5.106) (FT!I),1=1,10)
      READ!5,106) (WIOTHHCI),I'l,10)
      READJ5.106) AFRL
      READ!5,106) GPMM
      READ(5,106) (AW!I),1=1,10)
      READI5.106)  1BW1I),1=1,10)
      READC5.107) TLOW.FINC
  107  FORMAT12F10.0)
     READ(5,504) NOITT
     READI5.503)  (ELENG(I),I-1,1C)
 503  FORMAT!10F8.0)
     REACH 5, 555)  DIAM,DM1N
 555 FORMAK2F10.2)
     READ! 5, 504)  NNOTSI,NNOTS,NOWTSI,NOWTS,LOCATI,LOCATf=
 504 FORMAT(6I4)
     READ!5,106)  WTCDS,CHT,5LANDA.CMAINO
     READ(5,502)  CCNO.CCN1
 502 FORMATJ2F10.0)
     READ!5,506)  (NYEARII I,I»l,5),FC,WC.WH
 506 FORMATi5I4,
-------
      NTWCITWBF-ITW8II/nuD*l
      NTOMITDBF-ITH8II/I rBD*l
      NKN={IPLF-lPLI+O.Oll/MMtl
      REAIM5,509)  PATM.TPMAX
  509 FORMATOF10.0)
      READ*5,513)  FOGL,FOGM
  513 FORMATI2F10.0)
      REAO<5,505)  CA.CHl
  505 FORMATI2F10.2I
      READ(5,509)  TBP
      REAOI5.509)  EF.EN.EFI
^     R6AO(5,507)  IWRITE,IPUNCH,ITPMAX,IEXTRA,INUCAL,NEWCCN

      CONST»7.481/60./62.*10.**9
      OONST»CONST
      CONST1»0.124683/62.
C
C   CALCULATE CORRESPONDING FIXED CHARGE RATE
C
      DOIOOK'1,5
      Y«NYEAR
-------
       101-1 IIK-ITWBII/ITBO*!.
  2012 SS1»SS1+PERC£N«IW1,ID1.LP1I
       S-S*SS1»PL
       SS2«SS1
  2011 SS1-0.
       IFdPLI.EQ.lPLF) SS2-0.
       S«S*8760.
       TEl*PLMAX*<1.-SS2I+PLMAX*CF*SS2*(TOSTAR*d.-SS2)+TOST*SS21*293.067
       TE1-TEI/EFI
 C
       WRITE(6,610)  TWBD,TDBD,TWB10,PLMAX,CA,CWl,TTOn,PATM
   610 FORMAT! !Hl///lOXt'DtSIGN fcET-BULB TEMPERATURE  CF  AIR  »',F5.1,'  F'
      1/iOX,'DESIGN  DRY-BULB TEMPERATURE OF AIR «',F5.1,« F«/1CX,
      2'EXTREME WET  BULB TEMPERATURE »',F8.3,' DEG. F'/lOX,
      3'POWER  LEVEL  *',F6.0,' MW'/lOX,
      VSPECIFIC HEAT OF AIR AT CONSTANT PRESSURE =',F6.2,'  BTU/IB./F'/
      510X,'SPECIFIC HEAT  OF WATER =*|F6.2,' BTU/LB./F'/
      610X,'DESIGN  TERMINAL TEMP. DIFFERENCE ««,F5.1,« F'/lOX,
      7'ATMOSPHERIC  PRESSURE «'tF7.2,' PSIA')
 C
       WRITE(6,620)  FC ,WC,UW,AMANT.CCNO.CCNl
   620 FORMATdH ,9X,'UNIT FUEL COST *',F9.6,' t/KW-HR'/ 10X,
      1'UNIT  SUPPLY  WATER  COST =',F7.4,' t/1000 GAL'/lOX,
      2'UNIT  HASTE  WATER COST =«,F7.4,' $/10CO GAL'/lOX,
      3'ANNUAL MAINTENANCE COST «',F7.1,' t/CELL/YEAR«/10X,
      *'MAX. TOLERABLE CONCE^4TRAT ION OF PROCESS WATER =',F5.0,' PPM'/IOX,
      5'SUPPLY WATER CONCENTRATION =«,F5.0»' PPM«)
 C
       HRITE(6,630I  DIAM,DMIN,HTCOS,PLMAX,UC4PAB
   630 FORMATdH ,9X,•DIAMETER OF wET TOWER FAN =«,F6.2t' FT'/lOX,
      1'SPACE  BETWEEN TWO  rfET TOWER FANS =',F5.2t' FT'/lOX,
      2'UNIT WET TOWER COST =',F6.2,' S/TOWER UNIT'/lOX,
      3'HAXIMUM POWER OUTPUT *',F8.2,' MW'/lOX,
      «'UNIT CAPACITY LOSS COST =',F10.2,'  t/MW'I
 C
       WRITE(6,6311  UENER.ULAND,SLANDA,UDOWN,DAYS
   631 FORMATdH .9X,'UN1T ENERGY COST »',F7.3,' t/KW-HR'/IOX,
      I'UNIT LAND COST =',F8,.l,' t/ACRE"/10X,
      2'SPECIFIC LAND AREA =',F5.2,' ACRES/MW«/IOX,
      3«REPLACEMENT  ENERGY COST DURING DOWNTIME »',F7.4,« $/KW-HR'/10X,
      ^•DOWNTIME FOR CONSTRUCTION =',F6.l,' DAYS'I
 C
       WRITE I 6,640)  HEIGHT,EFFICH.UNCOND.UO
   640 FORMATdH ,9X,'PUMPING HEIGHT OF WATER THROUGH TOWER «',F8.l,
      1'  FEET'/lOX,'PUMPING EFFICIENCY FOR  WATER PUMP =',F7.3/10X,
      2'UNIT CONDENSER COST =',F6.Z,' S/SQ. FT.'/IOX,
      3»OVERALL CONDENSER  COEFFICIENT, U =',F6.1,' BTU/HR/FT2/F')
 C
       WRITE(6,662)  ITWBI,ITWBF,ITBD,ITDBF
   662 FORMATdH ,<3X, 'INITIAL hET BULB TEMPERATURE =',!*,' DEG. F'/lOX,
      1'FINAL  WET BULB TEMPERATURE =',15,'  OEG. F'/lOX,
      2'INCREMENT OF DRY AND WET BULB TEMPERATURE =',14,' DEG. F'/lOX,
      3'FINAL  DRY BULB TEMPERATURE "',15,'  OEG. F'l
 C
       HRITEJ6,650)  TLOW,FINC,NOITT,REFSV,FOGL,FDGK
   650 FORMATdH ,9X,"LOWEST TEMP. IN TURBINE CHARAC. CHART =',F5.1,
      1'  OEG.  F'/lOX,'TEMP. INCREMENT IN TURBINE CH4RAC. MATRIX =',F*.l,
      2*  DEG.  F'/lOX,'NUMBER OF ITERATIONS  IN NTU CALCULATICN =',15
      3/10X,'REFERENCE SPECIFIC VOLUME OF AIR =•,F7.3,'FT3/LB'/IOX,
      4'LOWER  BOUND  OF LIGHT FCGGING »',F7.3»' LB H20/LB AIR*F«
      S/10X,'LOWER BOUND OF MEDIUM FOGGING  =',F7.3,'  LB H20/LB AIR*F»)
 C
       1T-TW8D
       TSS=PSA(IT|t(PSA(IT+l)-PSA(IT))*(TW8D-ITI
       HAA=0.24*TWBD*0.622*TSS/(PATM-TSS)*<106l.8+0.NOWTSI,NOWTS
       TS-TSS
       HA'HAA
C
C  DETERMINE  HATER  FLOW RATE FOR EACH WET  TOMER
C  DETERMINE  AIR-FLOWS  FOR WET TOWERS, DETERMINE N.T.U. FOR WET TOWER
C
      NOTS(IH)*IFIX((£LENGdW>-DIAM+0,l>/
-------
    EGPM«CPM*NUMTOW
    AFR1.AFRL*FAWET/60.«REFSV
    AAFR-AFRL/60.*REFSV/50+1
    IAFR.AAFR

    PDROP"WP°RO(lAFR.,<*PDROUAFRni-MPDROnAFR»|. "tF5.2,« IN.HGH/10X,
   Z'***'F8'
                «                        .,
            ,F8.5,' OF THE TIME IS NOT OPERATED AT FULL LOADING ***•!

       AFR>AFR1*60./REFSV
       RLG«GPM/CONST*10.**9/AFR
       FNTU«AWUW)*GPMH*»8W(IW|*FILLHTUW>
       N-IFIXCFNTU/0.5)
       ENTU-FNTU/N
 C
 C   DETERMINE CAPITAL COST OF THE TOWER

       Hit— S
       TTO»TTOD
 C
       CALL MOOELW (TOBD.THBO, IW,NPL.TET,TQ,TWL,II I I.K.TT, IMI

       IF(TET.LT.OIGOT0999
       TTSTAR=1.
       IF(ICAP.EO.?»GOT0679
 C
       CALL POWERS (TET.TQ.TTSTARI
 C
   679 OQHR«(TQ/TTSTAR-TOSTAR)/(PLHAX*3. 6/1055. 04-TC/TTSTAR+TQSTAR)
       TQQ«(PLMAX»TTSTAR/J1.+OQHR)+TQ*1055. 04/3.6 J/EFI
       RP«TQ*CONST/EGPM
       AP-TET-TTD-RP-TWBO
       ITET=TET
       PDESI*
-------
       FPL1"FPL1+(FANW1»PUMOP1)/10CO.
       FPLMAX«FPL1
       CAPCAP-FPLl*UCAPAB
c
       WRITE(6,661)  EGPM,AFR,GPM,GPMH,AFRL,POROP,FNTU
  661  FORMATdHO, 10X,
      3'TOTAL  WATER  FLOW RATE  =',Fll.O,'  GPM'/llX,
      4«AIR  FLOW  RATE  THROUGH  tACH WET TDWER »',Fll.O,' LB./HR'/llX,
      5«WATER  FLOW  RATE  THUOUGH  EACH WET  TOWER «',Fll.O,1 GPM'/llX,
      6'WATER  LOADING  »',F11.2,'  GPM/SQ.  FT. PLAN AREA'/llX,
      7*AIR  LOADING  =•,F13.it1  LB./HR/SQ. FT. FACE AREA'/llX,
      B'PRESSURE  DROP  DUE  JO FAN  OPERATING »',F8.4,' IN. H20'/11X,
      9'TOTAL  NUMBER OF  TRANSFER  UNIT =',F9.4/I
       WRITE16.665)  ELENGT
  665  FORMATdHO, bX,'***  TOWER  SUE **.*'/HXt
      1'LENGTH OF WET  TOWERS =',F13.1,' FT')
       WRITE(6,664)  FILLHTIIW),WIDTH.NUMTOW
  664  FORMATdH  ,10X,'FILL  HEIGHT FOR WET SECTION =',F6.1,' FTVUX,
      2'FILL WIDTH  FOR  WET  SECTION =",F7.1,' FT'/UX,
      3'NUMBER OF WET  TOWER  FANS  =',I9)
       WR1TEI6.663)
  663  FORMAT!1HO,8X,'*»*  DESIGN  CONDITIONS «*»•!
       WRITE(6,666)  THW,TCW,RP,APtRF,PDESI,TQC
  666  FORMATdH  ,10X,'DESIGN  HOT  fcATER TEMPERATURE =',F8.3,« DEC. F»
      1/llXf'DESIGN  COLD WATER  TEMPERATURE »',F8.3,' DEG. F'/llX,
      2'DESIGN COOLING  RANGE =',F8.3,' DEG. F'/llX,
      3«OES1GN APPROACH  =',F8.3,'  DEG. F'/llX,
      ^•RATING FACTOR  'SF6.4/11X,
      5'OESIGN TURBINE  BACK  PRESSURE =',F8.4,' IN. HG'/llX,
      6'FUEL CONSUMPTION AT  DESIGN CONDITION =«,F9.2,'  MW«)
       IF(ICAP.EQ.l) WRITEI6.667)
  667  FORMATdH  ,12X,'NOT£  ... CAPACITY  LOSS AT DESIGN CONDITION')
C
C  COMPUTE  OPERATION  COST AND  TOTAL COST
C
       CALL  OPECOS  (IW.TOTOPE)
C
       IF(TOTOPE.GT.10.**ll)GOT0100l
       CAPCOS*CAPC01+PPCOST-PPCOSO+CONCOS-CCO-COO+CHT+ALANDC+CAPCAP
      1+DOWNCO
C
       WRITE(6,604)
  604  FORMAT(1HO,7X,'***  CAPITAL  COSTS ***•)
       WRITE(6,602)  CAPC01.PPCCST,PPCOSO,CONCOS,CCO,COO,CHT,ALANDC,
      ICAPCAP.DOWNCO.CAPCQS
  602  FORMATdH  ,9X,'CAPITAL COST OF TOWERS « *• .F20.0/10X,
      1'PUMP AND  PIPE  SYSTEM COST  = $•,F17.0/10X,
     2'PUMP AND  PIPE  SYSTEM SALVAGE » (  *',F12.0,«)'/10X,
     3'NEW  CONDENSER COST = t',F24.0/10X,
     ^'SALVAGE VALUE  OF OLD CONDENSER =  ( t',F10.0,'I'/10X,
     5'OTHER  OPEN-CYCLE COMPONENTS SALVAGE « ( »',F5.0,'I'/10X,
     6«HOOKUP  AND  TESTING COST  *  S•,F19.0/1 OX,
     7'ADOITIONAL LAND COST =  t'.F22.0/10X,
     8'REPLACEMENT  CAPABILITY COST = t•.F15.0/10X,
     9'DOWNTIME  COST » $ ' , F29.0/4CX, '	'	'/IOX,
      1'TOTAL  CAPITAL COST = $',F24.0I
C
       IF(IEXTRA.EQ.l) TOTOPE=TOTOP
       IF
-------
      STOP
      END
      SUBROUTINE OPECOS  UW.TCTOPEI

C«**»»»****««*****«,  .,»,,,  *,,*,,,«»*
C *  PROGRAM TO DETERMINE  TOTAL  ANNUAL OPERATING  CCST                  *
C*1**************^*******************
C
      DIMENSION HR(50,K) ,IHR (U) ,ARWT(10) ,PSA(250),AW110),BH( 101
     ItWTCOSTC10),S1(15I, S2U5),S3115).NYEARC5)
      COMMON/OENSIT/  DAIRI250)
      COMMON/1NPU/  PERCENl12,15,2 I,HW(101,EFI
      COMMON/INPUTA/  HPDRCM13)tFILLHTI10),POROP,MICTH.FANPOWJ20,131
      COMMON/TURBIN/  HR,IHR.TLOU,FINC
      COMMON/NCALA/ PSA,TFS,TS,TWBAL»OHl,wH2,HA
      COMMON/TOWERS/  ARWT , AW,BW,GPI*,CONST,NOI TT, APR
     1,AIJK,BIJK,RLG,ENTU,M,FNTUiFGPM,GPMw
      COMMON/AIRF/  AFR1,FANV.2,PUMCP1
      COMMON/NOT/ NUMTOW,ELENGT.AMANT
      COMMON/TURB/  POWER,TBP,TET,TTO.TTOKO,TTDO
      COMMON/TOWERC/ NOTS<10),WTCCST
      COMMON/CONSTA/ CONST 1 .OCNiST
      COMMON/TEMP/  ITWBI,iTHBF,U8D,ITDBF
      COMMON/ECONO/ NYEAR,FC,WC,l.w,DR,CCNO,CCNl, ANPOWEtHEIGHT,EFFICM
      COMMON/POWEKC/ IPLI,IPLF,V,PL,LP
      COMMON/ATMOS/ PATM
      COMMON/LOSS/  S,CWATEO,CBLOWO,CMAINO
      COMMON/CELL/  CELLTH.FAhET
      COMMON/WSS/  QHSUM(21ul,FOGL,FOGM
      COMMON/WITREF/ IWR!TE,I PUNCH,REFSV,FAWETT,PAHETT,AFRL,TWBREF
      COMMON/PLEVEL/ PLMAX.UCAPAB,CAPCAP,UENER,£NERLS,TEI,TOTOP
      COMMON/FPL11/ FPLMAX
      COMMON/TBPR/  ITPMAX,TETfAX,ICAP
      COMMON/TBPRE/ IPMAX,NPL,DPL.PLMIN
      COMMON/QSTAR/ TQSTAK.CF
 C
 C  OPERATION DUE TO NET COOLING TOWER
 C
       IF«FANW2.LT.0.1>HW
-------
        TWB'ItJ
        TS-PSAII!J)
        IW1»( IIJ-ITWBI 1/ITBDH
        KK'KKSAVE
        TTT'TTTSAV
        I2«0
        IJ'iU
        TOB=TWB
        ITOBMA-PSA)I1J)/(O.C0036T*PATM*(1.»«IIJ-32.I/1571.)1*11 J
        IF(ITOBMA.GT.ITDRF)ITOBMA«IfDBF
        I01=
-------
      COLDWT«HOTWTT-TO*CONST/FGPM
      ITET-TET
      P"HPSAUTET+l)-PSAdTETH*
      TOTFUE=TOTFUE+FUECOS*PERCENUW1,IDI,LP1)
      TOTWAT=TOTWAT+WATCOS*PERCENI[Ul,I01,LPlt
      TOTWAW3TOTWftW+WAWACO*PERCeNdWl,IDl,LPU
      AMANT1=AMANT*NUMTOW*PERCEN(IW1,ID1,LPU
      TOTMAN=TOTMAN+AMANT1
      FUECIS=FUECGS*P£RCEN(IWI,ID1,LP1)
      WATCOS=WATCOS*PERCEN([Ml,I01.LP1I
      HAWACO=WAWACO*PERCEN( IWl, 101,LPt)
      OPCOS = < FUEC.I S+WATCOS + WAfcACOtAMANTl I
     1+FPL1*PERCEN(IW1,ID1,LP1)*8760.*UEN£R*1000.
      TOTOPE=TOTO?E+OPCOS
      IFCPERCENtlwlfIOl,LPl).LT.0.000001)GOT0312
C
      CALL FOGSEN  ITDB,TWB,TWBAL,QH2,SENSII.SENS12.SENSI3I
C
      SEN1»SEN1+SENSI1*PERCEN(IW1,IOI,LP1)
      SEN2»SEN2+ScNSI2*PERCEN(Ihl,I01,l.Pl)
      SEN3«SEN3+SENSI3*PeKCEN(IHl,IDl,LPU
      IF(SENS!3.LT.0.00005)GOT0317
      IFGUT0316
      FOGHS-FOGHS*PERCEN(IHl.IOl.LPl)
      GOT0311
  315 FOGLS»FOGLS+PERCEN(IW1,I01,LP1>
      GOT0311
  316 FOGMS'FQGMS+PERCENdWl.IDltLPl)
      GOT0311
  312 SENSI1=0.
      SENSt2»0.
      SENSI3=0.
  317 FOGOS*FOGOS+PERCEN<1H1,ID1.LP1)
  311 SKID1I-SENSI1
      S2(ID1)=SENSI2
      S3U01)'SENSI3
      IF(1PUNCH.EQ.1)  WRITE(7,7C1) FUECOS,ANUCAP,TWL,OPCOS,BLDOWN,FPL1,
     1SENSI1,SENSI2,SENSI3,EI ,IH
  701 FORMAT(2F10.0,F6.0,F10.C,F5.0,F9.4,F7.5,F6.4,F8.5,F8.0fIII
  200 IFUM.LT.2)GOT0475
      IFd2.NE.DGO TO 902
      TTTSAV=TTT
      KKSAVE'KK
      GO  TO 902
  475 D09233IJK=IIJ,ITDBMA,ITBD
      IF(IWRITE.EO.11WRITt(6,666)
  666 FORMAT!5X,•WET COOLING  TOWER IS  TOO  LARGE  TO  OPERATE'I
      I01«( IJK-ITW8D/ITBO+1
      TOTLOS«TOTLOS + PLHAX«876COOO.*OENER»PERCEN(IW1,ID1,LP1I
      TOTOPE»TOTOPE+PLMAX*876COOO.*UENER*PERCENC IW1,ID1,LP1)
      FOGOS=>FOGOS + PERCEN( 1M1, ID1.LP1)
      IM«0
      IF(IPUNCH.EQ.l)WRITEC7,702)  IM
  702 FORMAT!180)
 9233 CONTINUE
      GO  TO 901
  902 IF(IWRITE.LT.1)GOT090222
      WRIT£{6,601)  PL.TWB
  601 FORMATdHO, 5X, -POWER  =',F5.0,« HW',10X,'TWB  =«,F8.3,' OEG. F'l
      WRITE(6,333)TET,HOTWTT,COLDV«T,P,TQ
333   FORMATC/6X,'TURB.TEMP.  = ' ,F10.4.IX,•OEG.F.  ',
     15X,«HOT WAT5R  TEMP. »  ' ,F 10.4,IX,'OEG.F.',
     25X,'COLO WATER TEMP.  -  • ,F I J.*», 1 X, «OEG.F. • ,
     3//.6X,'PRESSURE  * •,F8.5,IX,•IN.HG.',
     45X,'HEAT REJECTION  =  • ,F8.5,1X,«BTU*10**9«,/I
      WRITE(6,602)
  602 FORMATC1HU, IX,'TDBS3X,'WATER  EVA. • ,3X, -BLOWCOHN* ,3X
     1,'PROBABILITY',3X,'FUEL  COST',3X,
     2'WATER COST',3X,'WASTE  fcATER COST',3X,'SUBS  ENERGY LOSS',3X,
     3'OPERATING COST'/3X,«F',
     47X,'GPH',9X, 'GPM',22X,'»/YEAR',6X,
     5'$/YEAR',10X, 't/YEAR',13X,'t/YEAR',I2X,'*/Yc»R'/l
      WRITE(6,607l!j ,TWL.BLOCWN.PERCcNtIWl.IDl.LPU.FUECIS.WATCOS.WAHAC
     10,ANUCAP,OPCOS,FPL1
90222 IJ'IIJ+ITBD
      IFdJ.GT.ITDBMAIGO  TO 911
      009231JK*IJ, ITOBMA.1TBO
      TOB»IJK


                                       303

-------
       I01»( IJK-ITWBI)/[TBL>»1
       AM-TS-0.000367*PATM«0.*24. *J65./3260<«6
       eii=Emooo.
       TOTEl«TOTEI + EU*PERCENl IM1, IDltLPl)
       ENERLS*ENERI. S+FPL 1*P£RCEN( IH1 , ID1 ,LPl )*8760.
       FAPLS=FAPLS»FAP*PERCEN( (HI, IDl.LPl 1*8760.
       IF(ICAP.EO.l) C APPRO = CAPPRO*PERC EN 1 IWltlDltLPl)
       ANUCAP»ENERLS*UENER*ICCC.
       TOTPRO»TOTPRO+PERCEN( IHl.IOltLPl I
       TOTFUE=TOTFUE+FUECOS*PERCENx, • ( • tH4. {,, •  I'/IOX,
             GY LOSj  ''.riS.'J,'  fU-MK< , >X, •< ' ,F4.6, •  I'/KX,
             f, PUM'1  r-4;Pi,Y lOSi =',F11.4,'  WW-HR ', 5 A ,'(•,">. e t«  I1)
        WRI F t (6,606 I  TUT Ft IS, Til ThUl, A JUCAP . T J T rtA f , F ') T^A W , TOTMAN , CwATFO
       ItCULDWOtCMAI.NOiTOTOi't , TOTOP
   606  ri)Kv.Al I IHO/f-X,
       I'***  TOTAL  ANNUAL C  STS ***'/10X,
       2'TOTAL A'lNUA.L  TUFL UlST =«, F24.il,'  WYF.AU ' , r,X, 'OR ' /10X ,
       3'EXCPSS FJ5L  COST =',F10.0,' t/YE -\H • / 10X,
      4'TUIAL A'l\i),-L  REPLAL-EMEM  r ȣKGY LOSS  =',F10.C,'  J./VEAR ' /ICX ,
       S'TOIAL A'lNU'L  WATi;R  C'^T =',F?3.0,'  t/YK A-( • /I OX ,
      6'TOIAL AM-JUAL  tv'ASTP  ^ATrR  C'JST  -',F17.0,'  I /YLA* ' /I OX,
      7'TDIAL A-JNUAL  MA 1 NT A] \AJCK COST =',F16.0,'  t/YEAH'/tOX,
      R'MAM:UP UAT!-r<  COST ..ITH OPiM-CYl.Le  «',F13.3,«  t/YL A'< ' /I OX,
      SI'BLl'wrHU ! TKt:ATM£>IT  CDST WITH O.'i-M-CYCLL =', 1-7.0,'  t/YEAR'/lOX,
       I'MAINTcMANICF  COST WITh  OPEN-CYCte  =',F14.0,'  i/YE AR 'MOX,
      2« -------------------------- V10-<,
       3'TQTAL ANNIML  OPERA! riii COST s',F19.0t'  */Yt4R'/lOX,
      '•"EXTRA A>i(4U.'.L  OPERATIO'M  COST =',F19.0,'  I/YEAR')

              = TOTF'JE/S
       r!RITE(6,621 I  TOT FUE, TOT WAT, TOT WAV* , T3TMAN , A NUCAP.TCmvE, TOTOP
   621 FOR.«IATUHO,?/.i'*«* .WERAf.p  OPERATING  COSTS ---  IS  MILLS/KW-HR ***•
      1/10X, 'AV»RA'.E  FUEL ^OST  =',F22.6,' '-iILLS/HW-HK'/lCX,
      2'AV-RAGE r/AIc'R  CQ5T =',FZ1.6,' "• ILLS/KW-H^ • /I OX,
      3'AVFRAGE rJASTE  rtATE« COST  *«,FL3.6,'  M I LL S/N.V-HR ' /I OX,
      4'AVI'RAGE MAI.NTAI'JA'JCE COST  =',F14.6,' M I LL S/K W-HR ' / 1 OX,
      5' AVERAGE CAPACITY L-'SS =',F18.6,' Mi LL S/KH/iiR '/IOX,
      6'AVSRAGE TOTAL  OnERATTIG COST =',F11.6,'  M I LL S/K.W-HH ' /10X ,
      7'AVtRAGt LXIrtA  (JPE-RATING COST =',F11.6,'  MI LLS/KVJ-HR' I
       RETURN
  1002 KRITE(6,6?3I
   623 FORMAT! 1HO/10X, 'WtT COOLING  TOWCR IS  NOT  SUFFICIENT  TO  OPERATE' I
       TOTQPE*10.*-12
       RETURN
       END
       SUBROUTINE 1'GUELH  ( II)B, TWO, I W,L:- , TET , TO, TWL , 1 II I ,K,TT<1K)
C  *   THIS SUBROUTINE CALCULATES  THE  MODELING  RELATIONSHIPS  FOR POWER  *
C  *    PLANT  AMU COOLING  TOWER .    f.lV'N W-T AND  OKY BULK               *
C  *    Ti-M .-ERATURri, AND  R'T T TUWCK  SI/: ,   THE  Rt-.SULIS ARE TURBINE     *
C  *    fXJl-'.UjT  nrWPi'RATT.E,  ANC Hf.T  REJECTION.                          *
c**»**t********»******»*************

°      DIM'NSItH HlRJlN(^O.l4l,I-.NItTR« 14 I , AW ( 10) , 5h( 101 , ARWT (1 01 .PSA1250)
       CnHV.ON/TURHIN/ilTiJJI'i, U-NHTK , TLOV,, F I\C
       CUKvO'./T!'!irfEt'$/ A'-WT, AW,OW,Ot'''1,C "!,N ST , NOI TT , AFR

       C()M''0'I/N'.AL/./ ^SA, TPS, TS, T«.!AL , .(HI .-•H?,riA
       CtJW'OM/ N  I f /  MUM T DA' , c L f N 0 T , A M AN T
       CH.M ijrj/nmn/ r, IIL J, ni>, U'-KO.TTDO
                   / 1TPMAX, f FTf'AX, ICAH
C    IF  T^S IS MIU)  INOUr.H,  THEN CDHLINC CANNOT  TAKE PLACE  -\ T  ALL UNTIL
C    TUKfil it CO\Hf .iL< TtM.'E'.AIUrtE  IS  IIIbHiR.  THUS,  WILL  SKIP  TO
                                               305

-------
 C
 c
 C    ir 1 1.".  IS  i i«u i-VMUi'.H,   COOL IN".  WATE<-- r-'Ft/f.s, WHICH
 C    IS luvl'R I'lilt'll).   lllUi KM :JtVlk  .,li:)LlN5  WAIr-'K VirjULn  HAVE HFEM
 C    CnuL.-l''  lULn*  Ik /I- /ING  ANYnHcKi  IN TH" f.YCir.,  'in COHLINii IS
 C    PrKuj'xWhO  (IM'.'LYIMG  ALTLK.AH-  ^YSTrM USED  IN  I'l'.AC 1 1 CE I .
 C
 C   ASSI^M MOOFL l'.•.l^AMET(:R^  f-Ok TU.JEK  SCCT10N
 C
        ICA"=0.
        !M=?
        I t- < -• 0
        IFPF'-l
        IK I I ! I -
        w L = : .
        (JI12-0.
        IF( ! 1 I I.iH.1.-i)f.OT091U
        TIOO-HTRJKH l,LP)*TinKO
        GOT.]* 12
    9^1  irDn=TTU
 C
 C   ASSIGN INITIAL  TRIAL TURBINE TftMPEK ATUKE
 C
    9<>2  K = 0
     99  IFKc=IFR^*l
    201  K = K<1
        IFIK.iiT . lENHTP(LP) )oOT099<5
        Tl = i LUW+lK.-l )*F- IkC
        IFI I I I I .r.f.-t JGGT'j^u-'-.
   'tO'.  TTl = TT-TTD
 C
 C  CUOL THROUGH COOLING SYSTEM IF POSSIBLE TO GET  TQ1
 C
        IFITrftt.LT.TTl IGOT3A03
        GOI0201
   ^.03  WL2 = WL
        TPS2=TPS
        TWBAL2 = TKI'A!.
        '.'H2? = 'JH?
        IF(TT.GT.(TPTMAX+1.95) IGOTU^g
 C
        CALL NTUCAL  t TT I , TDti, TWB, RLG, EM I U, TT2 ,NOI TT , AFR ,WL , N)
 C
        IF(TT?.GT.3?.. 1GOT0503
        GQT09-J
 C
 C  DETERMINE DISFCTION DF APPROACH TO ' INTfcR SECTION  OF CURVES
 C
   503  T01 = (TT1-TT.->)*FGPM/CONST
        IHrai.LT.HIRJIMK.LPDCOTOlOO
 c
 C  ^tACH INTf.StCT ION RY L'cCRcASING TUP.B I Nt TEMPERATURE
 C
        IFIIFRE.CT.-; . IGOT02G6
        IF(TWB.GT.(lLO'rt-HINC-TTDO) )GOT010«
 C
 c  co'JLiM', cu^v?:-  :MOS MQR;  THAN  i OEC^E^EVT BELOW  TLOW
 c
   206  TT=TT-FINC
        TT1--TT-TTD'J
        IHIT l.LT .3 '. IGDTQ703
        IFI rwB.r.r.Ti i JGOTQSC-*
 c
 C  COCL1M1 TH^OUGJ' COOLING SYSTEM IF POSSIBLE TO GrT T02
 C
       WL2'HL
       TPS?=1PS
       TrillJi.,?=T«l!AI.
       CM2;> = OH?
        IT! f T .GT.l T! 1MAX1 1 . i-,\ )GOT[j'J')7
 C
       LJVLl  111 JCAL  ( TT1, TO'-. Twfl,KLl»,l NTU, TT2 , NOII I tA(-R,WL,M)
 C
       IT! t T^.'iT. J..1 . K.OT'lSG'i
       I F k -- 1
  535  Tu7*( TT1-TT • ) *FGr "/[.[V;S 1
       IK l'.?.LT..H>;j[N| 1 ,LP! l..l'T01
       ir { !<••<. re. i n,nrri703
       T(J| -T'J?
       c- in '.i? 06
c
                                                  306

-------
c   iNTnu'in AI E mi- TU,TFT,TWL
c
  10!<  TU-MTRJINUiLIM
       HTUIF IM IO-l'.?>/(TU|-Ig;>)
       THr = TT«lllt)If l*f PiC
       IF( I I 1 I .? Q.-'.)Cni()40t>
       TTL'-TU*1 TDKO
  405  TWL-I WL4Hini H*(VIL?-WL ) )»'
       1PS-«!t'S + lIf i*( T PS?- IPS I
       TWH/VL-TWBAI otTDiri*! rwi>,AL2- IWRALI
       OM^--OM?«ltn)! 'I- 1*IOH2.>-CH2)
       IK IFK.tg.OIGUTOPlC
C
C   (PREVIOUS  TOrf?;-' CUOLIN<;  INDICATES  THAI  THE  OPERATING
c    CURV£  FOR  me  couLiNt;  svsrcM F-IOS  IN  run  SAME  TEMPERATURE INTERVAL
C    AS Tel 1
C   COOL  TliKUUGH COOLIMO  SYSTFM USING  FET,  TO  FHK CHECK

  211  TT1=T£T-TTO
       IFI1 1 .OT.IT- IMAXi l.-7D))GC)TU999
C
       CALL  MTUCAL  t TT 1 , TUB, TWUiKLGt EMTU, T F3 ,Nni T T , APR ,WL , Ml

       1F(TT2.GT. ^?.)GOTO?10
       COT 07 03
  210  CONTINUE
       1111=1
       KETURN
  304  TT=TT+FIMC
C
C   COOLING  CimVfcS  L.ND  JUS1  DELOW TT AJD OECREMEMTI NG TURBIN5 TEMPERATURE
C    WILL NOT  1'JTERSfcCT  IT
C
C   DETERMINE  PROPER VALUE OF  HTR J IN ( 1 , LP )
C   DOUBLt  INTERPOLATE  FOR T2,1ET,THL
C
  104  IFIK.GT. 1 (0010106
       HO=MTRJlN(lt LP)
       GOT0107
  106  HQ=HTSJI!l(K-l,LPt
  107  IF( I 1 I I .ST.-i.lGOTQ-HC> I
  408  1F( 1 1 I I.Eg.-i )GOT0406
  406  TO=TQ1*HC/ITC1+HO-H1RJIN(K,LP) I
       1F( I I 1 I .'JO.-5lbOT0409
       TTO-T'J*ri !1K(1
  409  TWL = WL/T01*TC*NU«TOf,
       TPS-TPS/TOl'TU
       IFIK.GT. DK-K-1
       GOTO? 11

C  REACH INTERSECTION  BY  INCREMENTING TURH1NE  TEMPERATURE
C
  100  IFU.EU. IF^HTRILPI )UIT09'}9
  108  TT=IT + FIf,'C
       K = K» 1
       1F( I II I. L:'J.-5)GOT041u
       TTU'HTRjmi- , LP)*ITunO
  410  TI1-TT-TTD
C
c  COOL  THROUGH SYSTEM TD  G;T  TQ2
c
       IFl I T.OT.IT:-THAX+l.'i5)lt,OTO'»9q

      CALL  MTUCAL I T f 1 , TDU , T Wfl, RLG.ENfUt TT2,NOI T T , AFR ,WL
       IK f (j?.5l .II'KJIN(K.,LP) ) GOTO 101
       tr{-f..Cu. IcNHIKILP) )<•.'}! V I »
       T«1'T J?
       GUTtilOB
                                               307

-------
 C   INTl-KP JLATL  K).:  Tw. Ttl,  TWL
 C
   101 HTHIf 1 =MlKJ":(K,L'M-HriUlN(i<-l,LP)
       Ta-/< MIDI F2-
       TIT--TI-I Tu?-T<-)/HTIHF2«HNC
       IF( t I I J.FU.-i- 101111)4 1 1
       TTtn To*! TDK '
   411 T«L  U'L?«(rfi -WL21/HIDIH2M T'J-TOl ) )*'JUMTOW
       TPS-1I'S?« ( TPS-IP'j/M/HTDIf ?<•(!!.'- 101 I
                                    I TU-TglI
       TT = TT-fI'4C

       1111=1
       RETUR'4
 C
 C   RE TURN WITH  MESSAGE
 C
   703 T(J=-50

       TWL^-50.
       I II 1 = 0

       RETURN
 C
 C   FIND I JTfcRSECTION WHEN WET-BULB  TERPERATURE  INCREASES
 C
 C   ".EACH INTERSECTION HV INCREMENTING TURH1NE TElt'^RATURE
 C
  1000 TTD--HT3JINIK, LP)*TTI;KO
       TT1=TT-TTD
       lF(TT.GT.(TfTMAX-i-l.V^(l'jQT0999
 C
       CALL NTUCAL  ( TT1, TOh, TWO, RLG, FNTU, T I 2.NOI TT, AFR tWL ,t<
 C
       T01=(TT1-TT7)*FGPM/CONST
  1004 TT=1T+FINC
       IF(TT.LT.ITLGW + O.OOl) If.OTOlOOl
       IFIK.EC.IfcHHTRILPI). OT0999

       HQ=HTRJ1M(K,I.P)
       HTDIF1=HC-HTRJ1N(K-1,LP)
       GOT02070
 1001 Hi.''-TO)/HT[)II-2*KlNC
                                  IO-T01 I I*\UMTOW
                (Tl-:S-TP5?)/HTr;lF2*( TO-fOl )
                     TH»AL-IS.'nAL2)/HTI)IF?*t TQ-TQ1)
                                '
      IFIK.GT.l)  K=K-l
      TT=IT-F IMC
      KfcTURN
  999 ir.. TT2.LT. 52. IG010703
      TT1-TETMAX-1TD
                                                308

-------
      CALL  -IIUCAL  «TTl.lUB,rwn,RL(.,!:NlU.TI2,NOItr,A>R,wl.,N)
       TO=nn-TT?)I«ENSIilM Hwl 30) ,TW( 30) ,PSAI ?50I
       COMMON/ "ICALi'.X  PS\,TPS,TS. T^UAL , I'M I,; H2.HA
       COM'»Of»/CONSTA/ CONST I, CONST
       CnMMON/ATMOS/PATI
C
       1 T = 1 k I
       PS«PSA(IT) + I r-SA( ITtl)-PSA( IT) >*(TWI-IT>
       H = u.24*TWI+i.6?2*PS/(PArM-PS)*(I 061.8*0.44*TWl)
       I T = I W »
       TS = f'SA( IT1 + I PSA( tT+l )-PSA( I ! I )*( TWB-IT)
       AH=TS-O.OOO.KS7*PATM*( TDB-TWB)*! 1 .<• ( TWB-32. ) /I S71. )
       WL = 0 . 622 *AH/ ( PATW-AH I
       00 100 ' I'ltN
       Ttl( I )=TWI
  1 DC  HtHtt'H
      00  104 J*ltM
      H»HA
      Un  10 1 I = lfM
      KC=f)
      DH1-HKI J )-H
      OH=DMI/l.2*I'NTU
  102 KC=KC+l
      TW2-TWI I I-DH/RLG
      IT=FW2
                » + (FSA( IT+l)-PSA( IT»*(TW2-IT)
                        ??*i-S/(!:'ATM-PSI*( l06l.8+0.*'t-*TW2)
      DHH-(OH1+HH?-II-OM)/?.*UNTU
       IF(KC.GE.N(1!TT)  GO TO 106
       DH=DHH
       GO  rn  102
  106  TW( I ) = Trf( I )-OHH/riLG
       1T=T«( ! )
       PS = FSAMTI + V + 0.6?
      IF(ilA?.Sr.M) o() TU
      TWtt?'Twn2+l.
      r-o TO 40
  30  TWUI*TWrt?-C>1A2-fM/(HA2-HA?2»
  104 TWHAL=TWMAL< rwf
      TW(J. U.O
      i>01(:3 IO. M
  103 TWil-TW'J* Trt( 'i )
      Th':i=Twn/-:
      1 T-lril'-'-L
      Tt'I^PSM II ) • I»'-SA( If • 1 )-PSA( I T) !<•( TWtJAL-l T)
      On? = 0 . »• :' ? ' 1 ' -• / 1 P & I M-
                                           309

-------
        HI *WL*,U K*Cr'MSr/l ).** >
        JUTURi.1
        Ml)
        SUBROUTINE >'ATFA1  ( K ANGe , AP»RO i I WB , :* AFA )
 C
 £*»**»»*«**««  ***********************
 C *   OilL'iMlNb RA'ING  FAC1DK  IIY  G I V UK. TWi' , APPKOACHt AND KANGE        *
 C *   - AP.'LY MARLtY COMPANY'S METHOIJ -                                  *
 C»**»**************«****************
 C
        RtAL  LRFAltl KFA2.LRT
                   I 2/ P.FT(10i?Ot6)fDTWK(9)
        IF( rhH.LT.3h.O  .!>.  TWB .GT. fl
        1F(APPRO.LT .U.O  .OR.  APrJKfl .GT . IE THt LOHtR A 40  UPPER  BOUNDS TJf-' WET-BULH TEMPERATURE
 C
        11 = 35
        1)0  100 1 = 1,'J
        I2=I1+DTWB«1 )
        IF( fWB .LC. 12) GO  10  10
 100    11=12
 C
 C   DETERMINE THE LOWER A'40  UPPER  BOUNDS OF APPROACH
 C
    10  AP=I APPRO-6. 1/2.
        J = A.-
 C
 C   DETERMINE THE LOWER A.^U  UPPER  BOU'IDS OF RANGE
 C
        RA=(RAMGe-5. >/5.
        K = RA
 C
 C   INTERi-OLATlON BETWEEN  RANGE  FOR BOTH TABLES
 C
        IH '.FT( I i.JfiO .LT. U.I  .Ort.  RFT(I,J,K*1)  .LT.  0.1
      1.0k. RF-TI It J + lfK> .LT.  0.1 .OR. RF T ( I , J*l , M 1 ) .LT. 0.1
      2. OR. RFT(I + l,J,K> .LT.  0.1 .OR. RFT ( 1 + 1 , J ,K t I ) .LT. 0.1
      3. OR. rtFTI I + l iJ+ltK)  .LT.  0.1 .Ori. Rt- T ( I » 1 , J + l ,K+ I )  .LT. O.I)
      4 GO  TO 999
        RAT-RA-K
        LRFA1*RFT< I,J,K)+(RFT( I , J ,K+ 1 I-RFT ( I, J , K ) I*RAT
        LRFi2=R(LT( I , J+1,K) + («FT( It J + l ,K+ 1 1 -KF I ( I , J+l.K) )*^AT.
        URF.'.1 = RFT( It 1,J,KI + (KFT( 1 + 1, J,K< l)-?FT( I + l, J,K) )*HA1
 C
 c   INTERPOLATION;. BETWEEN  APPROACH  FOR BOTH  TABLES
 c
       LRF=LRFAl+(LRFA2-LRf Al)*( AP-J)
       URF»UHFAlt(ui:iFA2-URFAl )*( AP-J)
 C
 C   INTt^! OLATION BETWEEN  WET-BULB TcMOEKATURE
 C
       RAFA = LRF*IU,'F-LRFI/l I 2- I I ) *( TWB- i 1 )
       RiITUKN
   999 PAFy! = 0.
       RETURN
       END
       SUBROUTINE  t AN (ArR,P,FANl)
c *   FINLJ FAN Ha
-------
       lA'A
       IPI'IP* t
       IAl=IA«l
       IF(IP.GT.n>GnTC9<5-FANPOWUA,13))**(T'.-I
      OH=SHG-SHS
      IT2-IT
   70
                                             311

-------
        IFIMIG.LT .
        IT2«IT
        DH=SHG-SHS
        GOTC/0
    60  T3«IT2*l>H/(I.H«SHS-Sl-C)*CT
                   ) + |PSA(IIltll-PSA4UHSL"( IT2»l)-CHSUy( I T3 ) I * ( T3-I T3 I
       SENS I 1=(T3-)CB)/(TDA-TCP)
       SENS I 3 = 0.5*1 SI-'S1-KJH3I *( T 3-TCB )- ( OHSUM3-QHSUI"! )
       GOTC50
   ICO SE\SI1=1.0
       SENS I 3 = 0. 5*1 SHSl + SHS2)*(TCA-TOB)-((;HSl.1M2-i,TLr»,F INC
                I'Kf/  I I'f AX , \PL tt PL t PL^ I N
                                              312

-------
   CCmiN/PLt V!. L/  Pl.MAX,tjC/>PAH,CAIH;AP,UENlK,l NIKI S.TM ,IOI( P

   IFUFP.LT.TI UWIOmC.C
   TI = (TFH-TLO'.. + FU4C)/f INC
   n = n
   CI1=IIK( ITi 1 )<(Hi<( !T»l. 1 l-t-K< n,l II*(TT-ITI
   Ul? = HK{ ITf7)«O
-------
          Example Results




Mechanical-draft wet cooling tower




       Full loading pattern
                 314

-------
 DESIGN WET-bOLB  TEMPERATURE OF AIR . 78.0 f
 OES1CN DRY-BULB  TEMPERATURE OF AIR - 89.0 F
 EXTREME  WtT  DUL8 TtPPERATUft »  83.430 CEG  F
 POWER LEVEL  «   313. MW
 SPECIFIC  HEAT  OF MR AT CONSTANT PRESSURE «  0.24 BTU/IB /F
 SPECIFIC  HEAT  OF WATER =  1.00 BTU/LU /F          BTU/IB./F
 DESIGN TERMINAL  TEMP. DIFFERENCE •  5.0 F
 ATMOSPHERIC  PRESSURE -  14.70 PSIA
 UNIT FUEL COST = C.000751 WK*-HR
 UNIT SUPPLY  WATER COST = 0.10CO i/1000 GAL
 UNIT WASTE WATER COST > 0.0500 t/1000 GAL
 ANNUAL MAINTENANCE COST =  200.C S/CELL/YEAR
 MAX. TOLERABLE CCNCtNTRATICN CF PROCESS WATER = 330. PPM
 SUPPLY WATER CONCENTRATION = ICO. PPM
 DIAMETER  OF  WET  TOWER FAN * 28.00 FT
 SPACE BETWEEN  TkC WET TOWER FANS * 4.00 FT
 UNIT WET  TOWfcR COST «  7.50 WTCWER UNIT
 KAXIMtM  POWER  OUTPUT »  312.50 CW
 UNIT CAPACITY  LCSS COST =  9CCOC.OO S/Mh
 UNIT ENERGY  CCST -  0.010 i/KW-hR
 UNIT LAND COST =  30CC.O t/ACRb
 SPECIFIC  LAND  AKEA = 0.10 ACRES/MW
 REPLACEMENT  ENERGY CCST DURING DOWNTIME = 0.0070 1/KW-HR
 DOWNTIME  FOR CONSTRUCTION =  30.C DAYS
 PUMPING  (-EIGHT CF WATER THFCUGH TOWER »    75.0 FEET
 PUMPING  EFFICIENCY FOR WATER FUI»P =  0.782
 UNIT CONDENSER COST =  4.00 J/SC. FT.
 OVERALL  CONDENSER COEFFICIENT, U = 630.0 BTU/HR/FT2/F
 INITIAL  WET  BULB TEMPERATURE *   5 DEG. F
 FINAL WET BULB TEMPERATURE -  ICO DEG. F
 INCREMENT CF DRY AND WET BULB TE*PE^ATURE =  10 DEC. F
 FINAL DRY BULB TEMPERATURE »  110 DEG. F
 LOWEST TEMP. IN  TURBINE CHARAC. CHART » 60.0 DEG. F
 TEMP. INCREMENT  IN TURBINE CHARAC. PATP1X * 2.0 DEC. t
 NUMBER CF ITERATIONS IN NTU CALCULATION =    2
 REFERENCE SPECIFIC VCLUMt OF AIR = 13.333FT3/L8
 LOWER BOUND  OF LIGHT FOGGING -  0.400 LB H20/LB AIR*F
 LOWER BCUNO  OF MEDIUM FOGGING =  1.350 LB H20/L B AIR*F
  FUEL  CONSUMPTION WITHOUT COOLING SYSTEM « 1026.947 MH   (TUR. BACK PRE. - 1.00  IN.HGI
 ***  0.0      OF  THE TIME IS NOT OPERATED AT FULL LOADING  ***

  TOTAL WATER FLCW RATE =    180000. GPM
  AIR FLCW  RATE  THROUGH EACH WET TOWER »   53S9994. LB./HR
  HATER FLCW  RATE THROUGH EACH WET TOWER -     15000. GPM
  WATER LOADING  =      12.50 GPM/SC. FT. PLAN AREA
  AIR LOADING »       18CO.CO LE./HR/SQ. FT. FACE AREA
  PRESSURE  DROP  CUE TO FAN OPERATING «  0.2625 IN. H20
  TOTAL NUMBER OF TRANSFER UNIT «   2.4238


*** TOWER SIZE ***
  LENGTH OF WET  TOWERS «        400.0 FT
  FILL  HEIGHT FOR WET SECTICN •  45.0 FT
  FILL  WIDTH  FOR WET SECTION *   36.0 FT
  NUMBEF OF WET  TOWER FANS »       12

**» DESIGN  CtNOITIONS ***
  DESIGN HOT  WATER TEMPERATURE « 110.824 DEC. F
  DESIGN COLD WATER TECPtRATURE «  89.396 DEG. F
  DESIGN COOLING RANGE =  21.428 UEG. F
  DESIGN APPROACH -  11.396 DEG. F
  RATING FACTOR  •  0.98J4
  DESIGN TURBINE BACK PRESSURE «  3.0663 IN. HG
  FUEL CONSUMPTION AT DESIGN CONDITION "  1026.95 MW
                                                315

-------
  »•• FOGGING PARAMETERS •**

   AVERAGE SENSIBILITY OF FOGGING, BASED ON WESTINGHOUSE CALCULATION  » 0.40328
   AVERAGE FOGGING ANGLE, BASED CN CARIEY CALCULATION *   0.0014  RAO.
   AVERAGE fCGGING MAGNITUDE =   0.01281 UEG. F»LB. H2U/LB.  AIR
   PROBABILITY OF NO FOGGING * 0.58048     LIGHT FOGGING «  0.4 IS 52
        MEDIUM FOGGING * 0.0         HEAVY FCGGING « 0.0

   TOTAL ANNUAL BLChDCWN *          2030. ACRE-FT/YEAR
   TOTAL ANNUAL WATER EVAP. «       4668. ACP.E-FT/YEAR      (   8.32542 )
   TOTAL ENERGY PATE IN •    1026.945 MW
   AVERAGE ENERGY RATE IN DURING ACTUAL POWER PRODUCTION *   1026.945  MW

 ***  CAP/EILITY LOSSES ***
   EXCESS FUEL CONSUMPTION *   -0.003 MW      (-0.000009  )
   MAXIMUM CAPABILITY LOSS =    6.614 MM      ( 0.021166  )
   ENERGY ICSS •    46085.96484 KW-HR     t 0.016835 J
   FAN C PUPP ENERGY LOSS = 36966.3047 Mta-HR     ( 0.013504  )
 ***  TOTAL ANNUAL COSTS ***
   TOTAL  ANNUAL FUEL COST =
   EXCESS FUEL COST =
   TOTAL  ANNUAL REPLACEMENT ENERGY LCSS
   TOTAL  ANNUAL WATER COST =
   TOTAL  ANNUAL WASTE WATER CCST
   TOTAL  ANNUAL MAINTAINANCE CCS7
   MAKEUP WATER COST WITH UPEN-CYCLE
   SLOWDOWN TREATMENT COST HI1
   MAINTENANCE COST WITH OPEN-CYCLE
   TOTAL  ANNUAL OPERATING COST
   EXTRA  ANNUAL OPERATION COST
6756026.
-18.
Y LCSS » 460859.
218364.
33086.
2400 .
CLE = 0.
PEN-CYCLE * 0.
LE = 0.
$/YEAR
$/YEAR
S/YEAR
S/YEAR
$/Y£AR
S/YEAR
t/YEAR
I/YEAR
I /YEAR
                          7470727.  J/YEAR
                           714691.  J/YEAR
***  AVERAGE OPERATING COSTS 	 IN MILLS/KW-HR ***
   AVERAGE FUEL  COST =              2.467957 MILLS/KW-HR
   AVERAGE WATER CCST =             0.079768 MILLS/Kfcy-HR
   AVERAGE WASTE WATER COST =       0.012086 MILLS/KW-HR
   AVERAGE MAINTAINANCE COST *      C.000877 MILLS/KW-HR
   AVERAGE CAPACITY LCSS =          0.168351 MILLS/KW/HR
   AVERAGE TOTAL OPERATING COST =   2.729035 MILLS/KW-HR
   AVERAGE EXTRA OPERATING COST *   0.261075 MILLS/KW-HR

**»  CAPITAL COSTS **»
   CAPITAL COST  OF TOWERS = $            1327532.
   PUMP  AND PIPE SYSTEM CCST = 1         1655998.
   PUMP  AND PIPE SYSTEM SALVAGE • ( $     331200.)
   NEW CCNCENSER COST •= $                      0.
   SALVAGE VALUE OF CLD CONDENSER = ( $        0.)
   OTHER OPEN-CYCLE COMPONENTS SALVAGE  * <  $   0.)
   HOOKUP  AND TESTING COST = S                 0.
   ADDITIONAL LAND COST = i                93750.
   REPLACEMENT CAPABILITY COST « t         595283.
   DOWNTIME COST * S                     1574999.
                                              OR
  TOTAL CAPITAL  COST =  $
                                         4916361.
    NOTE  : OPERATING COSTS ARE BASED CN "EXTRA" OPERATING CCST

**» TOTAL COST    	 ANNUAL  BASIS 	 FIXED CHARGE RATE ***
  NO. OF YRS

       6
      10
      IS
      20
      30
CAPITAL COST
 MILLS/KW-HR
  0.5459633
  0.4552688
  0.3780437
  0.3214719
  0.26S3899
ANNUAL OPERATING COST
     MILLS/KW-HR
      0.2610746
      0.2610746
      0.2610746
      0.2610746
      0.2610746
 TCTAL COST
MILLS/KW-HR
 0.8070379
 0.7163434
 0.6391183
 0.5825465
 0.5304645
FIXEO CHARGE RATE

     0.304000
     0.253500
     0.210500
     0.179000
     0.150000
                                                 316

-------
          Example Results




Mechanical-draft wet cooling tower




     Variable loading pattern
                 317

-------
  DESIGN WET-BULB  TEMPERATURE OF AIR « 78.0  F
  DESIGN DRY-BULB  TEMPERATURE OF AIR = 89.0  F
  BITHEHE WET  BULB TEBPERATURE =  83.130 DEC.  F
  POiER LEVEL  *   313.  MW
  SPECIFIC  HEAT OF AIR AT CONSTANT PRESSURE  =  0.21 BTO/IB./F
  SPECIFIC  HEAT OF WATER =  1.00 DTU/LB./F
  DESIGN TERMINAL  TEMP.  DIFFERENCE =  5.0 F
  ATMOSPHERIC  PRESSURE =  11.70 PSIA
  UNIT FUEL COST  = 0.000751 J/KW-HR
  UNIT SUPPLY  WATER COST = 0.1000 1/1000 GAL
  UNIT WASTE WATER COST  = 0.0500 S/1000 GAL
  ANNUAL MAINTENANCE COST =  200.0 J/CELL/YEAR
  MAX. TOLERABLE  CONCENTRATION OF PROCESS WATER =  330.  PPM
  SUPPLY WATER CONCENTRATION = 100. PPM
  DIAMETER OF  WET  TOWER  FAN = 28.00 FT
  SPACE BETWEEN TWO WET  TOWER FANS = 1.00 FT
  UNIT WET TOWER  COST  =   7.50 S/TOWER UNIT
  HAXIHUM POWER OUTPUT =  312.50 MW
  OMIT CAPACITY LOSS COST =  90000.00 $/MW
  UNIT ENERGY  COST =  0.010 S/KW-HH
  UNIT LAND COST  =  3000.0 S/ACPE
  SPECIFIC LAND AREA = 0.10 ACHES/MW
  REPLACEMENT  ENERGY COST DURING DOWNTIME =  0.0070  $/Ki-HR
  DOWNTIME FOR CONSTRUCTION =  30.0 DAYS
  PUMPING HEIGHT  OF WATER THROUGH TOWER =    75.0  FEET
  PUMPING EFFICIENCY FOR WATER PUMP =  0.782
  OHIT CONDENSER  COST  =   1.00 $/SQ. FT.
  OVERALL CONDENSER COEFFICIENT, U = 630.0 BTU/HH/FT2/F
  INITIAL WET  BULB TEMPERATURE =   5 DEG. F
  FINAL WET BULB  TEMPERATURE =  100 DEG. F
  INCREMENT OF DRY AND WET BULB TEMPERATURE  =  10  DEG.  F
  FINAL DRY BULB  TEMPERATURE =  110 DEG. F
  LOWEST TEMP.  IN  TURBINE CHARAC.  CHART = 60.0 DEG.  F
  TEMP. INCREMENT  IN TURBINE CHAHAC. MATRIX.= 2.0  DEG.  F
  NUMBER OF ITERATIONS IN NTU CALCULATION =    2
  REFERENCE SPECIFIC VOLUME OF AIR = 13.333FT3/LB
  LOWER BOUND  OF  LIGHT FOGGING =  0.400 LB H20/LB  AIR*F
  LOWER BOUND OF MEDIDH  FOGGING =  1.350 LB  H2O/LB  AIH*F
   FUEL COSSUBPTION WITHOUT  COOLING SYSTEM =  889.350  HW   (TUR.  BACK PRE. =  1.00  IN.HG)
 »**  0.11662 OF THE TIflE  IS NOT OPERATED AT FULL LOADING  ***

   TOTAL WATER FLOW RATE =    180000.  GPM
   AIH FLOW RATE THROUGH EACH  WET TOWER =   5399991. LB./HR
   WATER FLOW RATE THROUGH EACH  WET TOWER =     15000.  GPH
   HATER LOADING =      12.50  GPM/SQ.  FT. PLAN AREA
   AIR LOADING =      1800.00  LB./HR/SQ. FT. FACE AREA
   PRESSURE DROP DOE TO FAN  OPERATING  =  0.2625 IN. H2O
   TOTAL NUMBER OF TRANSFER  UNIT =  2.4238


»»* TOiER  SIZE ***
   LEHGTH OF WET TOWERS =         100.0 FT
   FILL  HEIGHT FOR WET SECTION =  15.0 FT
   FILL  WIDTH FOR WET SECTION  =    36.0 FT
   RUBBER OF WET TOWER FANS  =        12

*** DESIGN CONDITIONS »»*
   DESIGN HOT WATER TEMPERATURE  = 110.820 DEG.  F
   DESIGN COLD WATER TEMPERATURE =  89.396 DEG.  F
   DESIGN COOLING RANGE =  21.428 DEG. F
   DESIGN APPROACH =  11.396 DEG.  F
  RATING FACTOR =  0.9830
  DESIGN TURBINE BACK PRESSURE  =  3.0663 IN.  HG
  FUEL CONSUMPTION AT DESIGN CONDITION =  1026.95 MW
                                                  318

-------
 ***  FOGGING PARAMETERS «**
           PSIBIiITY OF FOGGING. BASED ON  VESTINGHOUSE CALCULATION = 0.39725
           FOGGING ANGLE, BASED CN MARLEY  CALCULATION  =   0.0015 RAD.
  AVF.RAGE FOGGING MAGNITUDE =   0.01054 DEG.  F*LB.  H20/LB.  AIR
  PROBABILITY OF NO FOGGING = 0.60052     LIGHT  FOGGING = 0.39948
        HEDIUH FOGGING = 0.0         HEAVY FOGGING  = 0.0

  TOTAL ANNUAL SLOWDOWN =           1839.  ACRE-PT/YEAR
  TOTAL ANNUAL WATER EVAP. =        l»230.  ACRE-FT/YEAR     (   7.54851 )
  TOTAL ENERGY RATE IN =     896.183 BW
  AVERAGE ENERGY RATE IS DURING ACTUAL  POWER  PRODUCTION *   896.181 HW

*** CAPABILITY LOSSES ***
  EICESS FUEL CONSUBPTION =    6.829 HW      ( 0.021854 )
  BAXIHOB CAPABILITY LOSS =    6.614 MW      ( 0.021166 )
  EBEHGY LOSS «    27387.57422 MH-HH      (  0.010005 )
  TAN  6  PUMP ENERGY LOSS = 20414.7188 MW-HR
                                                  (  0.007457 )
*** TOTAL ANNUAL COSTS ***
  TOTAL  ANNUAL FUEL COST =
  EXCESS FUEL COST =
  TOTAL  ANNUAL REPLACEMENT
                WATER COST
                WASTE WATER COST =
                MAINTAINANCE COST
                COST WITH OPEN-CYCLE =
  SLOWDOWN TREATMENT COST WITH OPEN-CYCLE
  MAINTENANCE COST WITH OPEN-CYCLE
TOTAL  ANNUAL
TOTAL  ANNUAL
TOTAL  ANNUAL
MAKEUP WATER
5895782.
44929.
Y LOSS = 273875.
197892.
29984.
2400.
CLE = 0.
PEN-CYCLE = 0.
LE = 0.
6399926.
549083.
S/Y EAR
S/Y EAR
S/YEAR
S/YEAH
S/Y EAR
S/YEAR
S/YEAR
S/YEAH
S/XEAH
S/YEAR
S/YEAH
                                                              OR
  TOTAL  ANNUAL OPERATING COST
  EXTRA  ANNUAL OPERATION COST

**» AVERAGE OPERATING COSTS	IN  HILLS/KW-HR  ***
  AVERAGE FUEL COST =               2.486929 MILLS/KW-HR
  AVERAGE HATER COST =              0.083474 MILLS/KW-HR
  AVERAGE WASTE WATER COST =        0.012648 MILLS/KW-HR
  AVERAGE BAINTAINANCE COST =       0.001012 MILLS/KW-HH
  AVERAGE CAPACITY LOSS =           0.115525 MILLS/KW/HR
  AVERAGE TOTAL OPERATING COST =    2.699585 MILLS/KW-HH
  AVERAGE EXTRA OPERATING COST =    0.231611 MILLS/KW-HH

*** CAPITAL COSTS **»
  CAPITAL COST OF TOWERS = $             1327532.
  PJBP AND PIPE SYSTEM COST = $          1655998.
  POHP AND PIPE SYSTEM SALVAGE =  (  S      331200.)
  SEW CONDENSER COST = $                      0.
  SALVAGE VALUE OF OLD CONDENSER =  ( $        0.)
  OTHER  OPEN-CYCLE COMPONENTS SALVAGE =  (  S   0.)
  HOOKUP AND TESTING COST = S                 0.
  ADDITIONAL LAND COST = S                 93750.
  REPLACEMENT CAPABILITY COST = $         595283.
  DOHHTIME COST = $                      1102499.
  TOTAL CAPITAL COST
                                         4443861.
    HOTS  :  OPERATING COSTS ARE BASED ON "EXTRA" OPERATING  COST

*«• TOTAL COST    	ANNUAL BASIS	FIXED CHARGE  RATE  **«
  HO. OF  YRS

       6
      10
      15
      20
      30
               CAPITAL COST
                 HILLS/KW-HR
                  0.5698439
                  0.4751823
                  0.3945795
                  0.3355332
                  0.2811731
ANNUAL OPERATING COST
     HILLS/KW-HH
      0.2316115
      0.2316115
      0.2316115
      0.2316115
      0.2316115
 TOTAL COST
BILLS/KW-HR
 0.8014554
 0.7067938
 0.6261910
 0.5671447
 0.5127845
FIXED CHARGE RATE

     0.304000
     0.253500
     0.210500
     0.179000
     0.150000
                                               319

-------
          APPENDIX IV





        FORTRAN LISTING





NATURAL-DRAFT WET COOLING TOWER
              320

-------
c
c***********.**,,*,,,,**,,,
° I *T*05HJN*E*OF "*TURAL DRAFT w" COOLING TOWER
C                                **»***»«**
              I20>,PERCEDI15,2),AMANT(3,2)
      DIMENSION  WTCOST<10),AWCn),BWUO),CWUO>,FCRR(5»
      OIMtNSION  BASEOniO),WIDTHW(10),NYEAR(5),FCRIlll
      REAL KM
      COMMON/OENSIT/ DAIR1250)
      COMMON/INPUT4/ WPDRU1 13),fILLHT(101,POROP,WI CTH
      COMMON/TURBIN/ HR,I MR,TLQW,FINC
      COMMON/TOWERS/ A.B.ARWT.AW.BH.CW.GPM,CONST,NCITT,APR
      l.AIJK.BIJK,RLG,ENTU,N,FNTC,EGPMtGPMW
      COMMON/NOT/ NUMTOW
      COMMON/UTCOST/UC < 4,3,11,5),ORH(2 I
      COMMON/NATOR/H,HT,KM,D1,D2,ELEV,R,POHAFU5I
      COMMON/CONSTA/ CONSTl.DCNST
      COMMON/TURB/ POWER,TTDD.TET.TTD,TTDKO.TTDO
      COMMON/NCALA/ PSA,TPS,TS,TWBAL,CHl,OH2,HA
      COMMON/TOWERC/ NOTS(IOJ.HTCOST
      COMMON/INPU/ PERCENI 12, 15,2 ) .HTNDUO) , PERCEO
      COMMON/TEMP/ ITWBI,1TWBF,ITBO,ITOBF
      COMMON/ECONO/ NYEAR ,FC, ViC,fcM,DR,CCNO,CCNl, ANPCWE,HEIGHT,EFFICU
      COMMON/POWERC/ IPLI,IPLF.MM,PL,LP
      COMMON/LOSS/S,CWATEU,CBLOV,0,CMAI NO
      COMMON/ATMOS/ PATH
      COMMON/MAINTA/ AMANT.CF.EFI
      COMMON/WSS/ QHSUM»21C),FOGL,FOGM
      COMMON/WITREF/ IWRI fE , I PUNCH,REFSV.FAWETT, PAV.ETT, AFRL.TWBREF
      COMMON/PLEVEL/ PLMAX,UCAPAB.CAPCAP,UENER,ENERLS,TEI,TOTOP
      COMMON/TBPR/ ITPMAX,TETPAX,ICAP
      COMMON/TBPRE/ IPMAX,NPL,DPL,PLMIN
      COMMON/AREAS/P!PLAR,PIFAAR,h,DBAR
      COMMON/TEMPE/TWBD.TDBD
      COMMON/FRIC/FRIFACI18)
      COMMON/RENEW/TOSTAR
      COMMON/FPL11/FPLHAX
C
C  DRY-BULB  AND  WET-BULB  TEMPERATURE INTERVAL,  ITBC,  MUST  BE  GREATER  THAN  1
C
      READ! 5,1)  < UtUCtI, J,K,L) ,L = 1,5I ,K=1,11I ,4 = 1 ,3) ,I»1,4>
1     FORMATI5F10.4)
      READ!5,2)(DRHII),I»1,2)
2     FORMAT(2F10.4)
      READ(5,109) IPMAX,NPL.DPL.PLMIN
  109 FORMAT(2I10,2F10.0)
      REAO«5,110) (IHR(I,J),J=1,NPL),I=1,IPMAXI
  110 FQRMATUOF8.5)
      READ!5,101) (PSA(I),1=1,250)
  101 FORMATUOFB.5)
      READ(5,101I (DAIRfI 1,1 = 1,250)
      READI5.101I (QHSUMdI,1=1,210)
      READC5.102) (IHRMI,I=1,NPL»
  102 FORMAT!14I3>
      READ(5,106) (FCRI11,1=1,11)
      READ(5,106) (PAPCOSd1,1=1.20)
  106 FORMAT!10F8.0I
      READ(5,106) AFRL
      READ(5,106) GPMW
      READ(5,106) (AW
-------
  508 FORMAT!10F8.6)
      READ! 5,509)  PATM.TPMAX
                  .0)
                   ((ANANTI!,J>,t-1,3),J-1,2)
509 FORMATI3F10
    READ(5,510)
510 FORMATI6FIO.OI
    REAOI5.513) FDGL.FOGM
513 FORMAT(2F10.0)
    REAn(5,505) CA.CW1
505 FORMATUF10.2)
    READI5.509) TBP,TWB10.TDB10
    READI5.509) EF.EN.EFI
    READ!5,507) IwRlTE,I PUNCH,ITPMAX.tEXTRA,INUCAL.NEWCQN
                !FRIFAC(I 1,1 = 1,18)
                5)
                (POMAFI11,1-1,15)
    FORMAT!15F5.3)
    READ I 5,106) EFF1CH.UNCOND.UO,HEIGHT
    READ!5,106) (HIDTHHII),1=1,10)
    READI5.595IELEV
    FORMATI3F5.0)
    READ(5,596) IBASEDI(I),1=1,10)
                0)
                (HINDU 1,1 = 1,10)
    FORMATI10F8.2)
    READ(5,106I !FILLHT(I),I>1,10)
111

112
 595

 596

 105
       REAOI5.111)
       FORMAT!10F7.
       READ!5,112)
      FORMATUOF5.
      READ(5,105)
C
c
C
       NUMTOH'l
       R'53.35
       CONST«7.*81/60. /62.»10.**9
       DONST=CONST
       CONST1=0. 124683/62.

    CALCULATE CORRESPONDING FIXED CHARGE RATE

       D0100K«1,5
       NEAR-NYEAR(K)
                                        . + (IJK-32.)/157l.)
      IV»Y
  100 FCRR(K)=FCR( IY)+(FCRI I Y+l )-FCR( IV) )*
-------
  716
    l6
       FPL2»PLMAX*(CF*0.n/d.4DQHR)
       T?^™!i!i:!TQ*T2-TOSlll'  S/KW-HR* /10X,
      1'UNIT  LAND COST =',Fa.l,' $/ACRE'/10X,
      I'SPECIFIC LAND AREA =',F7.4,' ACRES/MW /10X,
      2'REPLACED ENERGY COST DURING DOWN TIME =',F7.4,« t/KW-HR« /10X,
      3'DOWNTIME FOR CONSTRUCTION =",F6.1,' DAYS' I
C
       WRITE C 6, 640) HEIGHT.EFFICWtL'NCOND.UO
   640 FORMATdH ,9X, 'PUMPING  HEIGHT OF WATER THROUGH TOWER ='.FB.l,
      2'  FEET'/lOX, 'PUMPING EFFICIENCY FOR HATER  PUMP ='tF7.3/lOX,
      3'UNIT  CONDENSER COST =',F6.2i' t/SO. FT.'/IOX,
      ^'OVERALL CONDENSER COEFFICIENT, U »', F6.lt' BTU/HR/FT2/F' I

       WRITE (6, 662 I ITrfBI, ITHBF, I TBD, ITDBF
   662 FORMATdH ,9X, 'INITIAL  hET BULB TEMPERATURE =',14,' DEC. FVIOX,
      1'FINAL WET BULB TEMPERATURE  »',IS,' DEG. F«/1CX,
      2'INCREMENT OF DRY A iD WET BULB TEMPERATURE =',I«t' DEG. F'/lOX,
      3'FINAL DRY BULB TEMPERATURE  ='.15,' DEG. F'l

       WRITE! 6, 650)  TLOW,FINC,NOITT,REFSV,FOGL,FOGf
   650 FORMATdH ,9X, 'LOWEST TEMP.  IN TURBINE CHARAC. CHART =',F5.1,
      1«  OEG   F'/1CX,'TEMP.  INCREMENT IN TURBINE CHARAC. MATRIX =',F4.1,
      2"  DEG.  F'/lOX, 'NUMB3R OF ITTEP.ATION IN NTU CALCULATION =',15
      3/lOX, 'REFERENCE SPECIFIC VOLUME OF AIR «' ,F7 .3, 'FT3/LB' /10X,
      4'LOWER BOUND OF LIGHT FCGGING »',F7.3,'  LB H20/LB AIR*F'
      6/lOX, 'LOWER BOUND OF  MEDIUM FOGGING =',F7.3,' LB H20/L8 AIR*F'»
C
       IT'TWBD
       TSS-PSA(IT)HPSA(IT*1)-PSA(IT)I*(TWBD-IT)
       HAA=0.24*TWBD*0.622*TSS/(PATM-TSS)*( 1061. 8+0. 44*THBD!
       D01000II»NNOTSI,NNOTS
       D01000IW»NOWTS1 .NOWTS
       IFI1W.GT.3)  IWRITE'O
       D1«BASEDH I I)
       W-WIDTHW(IW(
       WIDTH-W
       H-FILLHTdW)
       HT»HTND< II I+H

°      CALL GEOMETIOl,02,HT,H,DBAR»



                                       323

-------
       TS»TSS
       HA-HAA
 C
 C  DETERMINE MATER FLOW RATE FOR EACH WET TOWER
 C  DETERMINE AIR-HOWS FUR WET TOV.ERS, DETERMINE N.T.U. FOR WET TOMER
 C
       PIPLAR»-3.U15926535*01**2/4. +3. 141 5726535*1 D1+2«H I **2/4.
       P I FAAR» 3. 141 5926535*0 1*H
       GPM*GPMW*PIPLAR
       EGPM«GPM
       FAWET»H*Dl*3. 14 15926535
       FNTU*AM< IW)*GPMW**BW( IW)*H
       N«IFIXIFNTU/0.5)
       ENTU»FNTU/N
 C
 C
 c* ***************************************
 C  CALCULATION OF BEST "K" FOR AIR FLOW RATE CALCULATIONS
 c* ***«*»,,»***,**»***********************
 C
 c
       CALL BESTK(ENTU,NOITT,N,GPM,AFR,RLG,TCW,WL,KM
       TTO=TTDD
 C
       CALL HOOELW ( TDBO , TuBD, I W ,NPL , TET, TQ, TWL , 1 1 1 I , K,TT, I M )
 C
       IF
       TQQ»(PLMAX*TTSTAR/(1.+DCHR 1+10*1055.04/3. 6 1/EFI
       RP«TQ*CONST/EGPM
 C
 C  DETERMINE CONDENSER COST,  AND PUMP AND PIPE SYSTEM COST
 C
       THW=TET-TTD
       TCH=THW-TQ*CONST/EGPM
       RANGE=THW-TCW
       TTDkO»TTO/RANGE*CONST/EGPM
       RLL=ALOG( (RANGE+TTDI/TTC)
       CONCOS=UNCOND*EGPM/CONST/UO*RLL*10.**9
       IFINEWCO.M.EQ.l)  CONCOS'CCO
       IP»EGPM/10.**5
       PPCOST=PAPCOS(IP+H + 
-------
      CALL  POWERS (TET.TQ.TTSTAR)
681
       FPLl-PLMAX-FPL
       FPL1«FPL UPUMOPl/1000.
       FPLMAX»FPLl
       CAPCAP-FPLl*UCAPAB

       WRITE(6,607)  SS2
  607  FORMAT! IH0.10X, •***', F8. 5,
      I1  OF  THE  TIME IS NOT OPERATED AT FULL CONDITION ***•)
       WRITE16.661)  EGPM.AFR.GPM.GPMW
  661  FORMAT! 1HO.IOX,
      3'TOTAL  WATER  FLOW RATE »',F11.0,' GPM'/llX,
      4'A1R  FLOW RATE THROUGH EACH WET TOWcR ••.Fll.Ot* LB./HR'/llX,
      5'HATER  FLOW RATE THROUGH EACH WET TOWER = ',F11.0,' GPM'/UX,
      6'WATER  LOADING =',Fil.2,« GPM/SO. FT. PLAN AREA')
       WRITE16.665)  HT
  665  FORMAT! 1H0.8X, •*** TOWER SIZE ***'/10X,
      !•  HEIGHT  OF WET TOWER =',F6.2,' FT')
       WRITE (6, 664 1  FILLHTI I W) .WIOTH.NUMTOK.DI ,02
  664  FORMAT!1H , lOX.'FILL HEIGHT FOR WET SECTION =',F6.1,' FT'/llX,
      2«FILL WIDTH FOR WET SECTION =',F7.1,' FT'/llX,
      3«NUMBER  OF WET TOWERS  'SI3/11X,
      4"BASE DIAMETER OF THE TOWER =',F6.2.' FTV11X,
      5'EXIT DIAMETER OF THE TOWER =',F6.2,« FT')
       WRITEI6.663)
  663  FORMATtlHO.BX,'*** DESIGN CONDITIONS ***•)
       WRITE! 6, 666)  THW.TC M, RP ,AP ,PDESI ,TO,RH1 , TOO
  666  FORMATUH , 10X, 'DESIGN HOT WATER TEMPERATURE =',F8.3,' DEC. F'
      1/11X, 'DESIGN  COLO WATER TEMPERATURE *',F8.3t* DEC. FV11X,
      2'DESIGN  COOLING RANGE =',F8.3,' DEC. F'/llX,
      3'DESIGN  APPROACH =«,F8.3,« DEC. F'/llX,
      5'DESIGN  TURBINE BACK PRESSURE =',F8.4,» IN. HGV11X,
      5'DESIGN  HEAT  REJECTION =• ,F8.4, ' *10«*9  BTU'/llX,
      5'DESIGN  RELATIVE HUMIDITY *',F8.3/11X,
      5'FUEL CONSUMPTION AT DESIGN CONDITION =',F9.2,« MW' )
       IFIICAP.EO. 1 ) WRITE(6,667)
  667  FORMATC1H , 12X, 'NOTE ... CAPACITY LOSS AT DESIGN CONDITION')
c
C  COMPUTE OPERATION COST AND TOTAL COST
C
       CALL OPECOS (IW.TOTOPE)
C
       IFITOTOPE.GT.10.**11)GOT01001
       CAPCOS=CAPC01+PPCOST+CAPCAP+ALANDC+DOWNCQ -CCO-COO+CHT-PPCOSO
C
       HRITE(6,604)
  604  FORMATI1H0.7X,'*** CAPITAL COSTS ***•)
       WRITE I 6, 602 I  CAPC01 , PPCCST, PPCOSO.CONCOS.CCO .CCC.CHT , ALANOC,
      1CAPCAP,OOWNCO,CAPCOS
  602  FORMAT! IH , 
-------
      2I5/12X.'TURBINE TEMPERATURE ««,F10.4)
       TOTCOS»10.**12
  1000 CONTINUE
       STOP
  1001 TOTCOS-tO.**l2
       STOP
       END
       SUBROUTINE OPECOS (IW.TOTOPE)
 c
 c*»*****«******************
 C *  PROGRAM TO DETERMINE TOTAL ANNUAL OPERATING COST
 C
 C                                                                          .
       DIMENSION HR(50,14),IHR(14) tAUO)tB(lO) t ARHT ( 101 t PSA (250)
       DIMENSION AW(lO)tBHUO) ,CW< 10 ) ,PERCED( 15,2 I , AMANTO.2 )
      l.WTCOSTt 10),SK15),S2(15),S3tl5l,N¥cARI5)
       COMMON/DENSIT/ OAIRI250)
       COMMON/ I NPU/ PERCENt 12, 15,2 ( .HTNOC 1C ) ,PERCED
       COMMON/INPUT^/ WPDROt 13 > , F ILLHT ( 10 ) , POROP, hi CTH
       COMMON/TURBIN/ HR , I HR, TLOV«,F INC
       COMMON/NCALA/ PSA , TPS, T S , TWBAL.QH1 ,QH2 ,HA
       COMMON/TOWERS/ A,B, ARWT, AW, Brf,CW,GPM, CONST, NOITT, APR
      1,AIJK,BIJK,RLG,ENTU,N,FNTU,FGPM,GPMW
       COMMON/NOT/ NUMTOH
       COMMON/TURB/ POWER, TBP, TET, TTD.TTDKO.TTDC
       COMMON/TOWERC/ NOTS< 10) .WTCOST
       COMMON/CONSTA/ CONSTl, CONST
       COMMON/TEMP/ ITWBI , I TViBF, ITBD.ITDBF
       COMMON/ECONO/ NVE AR ,FC, ViC , VW , OR, CCNO.CCN1 , ANPOWE, HEIGHT, tFRCW
       COMMON/POWERC/ IPL I , I PLF, M,PL ,LP
       COMMON/ATMOS/ PATM
       COMMON/MAINTA/ AMANT.CF.EFI
       COMMON/LOSS/S,CWATEO,CBLOWO,CMAINO
       COMMON/WSS/ OHSUM(210I,FOGL,FOGM
       COMMON/WITREF/ IWR1 TE , I PUNCH ,REFSV,FAHETT, PAhETT, AFRL.TWflREF
       COMMON/PLEVEL/ PLMAX, UCAPAB .CAPCAP ,UENER,6NERLS,TE I .TOTOP
       COMMON/TBPR/ ITPMAX , TETMAX , 1C AP
       COMMON/TBPRE/ IPMAX ,NPL ,DPL ,PLMI N
       COMMON/RENEW/TOSTAR
       COMMON/FPL11/FPLMAX
 C
 C  OPERATION DUE TO WET COOLING TOWER
 C
 C  DRY-BULB AND WET-BULB TEMPERATURE INTERVAL, ITBC, MUST BE GREATER THAN  1
 C
       IFIHTNOI IW) .LT.0.01 IGOT01002
       PUMOPl=FGPM*HEIGHT*62./7. 48 1/60. /550./EFFICW*0. 7457
 C
       lFIIWRITE.EQ.l)MRITc(6,a99)
 C
       NUMTOW'l
       IM»0
       TOTOPE'O.
       TOTBLO«0.
       TOTWL'O.
       TOTEI'O.
       TOTFUE=0.
       TOTWAT=0.
       TOTWAW'O.
       TOTMAN-0.
       TOTLOS'O.
       TOTPRO»0.
       SENl'O.
       SENZ'O.
       SEN3-0.
       FOGOS'O.
       FOOLS «0.
       FOGMS'O.
       FOGHS-0.
      CAPLOS'O
      CAPPRO-0.
      FPLMAX'O.
      ENERLS»0.
      FAPLS'O.
C
      RLG'GPH/CONST*10.**9/AFR
      FNTU'AHI IH)*GPMW**BW( I W I *F I LLHT ( I H)
      N-IFIXIFNTU/0.5)
                                         326

-------
      ENTU-FNTU/N
      PLC»PLMAX*CFtPUMOPl/loOO.
      D01000LP«tPLI,IPLF,M
      LP1-ILP-IPLI )/M»l

      TTTSAV-0.
      KKSAVE>0
      JJJJ.Q

      0090UIJ«ITHBI,ITWBF,ITBO
      TWB=IIJ
      TS-PSAUIJ)
      IH1M IU-lTHBll/lTBD+1
      KK'KKSAVE
      TTT=TTTSAV
      12-0
      ITOBMA«PSA( nj|/tO.UC03t7*PATM»(l.*(IU-32.l/i571.) J + IIJ
      IFUTDBMA.GT.ITOBF) ITDBPA*ITDBF
      IF( I IJ.GT. 1TOBMA1GO  TO  901
      D09231JK-IIJ,ITD8MA,ITBD
      TOB=IJK
      ID1»( tJK-ITWBIl/ITBO+l
      AH=TS-0.000367*PATM*(TDB-TWBl*(l.t(TWB-32. 1/1571. »
      WLl=(0.622*TPS/(PATM-TPSI-0.622*AH/(PATM-AHI I*AFR*CONST/10.**9
      1*NUMTOW
      QH1-HL1
      FAP=PUHOP1/1000.
      NP'NPL
      IFtLP.NE.IPLl )  NP-tCF-
      CALL  MODELW  ( TDB, TWB, IH.NP t TETt TQ.THL , JJ JJ,KK.TTT, IM)
C
      IZ'IZ+l
      IF(TET.LT.O)GOT0200
      TTSTAR=1.
      tFlLP.NE.IPLI)  TTSTAR=CF
      !F( ICAP.EQ.: 1GOT09666
C
      CALL  POMERS  ITETtTQ, TTSTAR)
C
      CAPPRO=CAPPRO+PERCEN( IVi li 101 tLPl I
9666  DQHR=( TO /ITS TAR-TO STAR) /(PL PAX*3. 6/1055. 04-TC/TTSTAR+TOSTAR)
      FPL=PLMAX*TTSTAR/ ( 1 ,+DQHR )
      PL=FPL
      IFtLP.EQ.IPLI )GOT09668C
      IFC ICAP.EQ.01GOT096681
      FPL1«=CF*PLHAX-FPL
      PL»FPL
      FAP=PUMOP1/1000.
      GOT0966B2
96681 TETST=TET
      TUST«TQ
      FPLST=FPL
      THLST»THL
      NP=NP+1
      KKST'KK
      TTTST-TTT

C     CALL  MODELW  ( TDB, TNB, IW.NPrTETl .TQltTMLl , J JJ J.KKST.TTTST, IMI
C
      TTSTAR-CF+0.1
      IFIICAP.EO.CIGOT096683

      CALL  POWERS  (TETltTQl, TTSTAR)

96663 OQHR»(TQ1/TTSTAR-TOSTAR)/IPLMAX*3. 6/1055. 04- TQ1/TTSTAR*TOSTAR)
      FPL»PLMAX*TTSTAR/< 1 .+OQHR )

°     TET=TETST+(TETl-TETST)/|FPL-FPLST)*tPLC-FPLSTJ
      IF(TET.LT.(TETMAX»0.05) 1GOT096684
      FPL1-CF*PLMAX-FPL
      TO»T01
      TET»TETMAX
      TWL»TWL1
      PL-FPL
      FAP»PUMOPl/1000.
      CQTO96682
96684 TQ.TQST»(TQ1-TQST)/«FPL-FPLSTI»(PLC-FPLSTI
      }SL»TWLST+(TWLI-THLST)/(FPL-FPLSTI*
-------
96682  IFCFPLl.LT.. >  FPL1«C.
       FPL1*FPL1MPUMOP1 »/1000.
       lF(FPLl.Gr.n>LMAX.AfJU.PeRC£N< I HI, 1 01. LP I I .GT .0.000001 ) FPLMAX'FPL 1
96685  £NEKLS-eNtRLS*FPH*PERCEN( I V. 1 , 101 , If I I *8 760.
       FAPLS»FAPLS*(-AP*PERCEN( I W 1 , I Dl ,LPl I *U760.
       EI»*)/0.'V91lll
       TOTDLD=TOTBIO+BLOOWN*PERCEN( I Hi. 101 , LP I ) *60. *24.*365./326046
       TOTWL«TOTWL»TWL«PERCEN1 IM1, 101 ,LP1 1*60. *24 ,*365./326046
       EI1=EI/1000.
       TOTEI«TOTEI+EI1*PERCEN( IHI.IDI.LPI)
       TOTPRO«TOTPRO + PERCE,M( IV/liIOl.LPl)
       TOTFUE=TOTFUE + FUECOS*PERCEN(IW1,ID1,LPU
       TOTKAT=TOTWAT+WATCOS*PERCEN( IW1,!D1,LP1I
       TOTWAW=TOTWAH+HAWACO*PERCEN(IW1, ID1.LP1)
       TOTMAN=TOTMAN+AMANT(2,LPl)*PERCfcN(li.l,I01,LPI)*NUMTOW
       FUECIS=FUECQS»PERCEN(IV.1,ID1,LP1)
       WATCOS=WftTCOS*PERCEN! tVil,IOL,LPl)
       MAWACO'WAWACO*PERCEN( IWl, IDl.LPl)
       AMANTUAMANI12,LP1)*PERCEN( I Kl , I Dl ,LP1 ) *NUMTCH
       OPCOS = ( FUEC I S+WATCOS+WA&.ACO+AMANT1 )
      l+FPLl*PERCEN( IW1,IOI,LPU*8760.*UENER*1000.
       TOTOPE«TOTOPE+OPCDS
       IFIPERCENI IWl, IDl.LPl ).LT.O.OOC;01)GOT031Z
C
       CALL  FOGSEN  ( TDB, THB,TWBAL,QH2,SENSI 1 .SENS 12 .SENS 13)
                  ENSIl*PERCEN
-------
                                     cnsT''«.'^ ENERGY  tors-.ax,

                    'r,nM',22X,'i/YEAR',6X,
     >'*/VEAR',IOX,'$/Yi:*«',l?x,«t/YFA, F 1 1. 3, Fl 3.6, F 17.7, F 1 4. 5, F 17. 5 )
      WRI fF(6,399l
  899 FORM.M 1///1X,130( •*• I////)
  923 CrNTIMJr
  901 CCNT!NMF
 1003 CONTTMIE
      FU£LF.X=70TET -T = I
      TQTFUl=Fun FX»FC*1000.*P760.
                    -Tf !*FC*1000.*8760.
66667 FOtMATUHi), SX, '*** FOGGtNG P*.R/-MP1 ERS ***• I
      WP I TF. (6, 66666 )  SEN! , 5EM2 ,5 EN3 , FOGO^ , FCIGLS, FCGMS, FOGHS
66666 FOR^f'dH , / IdX, ' AVE^iGE SENSIBILITY  OF TOWSP. PLUME,  P-iSEO CN WEST
     1INGHHIJSE CAlfULATICN  =•, F8 . 5/ 1OX, • AVERAGE FOGGING *NGLE,  8ASEO ON
     ?MARLEY CALCUM VICN »<,F9.<»,'  PAO.'/IOX,
     3'AVFP^GE Ff'GGIJG  .'-ItGNITUDFj s'.FlO.S, • DEC. F*L3. H20/I.8.  MRV10X,
     *« PPOBAeil.ITY  DC MQ FPGGING =• , F8.5 , 5X, ' L IGH" FOGGING  ='>F8.5,5X,
     S'MFDIU". FOr,GIP~, = • ,F8. 5, 5X, «HFA VY  FOGGING =',F8.5I
      TOTEIl=TQTEl/TOTPRn
      TCTWI.1 =TOTUI. /( TOSTiR*1055.04/3.6)
      ENERL l=c NER! S / ( PLM AX*876(). )
12121 FPRMATC//10X, 'V'LUES IN PA"ANTHESIS ARE.THE VALUES  DIVIDED BY POME
     1R  OUTPUT EXCEPT  THF  LAST TWO WHICH  AF E« / 10X, 'THE VALUES DIVIDED BY
     Z THE  PCWER OUT°UT  PER YEAR'//)
      WPITF«6,605)  TOTBLO,T3TWL,TOTKLl,TOm,FUEl EX.FUELE1,

     l,T6TFUP,T01FiJl,TPTWAT,TOTWAW,TOTMAN,/iNUCAP,TCTOPF,70TC'P
  605 FORMATI1H ,/I OX,'TOTAL ANNUAL BLOWOHWN =',F15.0, ' ,'CRE-FT/YEAR ' /
     110X, "TD'AL ANNUAL  WATER EVAP. =',F12.0, • ACRE-FT/YEAR'
     1,5X, ' (', F10.5, '  )'/lUX,
     2'TUI'Al  ENERGY  RATE TN =',F12.?,'  MW//8X,
     2t**»  CAPABILITY  LOSSES ***'/10X,
     3'EXCESS FU^1   CCNSUMPTION =',(=9.3,'  MW ' , 5X, ' I • , F9.6, •  t'/lOX,
     3'M4X'MUM CAPABfLI^Y  LOSS =',F9.3,'  MW , 5X, ' (' , F9.6, '  I'/lOX,
     3'FNERGY LOSS  =',F15.5,' MW-HR • , 5X, ' < ', F9.6, • )'/10X,
     3«P'JMP ENERGY  LOSS  =',FH.*,' MW-HR ' , 5X, ' (' , F9.6, •  P//8X,
     3i*»*  T'lTAI. *NNUAI.  COSTS ***'/l'1X,
     3«"0'AL ANM"".L  FUEL COST =',F2n.O,'  $/Y=AR'/10X,
     4'FXCESi FUll   COST  =',F'6.0,' t/YEAf/10X,
     4«TOTAL .'MNUAl  WATER  COST =',F19.0,' »/YFAH •/10X,
     5'TCTAL ANNUM  WASTE  WATER COST  =',F13.0, •   $/YE4R'/10X,
     6'TOTAL AK"UML  MATN-AIN4NCE COST «',F12.U,'  $/YEAP-«/1UX,
     5«TOTAl  ANNUAL  CAPACITY LOSS =',F16.0,' t/YFAR'/lOX,
     7AV".«CF  WASTE W/.TE3  COfT = ' , F I S. 6 , •  MI LI S/KH-HR' /I'.'X ,
                MATNT4TNANiCe COST =',Fl*.6, • MtLL5/XW-HR'/lOX,
                ff,PAcr:Y loss  =',na.o,<  «" t LJ/K«/MR- /if»x,
                SXrKA OPERATING COST «',FU.6, •  MIUS/KW-HR • 1
      RETURN
      WRITF(6,623)
                                               329

-------
       PPPMATHHO/lOX, ' V.CT  COOl ING TOWER IS- NOT  SUFFICIfNl TO OPERATE1
       TL'Tf>PE*10.»»12
       PFTURN
       SUBROUTINE "lOOCLW  (T 08, 7W«, IW, L P, V ET.TQ.TWL, I111, K, TTt IM I


      THIS SUnROUTINF  CALCULATES THE MODE!  ING  RELATION"! HIP? FOR PPWER
       PI ANT iNO POOLING  TQWEH  .   GIVEN WET AND  DRY  BULB
       TEMPFR«TUP.:S, opfR»TinN  LEVELS or- WET TOWERS,  POWER LEVEI  CF
               9UY°UT,  "(HE  RESULTS ARE TURBINE  EXHAUST TEMPERATURE AND
       HEAT REJECTION.
     + ************  ****************
c
r
c
c
r
r
c
c
      DIMENSION  NT R JIN (50, 14), 1 1 NHTB ( 141 , A ( 10 ) , B( 10 ) ,AR WK IP I
     l,AW(10),flWUO),CW , B, ^RWT , J W, DW ,CW, GPM, CONST, NOITT , AFR
     1,AIJK,P! JK,RLG|SNTU,N, I=NTU,FGPM,r,pMW
      COXNON/NC/IUA/  PSA.TOS.TS.TWBM ,OHlf«H2,HA
      COMMON/MOT/ NUMTCW
      CCyMON'/TUP.n/  eLl,BL2,RL3,TTD,TTDKO,TTDO
      COKMONVTBPR/  I TP M4X,TETMAX , ICAP
 C
 C   IF TWB IS HIGH  EMCUOH,  THEN COOLING CANNOT TAKE PI AC E AT ALL UNTIL
 c   TURBINE CONDENSE-?  TEMPERATURE is HIGHER. THUS,  WILL SKIP TO
 C   HIGHER TU».BtNE  TEMPERATURE.
 C
 C   '(F TWB IS LOW ENOUGH,   COOLING WATC« FREEZES,  WHICH
 C   (S NEVER DESIRED.   THUS WHENEVER COOLING WATER  WOULD HAVE BEEN
 C   C301FD 8F.LOW FREEZING ANYWHERE IM THE CYCLE,  NO COOLING IS
 C   PERFORMED (IMPLYING ALTERNATE SYSTEM USED  IN  PRACTICE).
 C
 C  ASSIGN MO^EL PARAMETERS  FOR  TOWER SECTION
 C
       ICAP=0.
       IM=2
       IFR=0
       IFIIIII.GT.0.51GOT010QO
       WL=0.
       TPS=0.
       TWB»-L=0.
       OH2=0.
       IF(Iin.EO.-5)GOT09qi
       TTDO»HTRJ!M(1,LPI»TTDKO
       GPT09S2
   991  TTCO = TTD
 C
 C   ASSIGN INITIAL TPIAL  TURBINE TEMPERATURE
    97 IFRE=IFRE*1
   201  K«K*1
       TT=TLDW+ (K-l I'^INC
       IF(K.GT. JEfJHTP(LP>.ANO.TT.GT.(TETMAX + 1.95) )GC TO 999
       I F ( II II . E<3. -5 ) r,nTO«)4
       TTD=HTRJ!N(K,LPI*TTDKO
   404  TT1-TT-TTO
C
C   Com.  VHRO'JGH COCLTNG SYSTEM  IF Pc.SSIBlE TO  GET  TQ1
C
       IFITWB.LT.TTDGOT0403
       GOT0201
   403  WL2 = Wl
      TWB»L2=TWBAL
      OH22=CH2
      IF(TT.GT.(TETMAX»1.95) IGOT0999
C
      1WT=TT1
      CALl   AIRFLP (TWIfTnB,TWB,ENTU,NniTT,N,GPM,APR,Rl.G,TT2,WL I
r
      IF (TT2.r,r.32.AND.IHAG.NE. DGUTO501
      GCTT9S
C
C  RHEf^INE DIRECTION PF APPROACH TO INTERJECTION OF CURVES
                                              330

-------
c
   503  T01-«TTl-Ti2)»Fr,pM/CrWT
       IF U(H.LT.HTRjtNiKfLPMGf)TriOt>

C   BSACH  INTrrSECTlON  BY  OFCREASING TURBINE TEMPERATURE

       IFUFBE.GT.r». (GOTO 206
       IF ITWB.GT.lTLOhl-FINC-TmO) IGQT0104
C
C   COOLING OJPVE ENDS  MORE THAN 1  DECREMENT BELOW TLOW

   206  TT*TT-F!NC
       TTl=TT-TTnn
       IFITT1.LT.32. IGOTO703
       IF(Twn.GT.TTllGOY0204
C
C   CJ3L ING THROUGH  C"ni IMG SYSTEM  IF POSSIBLE TO GET TC2

       Wl 2 = WL
       TPS2=YPS
       TWBAL2=THBAL
       OH22=CH2
       IF (TT.GT.tTETMAX+1.95) JGOTC999
C
       TWI=TT1
       CALL  AIRFLR(TWI,TDR,TWB,ENTU,MOITT,N,GPM,AFRtRLG»TT2»hLI
\^
       IF(TT2.GT.32.ANO.IFLAG.ME. l)GDT05i)5
       IFR = 1
   505  T02=(T11-TT2 I*FGPM/CONST
       IF(TQ2.LT.wrRJIN(l,LPI)GOT0105
       IF( IFR.EQ.1IGOT0703
       TQ1=TC2
       GOT0206
C
C   INrEPPOI.ATE FOR TOtTETtTWL
C
   105  TQ = HTPJIN(1,LPI
       HTOIF1=(TO-TQ2>/(TC1-702I
       TET=TT + HTP1F1*FINC
       IF(IIII.EO.-5)GOT0405
       TTS=TQ*tTOKO
   405  TWl= ( V>L*HTOI Fl*l kL2-HLI )*NUMTOW
       TPS=TPS + H!D1F1*ITPS2-TPSI
       TWB'-t=TWeAL4-HTDIFl*fTWBAL2-TWBAL)
       QH2=OH2«-HTDIF1*(CH22-OH2I
       IF(IFR.eQ.OIGOTP210
C
C   CSFVIOUS TOWER COCl ING INDICATES TH4T THE OPERATING CHARACTERISTICS
C   CURVE FOR THE COOLING SYSTEM ENDS IN THE SA^E TEMPERATURE INTERVAL
r.   \*. TET)
C   C10L THROUGH COOLING SYSTEM  USING TETi TO FOR CHECK
C
   211  TT1-7ET-TTO
       IF(TT.GT.(TFTMAX + 1.95) IGOT0999
C
       TW1«=TT1
       CALL   MrtFI.P (rKIlTCBfTWBtENTU,NOITTfNtGPM,AFR,RlG|TT2tWLI
C
       IFCm.GT.32.AND.IFLAG.NE.llGCT0210
       GOT0703
   210  CONTINUE
       II IT»1
       RETURN
   304  TT»TT+FINC

C  COOIJNO  CUfV?'  EMI JUST BFLOW TT  AND  DECREMENTING TURBINE TEMPERATURE
r.   'NTLL  MOT iNTts^FCT IT

C  D = TErMINE PRrPFR VALUE OF HTR JIN1 lt I P I
C  DVJB1.E  INTfPPOl AT= FOR TO,TET|TWL
C
   10't  IFIK.CT.l IGnTHl06
      GCiT01O7
      HO>HTpjlN(K-l,LPt
      ir(ini.GT.-5IGOTf"V07
      HO"HQ*JTWB*TTr-TT*FINCI/F!NC*«HTRJIN(Kf LPJ-HOI
     1*1 HTP
      IF (II
  406
                                             331

-------
       TFT»TWO«TTr» (TT-TWO-TTO I *f C/TQ1
       IHH II. EC. -5K.r!7n<,o9
       TTO«TC*TTr)KO
       TPS-TPS/T01»TO
       T7-TT-FINC
       IFIK.CT.l )K*K-l
       GOT0211
 C
 C   REACH INTERSECTION BY  INCREMENTING TURBINE TEMPERATURE
 C
   100  IF{K.EQ.IEML2 I /HTOIF2MTQ-TQ1 I
       OH2=QH22 + ICIH2-QH22)/HTOIF2*(TQ-TQ1)
       TT=TT-FINC
      RETURN
t
C  P?rUF.N WITH MESSAGE
C
  703 T0=-50
      TET=-50.
      TWL«-5O.
      RETURN
C
C  FIND  INTEP.r ECTTON WHEN WET-BULB  TERPEPATURE INCREASES
C
C  P.PACH  INTERSECT ION PY INCREMENTING TURBINE TEMPERATURE
C
      TTD=HTRJIN(Ktl P)*TTDKO
      TTI=TT-TTD
      IFJTT.GT.(rET.MAX*1.95l
      Ctl.l.  A1RF1.R (TWIiTDBfTWBf ENTUtNOITTft*fGPM,AFRf RLG, TT2fuL )
      JF(TT.LT.
      tFIK.EO. IF.NHTR(LP) IGOTD599
      K»K«l
      HO = HTP JTNIK.LPI
      GOTP7070
 10-U  HJ«HT1JtM
      Ml OIF 1 = 0.
                                          332

-------
 2070 TTn»HO*TTDKO
      TTl^TT-TTD
      WL2-HI
      TPS2»7PS
      QM22=QM2
      IFUT.GT.nETMAXtl.95) IGOT0999

      Twt«TTl

      CALL   AlRHRJTWI,TDB,TWB,FNTU,NOm,N,GPM,AFR,RLG,TT2,WLI
c
      T02M1T1-TT2 1*FGPM/CCNS7
      IF (TQ2.GT.HQ IGOTOIQIO
      TQ1=T02
      GO TO 1004
C
C.  INTERPOLATE  FOR TO, TET, TWL

 1010 IFJK.GT.l )C,OTO'il2
      TTO = MT<*JIN6 H»100i l£0t 10
       TWI=I I
       DC  55555 J*lf30t4
       KK *J
       KM=KK
       CALL MP.FLMTWI , TD% TW-!t DNTiJt NOTTT ,Nt r,PMf AFR,RLGtTCWf WL I
       F.N*(V4*D2»<'2./OBrR**2. I *DB*!< "RH02/4. 2*10.** 7
       RI
       IF (LIE. 01 OC TO  44
       IFd.GT.17l GO TP 66
       Fr = FRIFAC(II *(FP IFACU*1)-FRIFACU
       GP TO  5«j
 44    FF = 64./RN
       GP TO  55
 66    FF*O.OOS
 67    LH^=1./SQRT1 FF)
             'f N*S(JRTC=F)
       IF((LHS/RH$ I.G-.0.99)  GO TO 55
       FF=FF-0.0001
       GO  TO  67
 55    AHF = FF*(HT-H)/DRAR*(V4*D2**2./OBAR's*2o)**2./64.348
       ML PI!. E=KK»CHP3wVl**2./?./32.174-AHF*HHJ2
       f FM=V1«60.
       HLP1.Tk(=Ht.PIl F/62.4*12.
       I J=CF^/50.
       IF(IJ.GT014)  GO TO- 65555
       HLPILA*PDWAF (I J)«-(PDWAFCJ+1 I-PDWAF(IJ) »*(CFM/ 50.-IJ )
       !F(HLPTI.A.G?.H.Pl.IW)  GO TO 65556
       x? . =HL.CAVI-HLS»VE
       X2=HLPLT W-HLPIL.*
                    V-X
       RE.«KK=ICFM£iftV-CFMACT)/ICFMSAV-CFMI*4.+(KK-4.J
       GC TO  55556
 65556 HLSAVF=HLPL!W
       HI SAVl = Hl_Ptl A
       CFMSAV=r. FM
 65555 CTNTTN'JE
 55555 CfNTINUE
 55554 CfNTtWE
       KM=REALK
       WriTF(6, 571
 57    FOPMAT('l')
       WRTTF(6f 56)KM
 56    FPPMAT(5Xf'  K =  'tF5.2)
       RETURN
       END
       JUI1ROUTIKIF  AlpCLfiJTWIirDBtTWO.DNTUf NCTTTtNtGPMtAFRfRLGtTCWt WL)
C
£******* ****4:*^**'*4t*#4: * * ***** * * * * * * ** **# * * **.* * ** # ^ *# ** *# # * **
C                                                                                *
C      THIS PROGP.«H CM CULATE*  THC ATR  P! OW PATE THP.U  THE                    *
r       +4-++    f.'i-i.jPt1,  P»JFT  WFT rnrL'KT, '''CWFR  »***                          »
r                              '                                                 *
T*#** *********** v-**4e*# «* *+**#*#**
C
C
C
C
C
C
       01 *EN; JC
       o. r*i. KM
       Ci:^MnH/N'TnR/H,HT, KM^OlinJtcLFV.P-! PDHAFI15I
                 /V4t VI ,hH|H ,PHC1?
                 rT A/
                                                  334
      C(

-------
      COMMON/1" rST/IFL»G
      IFLAC.rO
      BAAR»3. I 9?65?5
      TPBSL»TOP*t>«m J'iee'tl EV»'.59.67
                              . Fv»MT )-',
                                           .
      P'»*2116.22't*<(TDR5»<»i9.67l/rrm';i I** 5.256
      I-THR
                             SA.-i=P5AH )KPS^ (T til-PSA (I I IMT4-! I
      iF (HHCi?,G£.RH01) GO TO  124
      ».RGOM = 12*32ol7^*(-T*(RH01-RH021/PH02l/(l.-KM*RHr2/RH01*(AR/»/PJFAAR
     1 **'..!
                                I* 3600.
                     ) or TO  123
      AFR=1 ./?.*(AFR+AFRn|
      tf=(ABS(AFRC-AFRJ/AFR.I.f. 0.005 ) GO TO 55
      RI.G«f»PM/CONST*lO.*«9/AFR
      CALL  NTUCALtTWI,TDBtT^B|RLG,DNTU,TCW,NOITT,*FR,WLtNI
      INDEX-1
                  1/2.
      GO  TO 44
121   IFLAG=1
55    RETURN
      END
      SUBROUTINE CAPCO «TWBf RANGE ,APPRO|PHf 0, COST)
(,
f* ***************************************

C* DETERMINE THE NATURAL  DRAFT  WATER COOLING TOMER'S COST                       *
C*   -  USE KAPLEY COMPANY'S  CHARTS -                                             *
                                                  *******
C
c
      CPMMON/UTCOST/ UC( A,3r 1 1 1 51 ,ORH(2 )

      IF(RANr,5.LT.15.0  .C!?.  rANGE.GT.*5.i>  .OR.  RH.LT.25.0
      l.OfU TWB.I.T.60.0  .OP.  TV,3.GT.flO.O .OR.  APPRO.LT. 10.0
      2. OR. APPRO.GT.30.0)  GO TO 999

C DETERMINE THS LOWER BOU^JD  OF  RANGE
C
      RA = (RArgGE-5. 1/10.
       !=P.A
      H. >T*1

C  0=TErMINF THE 1 OWTR  BOUND OF RELATIVE HUMIDITY
C
      Jl'25.0
      DO  100 J=lt2
      J2 = Jl»nRH( J)
      IF (RH.LT.J2) GO TO  10
100   J1-J2
^O    JA«J+).

C  D:TER«IMF * HE LCHER  BOUND OF APPROACH
    -         THF LOWHR  RCUND OF W" BIH.B  TEMPERATURE
C
                                                335

-------
       TWMTwn-Vj.il/1>. 0
       L=TW
       IFU.F.Q. 3) JA'I
       IF(K.rg.ll) KA«n
       TFIL.C-O.SI IA-I
 C
       ]F(lir.(T, J,K,I  I. IT. 0.1 .OR. ljr.(!,J, K,l &I.I.T.0.1
      1.0*.  IK ( t f -)i XI-- ,1 I.LT.O.T .OR.  UCU > J,KA, t M.ir.0.1
      2. OR.  IICI !, J' |K,i  I.LT.!?. 1 .04.  (KIT i JA fKtLAI.LT.0.1
      3.015.  UC( '.JiSKI, LI.LT.O.l  .OR.  UC I ! t JA, KA, I A » .LT.O. 1 I  CD TH 999
 C
       IFIUCITA, J,K,l.).LT.O.l .OR.  UC.U4 , J, Kf'_A I.IT.0.1
      l.OR.  U( d«f J|KA(I l.l.T.O.l  .DR.  IJC< ' At J,KAtl Al.l.1.0. 1
      2. PR.  llf ( 1A,,I/>,K, I 1.1 >-.'.>.!  .OP..  l)C( !A, JAtK, I AJ.LT.0.1
      3. OR.  UC.(!Af JAtKAtl I.U'.O.l -0E.  UC ( I A» JA t 
-------
       TKB4L«0.
       00 104 J«l,N
       H«HA
       DO 101 t*\,N
       INDE-0
       KC«0
       DM1=HM1 I-H
       nH*DHl/1.2*r>NTtJ
       GO TO 102
 5566   KC=0
       DM»DH»5./£>.
       IM INOE.E0.5I  GO TC 555
                1-t'M/ftLS
       IFITW2.LT.1.0I  GC TO 5566
       TT=TW2
       PS»PS/.|JTI + { PSA (17+1 I-PSS(IT) |*|TH'-ITI
       HW2=i>.2A*TW2*0.622*PS/JPAT«-PS)*( 1061. a*
       DHH=(TH] +HW?-H-DHI/2.*ONVU
       nHH=(CHH+DH)/2.
       IFIKC.OF.NOITTI GO TO 106
       DH=OHH
       GO TO 102
   (06  TH(I ) =TW(I I-OHH/RIG
       IT=TW(T |
       PS=PSA(!TH( P?A< IT»1 I-PSAUTI I*(TW(I)-!T)
       HW{I 1=0. 2*«rw-II ) +0.6 22* PS/ < PATM-PS )* (1061.8 +0.'»4*TM< I ) I
   101  H=HtDHH
   20   !TWB2=TNB2
       H^ 2 = 0. 24*TW8 2*0. 622* PS/ (PATM-PS I* ( 1061 . 8*0 .
       IF (HA2.GF.H)  00  TO 10
       TVf32=TW32*5.
       HA22 = HA2
       GO TO 2!)
       TWS2=TWH2-4.
       PS=PS»(!TWH2 )*(Pr,AIITWB2*l}-PSA(!TWB2» I * ( Tvm2-ITWB2)
       H/2 = 0.2'»*TW«2+f).622*PS/( PATM-PS I* ( 106! . 8 +0.4't*TWB2 I
       !F(HA2.GE.H)  GO  TO 30
       TWB2=TWB2+1.
       HA22-HA2
       GO TO 40
   30   TW92=TWR2-(HA2-H)/(HA2-HA22)
       THC=0.0
       r
   103
       TWC=VWO/N
       IT=TW8A|,
       TPS=PSA(!TI*-(PSA(IT*ll-PSA(IT))*(TWBAt-ITI
       OH2=0.622»TP3/(PATM-TPSI
       Wl =OH2-WL
       Ml EWf»AFR*CC'NST/10«**9
       RETURN
555    WriTE (6,5561
556    FORMA "USX, ' TOWER  WILL NOT OPERATE  FOR THIS COMBINATION  CF  TEMPERA
       RETURN
       END
      SU9RCUTJN? POWERS  (TEM, OtTTSTAR I

(•»*»*******•*************'"***   *
C » OETFPMtNt THROTTLE ICVfcL  TF TURBINE  FOR  A  GIVEN CONDITION
c»**«***«**»***»***»"**********
      CC1MON/TURBIN/  MR, IHR ,TLCW, FI NC
                            NRI. ,cPLf PLITM
      CC M-ICW/Pl.fcVtt/

      TF(TFC.«.T.TLOWIGrT030
      TT= (TEM-T1
                                              337

-------
   IFIO.n.Qll IGOTC40
   IF IO.lT.Q12)GCm50
   01=C12
   !P = 2
21 (J2 = HO (II •fIP*lH-CHRUT*if !P*1I-HR< IT, TP+ 1)) *( fT-I
   IF(02.G7.Q)GC'TQ1.0
   01 = 02
   IP-IP41
   GOT05C
1') Pt = TP-(02-0)/IQ2-01) + l
   iTSTAr=( i PL-!. )*DPL*PLM:NI/PLMAX
   RETURN
3') TTSTAr'=( (NPL-1. ) *OPL*PLMIN )/PI. ^IAX
   RF7URN
5.) !P = 1
   02=012
   05=01]
   GO TO 1.0
40 DO=«211-C)/(C12-Cn)
   TTST/!R=(PLMTN-DQ*OP1.1/PLWAX
   PNO

   SU8ROUTTNE FDGSEN  (TDB, TWB,TO'-vi $H2tS ENS Tit S ENSI 2, SENS! 31


   See Appendix III .for  listing.
                                       338

-------
  APPENDIX V




FORTRAN LISTING




 COOLING POND
       339

-------
c
C * DETERMINE THE PERFORMANCE (IF COOLING PONOS
C

*

       DIMENSION HRI50, 14),IHR( 14 ), PSA 1250) tFCRR(5 »iAREAL (101
       DIMENSION NYEARI5),FC,J=-1, NPL), 1 = 1, IPMAX)
   110 FORMATI10FB.5)
       READ(5,101) (PSAIIlt 1=1,250)
   101 FORMAT(10F8.5)
       READ(5,102) ( IHR (I ), 1 = 1,NPL)
   102 FORMATU4I3)
       REAO(5,106) (FCR(I ),I = l,ll)
   106 FORMAT 110F8.0)
       READ(5,106) [GPMLODI I),I»1, 10)
       READ(5,107) UOW.FINC
   107 FORMATC2F10.0)
       READ(5,106) (AREALU I,I«1,10)
       REAOC5,504) NNOTSI ,Nr40TS,NOHTSI ,NOWTS,LOCAT I .LCCATF
   504 FORMATI6I4)
       READ(5,502) CCND.CCNl
   502 FORMATC2FIO.O)
       REAO(5,506) (HYEARCI I, 1-1, 5),FC,WC,WW
   506 FORMAT(5I4,AF10.0)
       RE AD 15,106) HEIGHT,EFFICM,UNCOND,UO
       REAO(5,106) (HW( 11,1=1,10)
       READI 5,507) ITWBI,IThBF,ITBO,ITDBF
   507 FORMATI6I4)
       READ(5,108) LP, TTOO.REFSV, TKBREF,PLMAX, UCAPAE
   108 FORMAT(HO,5F10.0)
       READ(5,106) UENER.UOOWM,DAYS,CF.CCC,COO,CWATEO,CBLOWO
       READ(5,507) IPLI,IPLF,MM
       NTW=IITWBF-ITWBI )/ITBO + l
       NTD*(ITOBF-ITWBI)/ITBO*1
       NKN-CIPLF-IPI. I+0.01I/MM*!
       READ(5,509) PATM.TPf'AX
   509 FORMATI4F10.0)
       READI5.505) CA.CM1
   505 FORMAT(4F10.2)
       READ(5,509) TBP
       REAO<5,509> EF,EN,EFI
       REAO<5,eoi) PHO.C,cio,MONTH,wz.osc
   801  FORMAT (3F10.0,110, 2F10.0)
       REAO(5,802) (AMO (I ),I = 1,12)
   802  FORMAT112F5.2)
       RE ADC 5,803) UFCNO,UPUMP,UMA!NT,CHT,CMAINC,ULANO
   803  FORMAT(6F10.0)
       REAOI5.507) IWR ITE, IPUNCH, I TPMAX, I EXTRA, INUC «Lt NEWCON
C
       CONST«7.481/60./62.*10.*»9
       DONST-CONST
       CONST1=0.124683/62.
C
C  CALCULATE  CORRESPONDING  FIXED CHARGE RATE
C
                                         340

-------
       00100K-l,5
       V«NVEARIK)/4.»1.
       1Y-Y

^  100 !=CRRBFt ITBO
       1H1«I IJK-ITWBI )/ ITBD + 1
       ITOBMA»PSA1IJK)/(O.000367*PATM*(1.*(JJK-32.1/157l.lJ+tJK
       IFIITDBMA.GT.ITDBF) ITDBMA«ITOBF
       D02012IIK-IJK, IT06MA, ITBD
       I01-I IfK-ITWBI J/IT80+1.
 2012  SSl-SSl+PERCENt Ihl.IOltLPlI
       S=S*SSl»PL
       SS2=SS1
 2011  SSl*0.
       IFUPLI-EQ.IPIFJ SS2-0.

       TEI*PLMAX*(l.-SS2)»PLMAX»CF*SS2»ITOSTAR*(1.-SS2I»TOST*SS2I*293.067
       TEI-TEI/EFI

C      WRITE(6,610) TWBOtTDBD, TWBlOtTOBlOtPI MAX,CA, CW1, TTDD, P ATM
  610 FORMATUH1///10X, 'DESIGN WET-BULB TEMPERATURE  OF  AIR -«,F5.1,'  F-
     l/10Xi'OESIGN DFY-BULB TEMPERATURE OF AIR ••,F5.l,< F'/lOXt
     2'EXTREME  WET BULB  TEMPERATURE =',F8.3, • DEC. F'/lOX,
     3«EXTREME  DITY BULB  TEMPERATURE .'fF8.3f' OEG. F'/lOXf
     4«POWER  LEVEL »',F6-Ot*  MW'/lOX,
     S'SPECIFIC  HfcAT OF  AIR AT CONSTANT PRESSURE -«,F6.2(« BTU/IB./F'/
     610X.'SPECIFIC  HEAT  OF WATER «',F6.2,« BTU/LB./F'/
                   TERMINAL  TEMP.  DIFFERENCE «',F5.l,'  F'/lOX,


                                       341

-------
      e'ATMOSPHEIlC  PRESSURE  «',F7.2,'  PSIAM
 C
       WRtTC (6,6201  FCtfeC,WW,CCNO,CCNI
   620 FORMATdH t^Xt'UNIT  FULL  COST »• ,F9.6t* »/KW-HR»/10Xf
      I'UNIT SUPPLY  WATER COST  «',F7.4,' M 1000 GAI.'/IOX,
      2'UNIT WASTE WATER  COST »>,F7.4i' t/1000 GAL'/10X,
      3'MAX. TOLERABLE  CONCENTRATION OF PROCESS WATER «'tF5.0,'  PPM'/IOX,
      ^•SUPPLY WATER CONCENTRATION -',F5.0f' PPM')
 C
       WRITE (61630)  TWBPEF, PI.MAX.UCAPAB
   630 FORMATdH ,9X,
      1'CRITICAL WET 8UL8 TEMPERATURE -'tF7.2t' DEC. F'/lOXi
      2'MAXIMUM POWER OUTPUT  *>lFS.2t>  MW'/lOX,
      3'UNIT CAPACITY LOSS  COST  ='fF10.2t' */MWM
 C
       WRITE(6,632)  UPOND,ULAND,UPUMP,UMAINT
   632 FORMATdH t9Xt'UNIT  POND  COST = ',F8.1t' $/ACPE'/10Xt
      1'UNIT ACCESS  LAND  COST = 'fFB.l,' i/ACPE'/lOXf
      2'UNIT PUMP AND PIPE  SYSTEM COST  =1fF7.2tt */GPM'/10Xf
      3'UNIT MAINTENANCE  COST "',F7.2,' J/ACRE-YEAR')
 C
       WRITE(6,631)  UENE«tfUOPHN,OAYS
   631 FORMAT! IH , 9Xt 'R EPLACEMENT ENERGY COST *',F8.4t' »/KW-HR ' /10Xf
      1'REPLACEMENT  ENERGY  COST  DURING  DOWNTIME *',f7.^,' t/KW-HR «/10Xf
      2«DOWNTIME FOR CONSTRUCTION «'tF6.1f' DAYS'J
 C
       WRITE(6t640)  HE IGHTiEFFICW,UNCOND.UQ
   6*0 FORMATdH f9X,'PUMPING HEIGHT OF WATER THROUGH TOWER «'fF8.l,
      2' FEET'/lOX,'PUMPING EFFICIENCY  FOR WATER PUKP »'»F7.3/10X,
      3'UNIT CONDENSER  COST *• , F6 .2 r ' $/SQ. FT.'/IOX,
      ^'OVERALL CONDENSER COEFFICIENT!  U ='fF6.1r'  8TU/HR/FT2/F')
 C
       WRITE(6,662)  ITWBI,ITWBF,ITBOtITDBF
   662 FORMATUH t9Xt ' INITIAL  WET BULB  TEMPERATURE ='fI4f' OEG. F«/10Xt
      I'FINAL WET BUI.8  TEMPERATURE »'fI5f' DEC. F'/10Xf
      2'INCREMENT OF DRY  AND  WET  BULB TEMPERATURE =',14,' DEG.  F'/10Xt
      3'FINAL DRY BUL8  TEMPERATURE ='fI5f' DEG. F'»
 C
       WRITEI6.650)  TLOWfFINCtREFSV
   650 FORMATdH t9X,'LCWEST  TEMP, IN TURBINE CHARAC. CHART ='|F5.1f
      1« OEG. F'/10Xf'TEMP. INCREMENT IN TURBINE CHARAC. MATRIX »',F4.1,
      2' OEG. F'
      3/lOXt'REFERENCE  SPECIFIC  VOLUME  OF AIR «', F7.3t'FT3/LB')
 C
       IT-TWBD
       TSS=PSA(ITJ + (PSA(IT+l)-PSAdT)J*ITW8D-ITI
       HAA=0.24*TWBD+0.622*TSS/(PATM-TSS)*(1061.8*0.44*TWBOI
       001000II=NNOTSIfNNOTS
       GPPL'GPMLODIII)
       0010001W=NOWTSI,NOWTS
       AREA=AREAL ( 1W )*PLM«X
       EGPM»GPML*AREA»43560.
       TS-TSS
       HA-HAA
 C
       WRITE(6,660I  TEI,TBP,SS2
   660 FORMATI1H1,10X,'FUEL CONSUMPTION WITHOUT COOLING SYSTEM  =>',F9.3f
      1-  MH  «TUR. BACK PRE.  =',F5.2f'  IN.HGl'/lOX,
      2'***'tF8.5t'  OF  THE TIME  IS NOT  OPERATED AT FULL LOADING ***•)
 C
 C DETERMINE CAPITAL CCST OF COOLING PONDS
 C
       IIII—5
       TTO-TTOD
 C
       CALL MODELw (Toec.TwBo, IW,NPL,TET,TO,TWL,IIiI,K,TT, IM)
 c
       IF(TET.LT.O)GOT0999
       TTSTAR-1.
       IF(ICAP.EQ.O)GQT0679
 C
       CALL POWERS (TET,TC,TTSTAR)
 C
   679  OQHR-ITO/TTS TAR-TOST AR )/
-------
       THH.TET-TTO
       KW»THW-TQ«CONST/EGPM
       RANGE«THW-TCW
       TTDKO»TTD/RANGE»CONST/EGPM
       RLL'ALOGI(RANGE+TT01/TTD)
       CONCOS-UNCONU*EGPM/CONST/UO*RLL»10.**9
       IF(NEWCON.EO.O)CONCOS«CCO
       PPCOST*UPUMP*AREA*GPML*43560.
       PPCOSO=0.20*PPCOST
 C
 C  DETERMINE DOWNTIME COST, AND REPLACEMENT CAPABILITY LOSS

       DOWNCO=UDOWN*PL*24.*DAYS*1000.
       P"MOP1=EGPM*HE!GHT*62.4/7.481/60./550./EFF1CH*0.7457

 C
 ^     CALL MODELW (TDB10.TWB10,1W.NPL.TET.TQ.TWL,IIII,K,TT,IMJ

       IF(TET.LT.O.IGOT0999
       TTSTAR=l.
       IF(ICAP.EO.OIGOT0681
 C
       CALL POWERS (TET.TQ.TTSTAR)

   681 DQHR=(TQ/TTSTAR-TQSTAR>/
-------
      2 COST»,5X( "TOTAL COST1 ,5Xf • FIXED C HAFGE RATEV26X,
      3'MILLS/KW-HR' , 10X, 'MILLS/Kh-HR" 19Xf' MILLS/KW-MR' I
       005000KK«1|5
       CAPCOl«CAPCOS*FCRP IKK)/S
       TOTOP2-TOTCPE
       TOTCOS»CAPC01+TOTCP2
  5000 WPITE(6,61l>  NYEAP (KK J tC APC011 TOTOP2t TOTCOSt FCPR1KKI
   611 FORMATUH  tl l5tF20.7tF21.7,F20.7tFl9.6l
       GOT01000
   999 HRITE(6,603I  EGPM.TF.T
   603 FORMATIIHO//10X, '**»*«•*»»****«/12X, 'TOTAL WATER FLOW RATE  THROUGH
      1THESE COOLING  PONDS = ',F11.0,'  GPM'
      2  /12XI1TUPBINE  TEMPERATURE  - ',F10.4/12X,
      3«PCNOS SIZE  IS TOO LARGE'J
  1001 TOTCOS=10.**12
  1000 CONTINUE
  6100 CONTINUE
       STOP
       END
       SUBROUTINE OPECOS  1 1 Wf TO TOPE)
C
C *
C

PROGRAM TO DETERMINE TOTAL ANNUAL OPERATING CCST


*

       DIMENSION HR 150,14 1, IHM 14 ) , PSA < 2 50) , SI < 15 > , 52 < 1 5) , S3U 5 I f NYEAR < 5 >
       COMCON/INPU/ PERCEN(12tl5f 2)tHW(10l
       COMMON/TURBIN/ HR , tHR, TLOW, F INC
       COKKON/NCALA/ PSA, TPS, TS , T WBAL, QH1,QH2, HA
       COMMON/WFR/ GPfLtEGP^, PUMOFl
       COMMON/TUR8/ POWER ,TBPfTET, TTOf TTDKOfTTDO
       COMMON/CONST A/ CCNST1, CONST, CONST
       COKMON/TEMP/ ITWBI , ITWBF , I T8D, ITDBF
       COMKON/ECONO/ NYEAR, FCfWC,WW,OR,CCNOtCCNl, ANPOWE,HEIGHTf EFFICW
       COMMCN/POHERC/ I PL! , IPLF ,M, FL.LP
       COMMON/ATMOS/ PATM
       COMMON /CLS/ S,CWATEC,CBLOWC,CfAINO
       COMMON/PAREA/ A^EA
       COM^ON/WITREF/ UR IT E, IPUNCH,«!.EFSV,TWBREF
       COMMON/PLEVEL/ PLMAX,UCAPA8,CAPCAP,UENER,ENEPLS, TEI,TOTOP
       COMMON/FPLU/ FPLMAX
       COMMON/TBPR/ ITPf»AX, TETMAX, ICAP
       COMMON/TBPP.E/ IP*AX,NPL,DPLt PLMIN
       COMMON/QSTA9/ TOSTAP
       COHMCN/MAINTE/ UPAINT
       COMMON/CAPFAC/ CF.EFI
 C
 C  OPERATION DUE TO COCLING PONDS
 C
       IF IHWdWI.LT.0.01  IGOT01002
 C
       IF« IWRITE.EO.l (WRITE (6, 899)
 C
       IM»0
       TOTOPE-0.
       TOTBLD=0.
       TOTWL-0.
       TOTEI«0.
       TOTFUE-0.
       TOTWAT«0.
       TOTWAW-0.
       TOTMAN=0.
       TOTLCS=0.
       TOTPRO-0.
       CAPLOS-0
       CAPPRO«0.
       ENERLS-0.
       FAPLS'O.
C
       PLC"PLMAX*CF*PUMPP I/ 1000.
       D01000LP*IPLI,IPLF,M
       LP1»(LP-IPLI J/M+1
C
       TTTSAV-0.
       KKSAVE'O
       JJJJ-0
G
      D0901IIJ-ITWBI ,ITHBF,ITBD
       TWB«IIJ
                                         344

-------
       TS-PSAUIJ)
       IU1-(I1J-ITWBI)/ITBO«1
       KK.KKSAVE
       TTT-TTfSAV
       D0910IJ-IIJ, ITDBHA.ITBD
       TDBMJ
       ID1-I IJ-ITWBI J/[TBO*1
 c
 c
      OHl'WLl
      FAP»PUNQP1/1000.
      NP«NPL
      IFCLP.NE.IPLI)  NP«(CF-O.VM*10.

      CALL MODELW  (TDB, TWB,IW,NP,TET, TO, TWL, JJ JJ, KK.TTT, IM»

      I2-I2+1
      IF (TEI.LT.O) GOT0200
      TTSTAR=1.
      IFILP.NE.IPL t I  TTSTAR=CF
      IF( ICAP.EQ.OJGOT09666
C
      CALL POWERS  JTET.TCtTTSTAP)

      CAFPRO=CAPPPC+PERCEN(IW1, IDltLPlI
 9566 OOHR«(TO/TTSTAR-TOSTAR|/(PLHAX*3.6/1055.04-TC/TTSTAR*TOSTARI
      FPL«PLMAX*TT STAR/ ( l.*OQHR )
      PL-FPL
      IFILP.EO.IPLI 1GOT096680
      IF( ICAP.EQ.O 1GOTC96681
      FPLl=CF*PLMAX-FPL
      PL-FPL                   '
      FAP-PUMOPl/1000.
      GOT096682
96681 TE1ST-TET
      TQST»TQ
      FPLST«FPL
      TWLST=TWL
      NP-NP+1
      KKST-KK
      TTtST«TTT
C

C
C
96683
96684
96680
96682
96685
      CALL MODELW  ITDB.TWBf rW,NP,TETlt TO It TWt I, J J J J, KKST, TTTST.I MJ

      TTSTAR»CF+0. 1
      IF(ICAP.EO.OJGOTC96683

      CALL POWERS  (TETl.TQl,TTSTAR)

      OQHR»(T01/TTSTAR-TCSTAR)/(FIMAX*3.6/1055.0*-TQ1/TTSTAR+TCSTAR)
      FPL"PLMAX*TTSTA1/( l.+DOHR}

      TET"TETST*(TETl-TETST)/(FPt-FPLSTI*(FLC-FPtSTI
      IF(TET.LT.(TETMAX*0.05)1GOT0966B*
      FPL1=CF*PLMAX-FPI
      TQ-TQ1
      TET-TETMAX
      TWL-TWL1
      PL»FPL
      FAP
-------
       TOTBLD«TOTBLO*BLDOWN*PERCENII WitID1,LPl)*60.*24.»365./326046
       TOTWL-TOTWL+TWL*PERCEN< IHl , IDltLPl )*60.*24 . »365./326046
       Ell-EI/1000.
       TOTEI-TOTEI»EI1*PERCEN
       TOTMAN=TOTMAN+AMANT1
       FUECIS=FUECOS*PERCEN(IWltIDl,LPll
       WATCOS=WATCOS*PERCEN(IWl,IDl.LPl)
       WAWACO*WAWACO*PERCEN(IMl.IDl.LPl)
       OPCOS*(FUEClS+WATCOS+WAt IM
   702 FORMAT!180)                               ^
  9233 CONTINUE
       GO TO 901
   902 IFUWRITE.LT.1)GOT0910
       WRITE(6,601) PLtTWB
   601 FORMAT(lHOt//6X, «PO»(ER ='»F5.0,'  MM',10X,«TWO =',rs.3,' DEG. F* I
       HRITE(6i333)TET,HOTWTTtCOLOWTtPtTO
 333    FORMAT(/6Xt'TURB.TEMP. » •,F10.4,IX,•DEG.F . ',
      ISXi'HOT  WATER TEMP. = •,F10.4,IX,"OEG.F.•,
      25Xt'COLD WATER TEMP. = •,F10.4,1X,'OEG.F.• ,
      3//.6X,'PRESSURE = •,F8.5,IX,•IN.HG.•,
      «X,«HEAT REJECTION = • , F8. 5, IX, «BTU*10**9« ,/ I
       HRITE(6,602).
   602 FORHATUHO,IX,«TDB«,3X,'HATER EVA.•,3X,'SLOWDOWN*,3X
      It'PROBABILITY'tSX.'FUEL COST«,3Xt
      2'HATER COST",3Xt'WASTE ViATER COST't3X, • SUBS ENERGY LOSS',3X,
      3'OPERATING COST'/3X,«F',
      47X,«GPH',9X,'GPM',22X,'J/YEAR•,6X,
      5'i/YEAR't10X,'$/YEAR't!3X,'$/YEAR'tl2X,'$/YEAR'/)
       WRITE(6,607IIJ ,TWU,BLOCWM,PERCEN(I Hi,IDl,LP11,FUECIS,WATCOS,WAWAC
      10,ANUCAP,DPCOS,FPL1
   607 FORMAT!1H ,13,F15.5.F11.4,F13.6.F13.0,F12.1,F16.1,F20.3,F18.1,
      1F10.3)
   910 CONTINUE
       IF(IWRITE.LT.1)GOT0901
       WRITE«6,899)
   899 FORMAT(///1X,130«'*•)//)
   901  CONTINUE
  1000 CONTINUE
       FUELEX=TOTEI-TEI
       TOTFU1»FUELEX*FC*1000.*8760.
       TOTOPF=TOTOPE-CBLOWO-CMAINO
       TOTOP»TOTOP£-TEI*FC*100C.*8760.
       TOTEI1*TOTEI/TOTPRO
       TOTWL1-TOTWL/«TQSTAR* 1055.04/3.6)
       FUELE1=FUELEX/PLMAX
       FPLMA1=FPLMAX/PLMAX
       ENERLl=ENERLS/(PLMAX*8760.I
       FAPLS1=FAPLS/(PLMAX*8760.)
C
      WRITE*6,6051  TOTBLO.TOTWL,TOTWL11TOTE ItTOTEI1tFUELEX.FUELEl,
      IFPLMAXtFPLMAl,ENERLStENERLl.FAPLS.FApLSI
  605 FORMATUH  ,/lOX,'TOTAL  ANNUAL  BLOWOOWN »«,F15.0t' ACRE-FT/YEAR'/
      110X,'TOTAL ANNUAL  WATER EVAP.  »',F12.0,'  ACRE-FT/YEAR'
     2i5Xt M*f  FlO.St*  )'/10X,
     3'TOTAL ENERGY RATE  IN  »',F12.3,'  MW'/lOX,
     4'AVERAGE   ENERGY  RATE  IN DURING ACTUAL POWER PRODUCTION ••
     5,F10.3,'  MW'//8X,'*»* CAPABILITY  LOSSES ***'/10X,
     6'EXCESS  FUEL  CONSUMPTION  »I,F9.3,'  MW't5Xt'(•»F9.6f• )«/10Xf
                                          346

-------
                                                            I./IOX.
 606  FORMAT! IHO/liX,
     II*** TOTAL ANNUAL COSTS ***'/10X,
                cAt FUEL C°ST -••«*•»:.•  t/YEAR',5X,'OR'/10X,
               UEL C°ST = ''F3<:.0,'  WYEAR'/lOX,
     s  n    ANNUAL REPLACEMENT ENERGY LOSS  =',F10.C,'  t/YEAR'/10X,
     5 TOTAL ANNUAL WATER COST ...F23.0,'  S/YEAR'/lOX,
     S IS™  ANNUAL WASTE WAfER COST •••Flf.O,'  I/YEAR'/ICX,
     7'TOTAL ANNUAL MAINTA1NANCE COST = ',F16.0,'  t/YEAR'/10X,
     ! oA£E™ WATER COST WITH OPEN-CYCLE  =',F13.0,'  t/YEAR'/lOX.
     9 BLOW DOWN TREATMENT COST WITH OPEN-CYCLE  »',F7.0,«  t/YEAR«/10X,
     1'MAINTENANCE COST WITH OPEN-CYCLE -'.Fl'V.O,'  WYEAR'MOX,
     Z -------------------------- • / IOX ,
     3'TOTAL ANNUAL OPERATING COST  «',F19.0,' J/YEAR'/lOX,
     4'EXTRA ANNUAL OPERATION COST  ='tF19.0,' t/YEAR')
v
      TOTFUE=TOTFUE/S
      TOTWAT=TOTWAT/S
      TOTWAW=TOTWAW/S
      TOTMAN=TOTMAN/S
      ANUCAP=ANUCAP/S
      TOTOP=TOTOP/S
      TOTOPE=TOTOPE/S
      WRITE (6, 621) TOTFUE,TOTHAT,TOTKAW,TOTMAN,ANUCAP,TOTCPE,TOTOP
 621  FORMAT! 1H0.7X, •*** AVERAGE OPERATING COSTS  --- IN  MILLS/KW-HR
     1/10X, 'AVERAGE FUEL COST =',F22.6,1  MI LLS/KW-HR« /IOX,
     1'AVERAGE WATER COST =',F21.6,' MI LLS/KW-HR' / IOX,
     2'AVERAGE WASTE WATER COST =',F15.6,' MI LLS/KW-HR' /KX,
     VAVERAGE MAINTAINANCE COST =',F1A.6,«  MI LL S/KW-HR ' / IOX,
     5'AVERAGE CAPACITY LOSS =',F18.6,' MI LLS/KW/HR' /IOX,
     6«AVERAGE TOTAL OPERATING COST =',F11.6»'  MILLS/KW-HR' /IOX,
     7»AVERAGE EXTRA OPERATING COST =',F11.6,'  MILLS/KW-HR')
      RETURN
 1002  WRITE(6,623)
 623  FORMAT! 1HO/10X, 'WET COOLING TOWER IS NOT  SUFFICIENT TO OPERATE1)
      TOTOPE=10.**12
      RETURN
      'END
      SUBROUTINE  MODELW (TDB,THB,IW,LP,TET,TQ,TWL,1111,K,TT,IM)
                                                                     **»•
C
C
C
C
C
C
C
C

*
*
*
*
*
*


THIS SUBROUTINE CALCULATES THE MODELING RELATIONSHIPS FOR POWER
PLANT AND COOLING TOWER . GIVEN WET AND DRY BULB
TEMPERATURES, AND WET TCHER SIZE, THE RESULTS ARE TURBINE
EXHAUST T£MPERATURE, AND HEAT REJECTION.
*********************************


*
*
*
*
*

      DIMENSION  HTRJINI50.14) ,IENHTR(U) ,PSA(250)
      COMMON/TURBIN/HTRJIN,IENHTR,TLOW,FINC
      COMMON/NCALA/ PSA,TPS,TS,TWSAL.QH1,QH2,HA
      COMMON/PAREA/ AREA
      COMMON/TURB/ BL 1,BL2,BL3,TTD,TTDKO,TTDO
      COMMON/TBPR/ ITPMAX,TETVAX,ICAP
      COMMON/WFR/ GPML,FGPM,PLMOP1
      COMMON/CONSTA/  CONST1.DCNST,CONST

C   IF  TWB  IS  HIGH ENOUGH,  THEN COOLING CANNOT TAKE PLACE AT ALL UNTIL
C   TURBINE  CONDENSER TEMPERATURE  15 "IGHER. THUS, WILL SKIP TO
C   HIGHER  TURBINE TEMPERATURE.

r   IF  TWR  IS  LOW ENOUGH,  COCLING WATER FREEZES, WHICH
r   IS  NEVER DESIRED.  THUS WHENEVER COOLING WATER WOULD HAVE BEEN
C   COOLED  BELOW FREEZING ANYKHERE IN THE CYCLE, NO COOLING IS
C   PERFORMED  (IMPLYING  ALTERNATE  SYSTEM USED IN PRACTICE).

C  ASSIGN MODEL  PARAMETERS  FOR TOWER SECTION
C
      ICAP-0.
      IM=2
      IFR=0
      IFRE»-1
      IF(II1I.GT.0.5)GOTOIOOO
      WL=0.
      TPS=0.
      TWBAL'O.
                                         347

-------
       QH2-0.
       IF( II II.EO.-5)GOT0991
       TTDO-HTRJ1NIl,LP)*TTDKO
       GOT0992
   991  TTOO-TTD
 C
 C  ASSIGN  INITIAL  TRIAL TURBINE TEMPERATURE
 C
   992  K*0
    99  IFREMFRE+1
   201  K«K+1
       IFCK.GT.IENHTR(LP))GOT0999
       TT«TLOW+(K-1I*FINC
       IF)II11.EO.-51GOT0404
       TTD=HTRJIN(K,LP)*TTDKO
   404  TT1=TT-TTD
 C
 C  COOL THROUGH COOLING SYSTEM IF POSSIBLE TO GET TQ1
 C
       IFTHBAL+HTDIF1*(TWBAL2-TWBAL)
       OH2=QH2*HT01Fl*(QH22-OH2)
       IF( IFR.EQ.01GOT0210
C   (PREVIOUS TOWER COOLING  INDICATES THAT  THE OPERATING  CHARACTERISTICS
C   CURVE FOR  THE COOLING  SYSTEM  ENDS IN THE  SAME TEMPERATURE INTERVAL
C   AS TET)
C  COOL THROUGH COOLING  SYSTEf USING TET,  TO  FOR CHECK
                                          348

-------
 c
   211 TT1-TET-TTD
 ^     lF(TT.GT.(TETMAXn.95)IGOT09<>9

 c     CALL COOL 
       GOT0408
   407 HQ=(HQ+(TWB-TT*FINC)/FINC*(HTRJIN(K,LPI-HOM/(1.-TTOKO/FINC
      1*(HTRJIN(K,LP)-HQI)
   408 IF(IIII.EO.-5JGOT0406
       TTO=HQ*TTOKO
   406 TQ=TQ1*HQ/(TQH-HQ-HTRJIN(K,LP))
       TET=TWB+TTO*(TT-TWB-TTO)*TQ/TQ1
       1F(IIII.EQ.-5)GOT0409
       TTD=TO*TTDKO
   409 TWL=WL/T01*TQ
       TPS=TPS/TQ1*TQ
       THBAL=TWBAL/T01*TQ
       QH2=QH2/TQ1*TQ
       TT=TT-FINC
       IF(K.GT.1IK=K-1
       GOT0211
 C
 C  REACH INTERSECTION BY INCREMENTING TURBINE TEMPERATURE
 C
   100 IFIK.EO.IENHTR(LP)JGOT0999
   108 TT-TT+FINC
       K=K+1
       IF(IIII.EQ.-B)GOT0410
       TTD=HTRJIN(K,LP)*TTDKO
   410 TT1=TT-TTD
 C
 C  COOL  THROUGH SYSTEM TO GET TQ2
 C
       WL2=WL
       TPS2=TPS
       TWBAL2=TWBAL
       OH22=QH2
       IF(TT.GT.(TETMAX+1.95I)GOT0999
 C
       CALL COOL (TT1,FGPM,AREA,TDB,TWB,TT2|WL)
 C
       T02=(TT1-TT2)*FGPM/CONST
       IF(T02.GT.HTRJIN(KtLP))GOTO 101
       IF(K.EQ.IENHTR(LPIIGOT0999
       TQ1=TQ2
       GOT0108

 C  INTERPOLATE FOR  TO,  TETt  TWL

   101  HTDIFl-HTRJINCK.LP)-HTRJIN(K-liLP)
       HTDIF2=TQ2-TQ1
       TQ=(HTRJIN«K,LPI*HTOIF2-T02*HTDIF1)/(HTDIF2-HTOIF1I
       TET=TT_(T02-TO)/HTDIF2*FINC
       IF(IIII.EO.-51GOTQ411
       TTD=TQ*TTOKO
  411  TWL= WL2+(WL-HL2)/HTDIF2*(TQ-T01)
       TPS=TPS2+
-------
c
c
c
c
c
c
c
   RETURN WITH MESSAGE

  703 TQ«-50
      TET«-50.
      TWL—50.
      IIII-O
      IM—50
      RETURN

   FIND INTERSECTION WHEN WET-BULB TERPERATURE INCREASES

   REACH INTERSECTION BY INCREMENTING TURBINE TEMPERATURE

 1000 TTO=HTRJIN(K,LP)*TTDKO
      TTUTT-TTD
      IF«TT.GT.(TETMAX+1.95))GOT0999
:
      CALL COOL ITT1,FGPM,AREA,TOB,TWB,TT2,WLI
C
      TOl=tm-TT2l*FGPM/CONST
 1004 TT=TT+FINC
      IF
      GOT02070
 1001 HQ=HTRJIN{1,LP)
      MTDIF1»0.
 2070 TTO=HQ*TTDKO
      TT1=TT-TTD
      HL2-ML
      TPS2=TPS
      TWBAL2=TWBAL
      QH22=QH2
      IF(TT.GT.(TETMAX+l.95))GOT0999

      CALL COOL (TT1,FGPM,AREA,TDB,TWB,TT2,WL)

      TQ2=
-------
      CDMMON/CPONn?/  RHO.C
      COMMON/ATMOS/ PAIM
      COMMON/NCALA/ PSA.TPS.TSK.TKBAL,QH1,gH2,HA

C  * * * *  COOLING POND  NO.1  *  *  * *
C  DEFINITION OF  TERMS
C  A*POND AREA  FT**2  t1ACRE=43560 FT**2I
C  RHO=DENITY OF  WATER
C  C»SPECIFIC HEAT OF WATER
C  OELTC=TEMPERATURE  DIFFERENCE ACROSS CONDENSER    TIN-TOUT
C  H=HATER  FLOW RATE    FT**3/DAY
C  HREJ-HEAT REJECTION  RATE  AT  THE  CONDENSER  BTU/DAY   PER ACRE
C  X-CUMMY  SURFACE TEMP.
C  FX-DUMMY RESISUAL  OF HEAT BALANCE EQ.

C  WATER DATA FROM P.439  J.P.HOLMAN
C     *     *     *      *
C        BISECTION METHOD
C
C      CALCULATE  SURFACE  TEMPERATURE
C           COLD MATER TEMPERATURE
C
C  CONVERT  "ACRE1 TO  'Ff**2<
      A»A*43560.
C  CONVERT  'GPH«  TO  'FT**3/DAY«
      W=W*192.4992
C
      X(l)=32.0
      X(2I=150.
      XBAR»IX(1)+X(2))/2.0
      CALL  M1X(X(1),RES,A,TA,W,TWB,THOT,WLOSS)
      FX(1)=RES
      CALL  MIX(X(2)fRESiA,TA,y.,TWB,THOT,WLOSS)
      FX(2)-RES
C  TEST  TO  BE  SURE  THERE  IS XERO  BWTWEEN  X(1)£X(2)
      PROO=FX(1)*FX(2)
      IF(PROD)  21,22,22
22    CONTINUE
C    FLAG THAT  PROO  IS POSITIVE
      GO TO 10
21    CONTINUE
C
C  NBI=NO.  OF  BISECTIONS TO SEARCH  FOR  SURFACE  TEMP.
      NBI-15
      DO 23 KK«1,NBI
      XBARMXI 1)+X(2) 1/2.0
      CALL  MIX
-------
 C   QAN-OA-QAR
 C   AMRMI-AVE. MONTHLY RFLECTION
 C   OSC'CLEAR SKY SOLAR RAO.  (FROM  1001  CURVE  RCS P.  l-14»
 C   MONTH*INDEX OF MONTH UF YEAR
 C   LINEAR APPROXIMATION (P.1-21 RCS)
 C
 C  CONVERT 'PSIA* TO  «MMHG'
       P»PATM*51.719
       QAN=800.+28.*TA
       QS-OSC*(1.0-.65*CLD**2)
       QSR=AMR(MONTH)*QS
       OR*QAN*QS-QSR
 C
 C   OW=BACK RAO. TERM-LARGEST SINGLE ITEM  IN ENERGY BUDGET
 C   TS=WATER SURFACE  TEMPERATIRE DEGREES F
 C   A GOOD LINEAR APPROXIMATICN (P. 1-24 RtSI
       QW»1600.*23.*TS
 C   THE EXACT EXPRESSION
       RAN=TS*460.
       QW».41E-7*RAN*RAN*RAN*RAN
 C
 C  OEVAP«EVAPORATION  HEAT FLOh/UNIT AREA
 C
 C  H2-WIND SPEED (MPH) AT 2 METERS
 C   P=ATMOSPHERIC PRESSURE (MMHG)
 C  EAcAIR VAPOR PRESSURE IMMHG)
 C  TS'WATER SURFACE TEMPERATURE (DEGREES F)
 C  ES*SATURATION VAPOR PRESSURE AT TS
 C
 C
 C  CALCULATE THE  SAT. VAPOR PRESSURE OF AIR MUST CVER  THE  POND SURFACE
 C  I.E. THE AIR TEMPERATURE IS EQUAL TH  THE HATER SURFACE TEMP.
       ITS=TS
       T1*ITS
       T2=ITS+1
 C  CF IS CONVERSION FACTOR (PSI TO MMHG)
       CF-51.6144
 C  USE LINEAR INTERPOLATION TO APPROX ES FOR NON-INTERBER VALUES OF TS
       ES»PSAUTS) + (PSA(ITS+1)-PSA(ITS))*
-------
C  CONDUCTION (SENSIBLE)  HEAT  LOSS.
C  USUALLY SMALL COMAARED TO QEVAP
C  REF.(P.l-42 KtS) BEST  METHCO AVAILABLE
C  R-80HEN RATIO
C  C IS CONSTANT (.255 MMHO/DEG. Fl
      R».255*ABS(ITS-TAI/UELTE)
      QC«QEC*R
C   *      *      *     *
C
c    *    *    *
C C  H=HEAT LOAD f)N POND FROM PLANT 8TU/DAY
C  HP/UHEAT LOAD ON POND FROM PLANT BTU/DAY-FT**2
C
      H»RHO*C*W*(THOT-TS)
      HPA=H/A
C     *     *     *     *
C             HEAT BALANCE   MIXED POND
C
C  RES=RESIDUAL OF HAEAT BALANCE EQUATION
C  RES*0  INDICATES THAT THE VALUE OF TS IS CORRECT
      RES=HPA+QR-(QW+OEVAP+QC)
C
      RETURN
      END
       SUBROUTINE  POWERS  (TEM,Q,TTSTAR)


      See Appendix  III  for listing.
                                           353

-------
  APPENDIX VI





FORTRAN LISTING





  SPRAY CANAL
      354

-------
c

c



       REAL NEHCON.LINCCS, LENGTH, KM
       DIMENSION HRt50,U),IHR(14)fPSA(250),PAPCOS(20),
      lAMANT(3,2),FCR^(5),NYEAR(5»,FCR(n»     t-us"o'>
       COMMON/DENS IT/  DAlft(250>
       COMMON/TURBIN/  HR,IHR,TLC!W,FINC
       COMMON/CONST A/  CONST 1, DONS T .CONST
       COMMON/TURB/ POWER, TTOD, TET.TTO.TTDKO, TTOQ
       COMMON/NCALA/ PSA.TPS, TS.TV.8AI ,CH1,OH2,HA
       COMMON/IMPU/ P£RCEN(12,15,2)
       COPMCN/TEMP/ ItWei.ITWSF.ITBD, 1TDBF
       COMMON/ECONO/ NYEAR,FC,WC,UW,or>,,CCNO,CCNl,ANFOWE,HEIGHT,EFFICW
       COPMCN/POWERC/  IPl I, IP|.F,MI»,PL,LP
       COHMCN/LOSS/S,CWATEO,Ct)LGWC,CMAINO
       COMMON/ATMOS/ PATM
       COMPCN/MAINTA/  AMANT.CF, EFI
       COMMON/WITPEF/  I h7 ITE, I PUNCH.REFS V, AFRL .THBREF
       COMMON/PLEVEL/  PLMAX,UCAPAB,CAPCAP,U£NER,ENERLS, TEI, TOTOP
       COHHON/TBPP/ ITPf«AX,TETMAX,ICAP
       COMMON/TBPFE/ IPt'AX, NPL.OPL, PtMIN, POP.TIO
       COfMCN/TEMPE/TWBC.TDBD
       COMMON/RENE W/TQS TAR
       COMMON/FPL U/FPLMAX
       COt'MCN/SPRAY/PtMK.KfWINOSPtFF.TFILM
       COMMON/SPROIS/F(6,3),ROWOIS
       COMMON/PItlC/GPM
 C
 C   DRY-BULB AND WET-BULB TEMPERATURE  INTERVALt 1T60. MUST BE GREATER THAN 1
 C
       RE AD (5, 5555) ( IF < I , J ) , 1 = 1, 6) , J*l, 3 )
 5555   FORMAT16F5.2)
       READ(5,109> IPMAX,N'PL,OPL,PLMIN
   109 FORMAT12tlO.2F10.OI
       RE AD ( 5, 1 10 ) I ( HR ( I , J ) , J= 1 , NPL ) , 1= I , I PMAX)
   110 FORMATUOF8.5)
       READ15.101) JPSAII ), 1 = 1,250)
   101 FORMATI10F8.5I
       READI5.101) (OAIRI I ),[-!, 250)
       READ15.102) ( IHR< I ), I=1,NPL>
   102 FORM AT II 41 3)
       READI5.106) (FCRd ), 1=1, 11)
       READ15.106) IPAPCOS(I), 1 = 1,20)
   106 FORMAT C1CF8. 01
       REAC(5, 107) TLOW,FINC
   107 FOFMATC2F10.0)
       READ(5,106) UTCOST
       READ(5,502J CCNO.CCN1
   502 FORMATI2F10.0)
       READ(5,506) (rjYEARd), I" 1, 5) ,FC,WC ,WW
   506 FORMAT15I4.4F10.0)
       REAO(5,507) I TWBI , ITWBF, ITBO, ITDBF
   507 FORMAT <6 14 >
       RE AD (5, 108) TWBD,TCBD,LP,TTDD,ReFSV,TWBREF, PLMAX.UCAPAB
   108 FORMAT) 2F10. 0, I 1C, 5F 10.0)
       REAO(5, 106) UE,vjeP.,ULANO,UDOHN,OAYS,CF,CCO,COC,CWATEO,CBLCWO
       READ(5,507) IPi.I,IPLF,HM
       NTW«(ITHflF-ITWBI )/ITBO*l
       NTD«( I TDBF-ITV.fi I )/lTBD*l
       NKK'C IPLF-IPLI )/MH*l
       REAOi5,50B) I ( ( PERCFNI I, J, KJ, J=1,NTD), I-l.NTV.) ,K«1, NKK I
   508 FORMAT(10F8.6 )
       REAO(5,509) PATM.TPMAX
   509 FORMAT(JFIO.O)
       READ«5,505) CA.CV.1
   505 FORHATC4F10.2)
       READ(5,5C9)  TBP, TWBIO.TDBIO

       ""SI''."?! .WS.TF!, PUNCH, ITPMAX,, EXTRA, .NUCAL
       READ«5,106)  EFFICM.UNCOND,UO,EFFIC*,HEICHT
       READ(5,106)CHT,CMAINO
       READ(5,12U>NEWCCN
 1212   FORMAT(FS.O)
       READ(5,106) RP
             T^ 1/60 ./62 .*io.**«J
      DONST«CONST
      CONST1-0. 12*683/62.

I  CALCULATE CORRESPONDING FIXED  CHARGE  RATE


                                            355

-------
       D0100K-1,5
       NEAR-NYEARCK)
       V"NYEAR(K)/4.+l.
       IV»V
 100    FCRRtKI-FCRI IV )»«FCR IIY>l)-FCR C I VI 1*1 Y-I V)
 C
       IF< I NUCAL.EO. OIGQT0300
       PARAME»< l.-EN)»EF/(l.-EF)/EN
       004001-1, IPMAX
       00400J»1(NP1.
   400  HRU,J)»HR(If J)*PAPAME
 C
   300  SSl'O.
       S«0.
       D02011LP = IPI.lt IPLF.PM
       LPl'ILP-IPLI )^M«1
       PL = PLMAX
       IFILP.NE.tPLI) Pl = PLMAX*CF
       D02012lJK=tTW8l( ITV.EF, ITBD
       IW1«IIJK-ITWBI)/ITBO*1
       1TOBMA=PSA{ JJK)/I0.000367*PATM*J1.*< IJK-32. >/1571. I J + IJK
       IFIITDBMA.GT.ITOBF) [TOBMA=ITOBF
       002012IIK=IJK,ITDBMAf JTBD
       ID1«I ! IK-ITWBI >/IT80»l.
 2012  SS1«SS1 + PERCEN( 1^1,101, LP1 )
       S«S+SS1*PL
       SS2«SS1
 2011  SSl'O.
       IF(IPLI.EO.IPLF) SS2=0.
       S=S*8760.
 C
 C  FIND  FUEL CONSUMPTION WITH OPEN CYCLE COOLING  SYSTEM
 C
       TBP1»TBP*62. 4*13. 6/1728.
       NP«(CF-0.49J*10.
       LP*NPL
       IT-TLOW
       IFtTBPl.GT.PSAt IT) JGOT0710
       TQSTAR'HRdf LP)
       TOSTl«HRIlfNP)
       TQST2=HR(lfNP+l>
       GOT0716
   710  IT-IT+5
       IFITBPl.GT.PSA(IT) JGOT0710
   714  IT=IT-1
       IFtTBPl.LT.PSA(IT) 1GOT0714
       TTEMP=IT*(TBP1-PSA(IT) I / ( PSA{ IT+U-PSAC ITJ I
       TTEMP»CTTEMP-TLOh)/2.+l
       IT-TTEMP
       TQSTAR=HR(ITfLP>*(HRUT + l,LP)-HRUTflP> )*(TTEMP-ITI
       TQST1»HR( tT.NP ) + ( HP ( IT»1,NP)-HR ( IT ,NP» * (TTEI'P-I T»
       TQST2=HRtIT,NP*l) + (HP< IT+l.NP + 1 )-HR( IT,NP*1) )*(TTEMP-IT)
   716  DOHa«(TQSTl/CF-T5STAS)/(PlA'AX*3.6/1055.04-TOSTl/CF*TOSTAR>
       FPL1 = PLMAX*CF/ ( 1 , + COHP. )
       DOHR-CTQST2/(CF»0.1)-TQSTARJ/(PLMAX*3.6/105S.04-TOST2/(CF+0.1)
     l+TQSTAR)
       FP12=PLM«X*(CF+0.1 )/(l.*DOHRI
       TQST»TOST1+(TQST2-TOST1I*(PL«AX*CF-FPL1)/(FPL2-FPL1)
       TEI*PLMAX*(l.-SS2>+PLMAX*CF*SS2+«TQSTAR»ll.-SS2)+fQST*SS2»*293. 067
       TEI-TEI/EFI
       eGPM«TQSTAR*CONST/RP
       GPf-EGPM
C
C  DETERMINE MAXIMUM ALLOWABLE TURBINE  TEMPERATURE
C
       TETMAX«1COO.
       IF(ITPMAX.EQ.O>GCTn717
       TBF2»TPMAX*62.4* 13. 6/1728.
  718  IT«IT+5
       IF(TBP2.GT.PSA( IT) JGOT0718
  719  IT»IT-1
       IF(TBP2.LT.PSA(IT))GOTC719
      TETMAX«IT*«TBP2-PSA(IT))/(PSA(IT + H-PSA( IT I )
  717 WRlTE(6f610) TW80t TDBOt TWB 10t!>LMAX,CA,CHlt TTDD.PATM
  610 FORMAT(lHl///10Xt'CeSlGN  WET-BULB TEMPERATURE CF AIR  -SFS-lt* F«
     1/10X, 'DESIGN DRY-BUB  TEMPEPATUPE CF AIR c«,F5.1,' F«/10Xt
     2'EXTREME WET BULB  TEMPERATURE  ='fF8.5f' DEG.F'/10Xf
     2'PDWER LEVEL =«tF6.0t"  *»W« /10X,
     5'SPECIFIC HEAT OF  AIR  AT  CONSTANT PRESSURE "SFft^i1  BTU/IB./F1/
     610Xt 'SPECIFIC HEAT f.f  WATER  «»,F6.2i' BTU/I.B./F1/
     710Xf 'DESIGN TERMINAL TEMP. DIFFERENCE «'tF5.1f' F'/iOXt
     8»ATMDSPHERIC PRESSURE  -«fF7.2,'  PSIA')
                                          356

-------
c
      WRITE(6,620I  FC, WC,WW,CCNO,CCNl
  620 FORMAT(IH ,9X,
     VUNIT  FUEL COST -',F10.6,' */KW-HR'/10X,
     5'UNIT  SUPPLY  WATER COST "',F7.4,'  S/1000  GAL'/lOX,
     6'UNIT  WASTE WATER CCST -'.F7.4, '  */lOOO GAL'/lOX,
     7«MAX.  TOLERABLE CONCENTRATION OF  PROCESS  WATEP  «',F5.0,' PPM'/IOX,
     B'SUPPLY WATER CONCENTRATION = ',F5.0, • PPM'I
C
      WRITE(6,630)  TWBREF.PLMAX,UCAPAB
  630 FORMATUH ,9X,
     6'CRITICAL WET BULB TEMPERATURE  «',F7.2, '  OEG.  F'/IOX,
     7«MAXIMUM PPWEP OUTPUT =',F8.2,' MW'/lOX,
     B'UNIT  CAPACITY LCSS CCST =',F10.2,•  i/MW')
C
      WRITE (6, 631J  UENER, UL AND, UCOWN, DAYS
  631 FORMATUH , 9X,'REPLACED ENERGY  COST  =',F8.4,'  $/KW-HR'/10X,
     I'UNIT  LAND COST »',F8.3,' t/ACP.E ' / 10X,
     2'REPLACEO ENERGY COST DURING DOWNTIME =',F7.4, •  J/KW-HR' /10X,
     3'DOWNTIME FOR CONSTRUCTION =',F6.1,' DAYS')

      WRITE(6,640)  HE IGHT,EFFICW.UNCOND,UO
  640 FORMATUH ,9X,'PIMPING HEIGHT OF  WATER THROUGH  CANAL  =',F8.l,
     2'  FEET'/iOX,'PUMPING EFFICIENCY FOR  WATER PU*P  «',F7.3/10X,
     3'UNIT  CONDENSER COST =',F6.2,'  $/SQ. FT.'/IOX,
     4'OVERALL CONDENSER COEFFICIENT, U  =',F6.1, '  6TU/HR/FT2/F')
C
      WRITE!6,662»  ITWBI,ITWBF,ITBD,IT08F
  662 FORMATUH ,9X,'IRITIAI  WET BULB TEMPERATURE  =',14,'  DEG. F'/IOX,
     1'FINAL WET BULB TEMPERATURE «',I5,'  DEG.  F'/IOX,
     2'INCREMENT PF DRY AND WET BULB  TEMPERATURE  =',14,'  OEG. F'/IOX,
     3'FINAL DRY BUL 8 TEMPERATURE =',15, '  DEG.  ft
C
      WRITE(6,650)  Tl.nK.FINC
  650 FORMATUH ,9X,'LOWEST TEMP. IN  TURBINE CHARAC.  CHART  =',F5.l,
     1*  DEG. F'/IOX,'TEMP. INCREMENT  IN  TURBINE CHARAC.  MATRIX «',F4.1,
     21  OEG. F')
C
      IT»THBD
      TSS-PSAI IT)* (PSA I IT + l)-PSA(IT))*tTWBD-IT)
      HAA=0.24*TWBD+0.622*TSS/(PATM-TSS)*(1061.8*0.44*TW8DI
C
      00 1000 MK=1,4,3
      IF(MK.EQ.l) NNN=170
      IF(MK.E0.4) NNN=90
      00 1000 N-10»WN,10
      1FIMK.EQ.1I ROWOIS»40.
      IF(MK.E0.4) POWOIS=60.
      GPMMOD'10000.
      R'GPMMOO/GPM
C
      TS«TSS
      HA«HAA
C
      mi—5
      TTOTTOO

      CALL MODELW (TDBO,TW30,IW,NFL.TET,TQ.TWL,I I 11,K,TT,IM)
C
      IF|TET.LT.O)GOT0999
      TTSTAR=1.
      IF(ICAP.EO.O)GOT0679

      CALL POWERS (TET,TO,TTSTARI

      DOHR»( TO/TTSTAR-TQSTAR )/ ! PLMAX»3 .6/1055. 04-TC/TT STAR *TOSTAR I
      TQO»(PLMAX*TTSTAR/(l.*DOHR)+TO*1055.04/3.6)/EFI
      RP»TQ*CONST/EGPM
      AP-TET-TTO-RP-TWED

      PDEsI-CPSA(ITET)*(PSAIITET*l)-PSA(lTET)>*(TET-ITET))«1728./848.64

C  DETERMINE  CONDENSER COST, AND PUMP AND  PIPE  SYSTEM  COST

      THW-TET-TTD
      TCW«THW-TQ*CONST/EGPM
      RANGE'THW-TCW
      TTDKO-TTD/RANGE*CCNST/EGPM
      RLL«ALOGl(RANGE+TTDI/TTDI
      CONCOS=UNCaNO-EGPM/CCNST/UC*RLL*10.**9
      IF(NEWCON.EO.O)  CONCOS'CCO
      PMPHD-40
      PPCOSO-0.20+PPCOST

                                          357

-------
 c
 C  DETERMINE CAPITAL COST OF THE CANAL
 C
       COST-UTCOST»MK*N
       CAPC01-COST
 C  DETERMINE DOWNTIME, LINING, EXCAVATION. AND ADDITIONAL LAND COSTS
 C
       WIDTH«*!TET-ITET)) *1728./848.64
       THW=TET-TTO
       TCW=THW-TQ*CONST/EGPM
       RANGE=THW-TCW
       WRITEI6,12345)
       WRITE(6,98765 ITHW,TCW,RANG£,PDESI
 98765 FORMAT(5x,'HOT WATER TEMPERATURE =',F8.3,5x,«coLD WATER TEMPERATUR
      IE =',F8.3,/5X,'RANGE «',F8.3,5X,«TURBINE BACK PRESSURE =',F8.3>
 65656 CONTINUE
 C
       IFITET.LT.O)  GO TO 999
       TTSTAR*!.
       IFIICAP.EQ.O)GOT0681
       WRITE(6,55555)TWB10,TET ,TQ
 55555 FORMAT(2X,F17.5)
 C
       CALL POWERS (TET.TQ,TTSTAR)
 C
 681    DQHR=(TQ/TTSTAR-TQSTAR)/(PLMAX*3.6/1055.04-TO/TTSTARtTQSTAR)
       FPL=PLMAX*TTSTAR/(l.+DQHRJ
       FPL1«PLMAX-FPL
       FPL1»FPL1*PUMOP1/10CO.
       FPLMAX=FPL1
       CAPCAP=FPL1*UCAPAB
 C
       WRITEI6,12345)
 12345 FORMAT(///100('*•))
       WRITE(6t66666)N,HK
 66666 FORMATI///10X.'NUMBER ALONG THE CANAL =',I4,/10X,
      1'NUMBER  ACROSS THE CANAL =',I4///)
       WRITE 16,676)LENGTH.WIDTH
 676    FORMATC/10X,'LENGTH OF THE CANAL =',F8.2.' FT'/lOX,
      1'MIOTH OF THE CANAL  =",F8.2,' FT')
       HRITEI6.661)  EGPM
  661 FORMAT!1HO,10X,
      3'TOTAL HATER  FLOW RATE *',FU.O,«  GPM'l
       WRITE(6,663)
  663 FORMAT!1H0.8X,'***  DESIGN CONDITIONS ***•I
       WRITE(6,666)  THW,TCM,RP,AP,PDF SI,fU.TQQ
  666 FORMATdH .lOX.'DCSIGN HOT WATER TEMPERATURE =',Fa.3,' DEG. F1
      1/11X,'DESIGN  COLD WATER  TEMPERATURE «',F8.3,« DEG. FV11X,
      2'DESIGN  COOLING  RANGE =«,F8.3,' DEG. F'/HX,
      3'DESIGN  APPROACH =',F8.3,' OEG. F'/UX,
      5'DESIGN  TURBINE  BACK PRESSURE «',F8.4,« IN. HG'/llX,
      5'DESIGN  HEAT  REJECTION =• .F8.4,'*10**9  BTU'/llX,
      5'FUEL  CONSUMPTION AT DESIGN CONDITION »',F9.2,« MW*)
       IFIICAP.EO.l)  WRITEI6.667)
  667  FORMATUH ,12X,'NOTE ...  CAPACITY  LOSS AT DESIGN CONDITION1)
C
C  COMPUTE  OPERATION COST  AND  TOTAL COST
C
      CALL  OPECOS ilW.TOTOPE)
C
       IF
-------
c
       WRITEI6,601) COST
  601
  604  FORMATUH0.7X, •***  CAPITAL  COSTS ***•)
      nW?i!Jnc6c6021 CAPCnl'PPCOST'PPC(:lSO,CONCDS,CCCfCOO,CHT,ALANOC,
      lLINCOS,EXCCOS,CAPCAP,OnwNCC,CAPCnS
                 •9X''C'PIT«-  COST  OF MODULES  « $• ,F 18.0/ 10X,
             AND PIPE  SYSTEM COST  • $• ,F1 7. 0/10X,
     2'PUMP AND PIPE  SYSTEM SALVAGE -  (  t • ,F 12.0, • ) • /IOX,
     3'NEW CONDENSER  COST  « $ • .F24.0/10X,
     4'SALVAGE VALUE  OF CIO CONDENSER  =  ( $• , F 10 .0, • ) • /IOX,
     5'OTHER OPEN-CYCLE COMPONENTS SALVAGE » ( S ', F5 .0, • ) • /10X,
     6»HOOKUP AND TESTING  COST  =  $• ,F19. 0/10X,
     7'ADDITIONAL LAND COST = ( • , F22.0/10X,
     7«CANAL LINING COST = t • , F25.0/10X,
     7'CANAL EXCAVATION COST  =  $ • ,F21.0/ IOX,
     8'REPLACEMENT CAPABILITY  COST = $', F15.0/10X,
     9'OOWNTIME COST  = $ « , F29.0/40X, ' ----------------- «/10X,
     1'TOTAL CAPITAL  COST  - S',F24.0)

       IFdEXTRA.EO.l J TTTOPE-TOTTP
       IF( IEXTRA.EQ.1 I WR ITE(6, 614)
  614  FORMATUHO/12X,'NOTE :  OPERATING COSTS ARE BASED ON "EXTRA" OPERAT
     1ING COST')
C
       NRITEI6,612)
  612  FORMAT tlHO,8X, '**» TOTAL  COST 1  --- ANNUAL BASIS --- FIXED CHARGE
     IRATE *»*'//12X,'NO.  CF  YRS ' ,5X, ' CAPI TAL  COST ', 5X, • ANNUAL OPERATING
     2 COST', 4X, 'ANNUAL CCST • , 5X, ' F I XEO  CHARGE RATE'/28X,
     3"M1LLS/KW-HR ',10X, "MILl.S/Kn-HR ' ,9X, 'M1LLS/KV»-HR' )
       D05000KK=1,5
       CAPC01=CAPCOS*FCRR(KK)/S
       TOTCF2*TOTOPE
       TOTCOS=CAPC01 + TOTOP2
 5000  WRITEI6.611) NYEAR (KK ) ,CAPCC1, TOTOP2,TOTCOS, FCRR IKK)
  611  FORMATdH , t 1 7, F21 .9i F22.9, F20.9, F 17.6 )
       GOTO 1000
999    WRITE(6,603)EGPM,TET
603    FORMAT(//10X,'********':*******'/12Xt 'TOTAL WATER FLOW RATE THROUGH
     I  THE SPRAY CANAL =«,F11.0, •  GPM' /1 2X, ' TURBINE TEMPERATURE -• ,F10.4
     1)
       WRITE(6,623)
623    FORMAT (IOX, 'SPRAY CrOLING SYSTEM IS TOO  LARGE TO OPERATE')
       TOTCOS»10.**12
 1000  CONTINUE
       STOP
 1001  TQTCOS»10.**12
       STOP
       END
      SUBROUTINE OPECOS UW.TOTOPE)

r***********************************
C *  PROGRAM TO DETERMINE TOTAL  ANNUAL OPERATING CCST                 *
C***»*******************************
C
c

      DlMENSIGN°HR(50t14),IHRJ14),AUO),B(10),ARWT(10),PSAI250)
      DIMENSION AW(10),BW(10),CW(10),AMANT(3,2>
     1,WTCOST(10),S1(15),S2(15),S3(15),NYEAR15)
      COMNON/DENSIT/ DAIR(250)
      COMMON/INPU/ PE?CEN(12,15,2)
      COMHON/TtlRBIN/ HR, IHR, TLOH,F INC
      COfCON/NCALA/ PSA.TPS, TS,T WBAL.CH1 ,OH2, HA
      COMMGN/TUSB/ POWER t TBP, TET, TTO, TTOKO.TTOO
      COCMCN/CCNSTA/ CONST 1, nPNST.CCNST
      rnminnw/TEMP/ ITWBI,ITWBF,IIBO,ITOBF
      COMMON/ECONO/ NYEAR, FC, WC, WW.DR ,CC NO.CCN1, ANFOV.E.HE IGHT, EFFICW
      COWCCN/POHERC/ IPLltlPI F.M.FP.LP
      COMMON/ATMOS/ PATM
      COMMON/MAINTA/ AMANT.CF.EFI
                                           359

-------
       COMMON/RgNEW/TQSTAR
       COMMON/TPLI1/TPLMAX
       COMMON/SPKAY/R.MK.N.HINOSPtFF.TFILM
       COMMON/SPROIS/F(6,3I .ROfcOIS
       COHMON/PILIC/CPM
       FGPM=GP«
       EGPM-FGPM
 C
 C  OPERATION DUE TO SPRAY CANAL
 C
 C  DRY-BULB AND WET-BULB TEMPERATURE INTERVAL,  I TBO, MUST BE  GREATER  THAN  1
 C
       PUMOPl»FGPM*HEIGHT*62./7.481/ftO./550./EFFICH*0.7457
       PUMOP2«MK»N*75.*0.7457
       PUMOP1=PUMOP1+PUMOP2
 C
       IF! IWRITE.EQ.l)WRITE(6,a/(0.000367*PATM*(l.+(IIJ-32.)/1571.)l+IIJ
       IFCITDBMA.GT.ITDBFIITDByA=ITDBF
       IFIMJ.GT.ITDBMAIGO TO SOI
       D0923UK = I I J, ITDBMA.ITBO
       TDB=IJK
       I01 = ( IJK-ITWBD/ITBD+1
       AH=T5-0.000367*PATM*(TOB-TWB)*(l.+(TWB-32.)/1571.)
 C
       1F(PERCEN(IMliIDltLPD.LT.0.00000001) GO TO 923
       FAP=PUMOP1/1000.
       NP'NPL
       IFCLP.NE.IPLI)  NP=(CF-0.491*10.
 C
       CALL HOOELW  ITOB.TWB,IW,MP,TET.TO.TWL,JJJJ,KK,TTT,IMI
 C
       IFITET.LT.O.OI  GO TO 1002
       IF(TUB.EQ.5.AND.TDB.EQ.5 ) GO TO  95135
       GO  TO  8*951
 95135  ITET=TET
       PDESI«(PSAUTET)*(PSA»ITET+l)-PSA(lTET))*tTET-ITET»*1728./8AB.6«
       THM=TET-TTO
       TCW=THH-TO*CONST/EGPM
       RANGE=THW-TCW
       WRITE(6,147251
 14725  FORMAT15X,'LEAST  CONDITIONS')
       WRITE(6,?6159)THW,TCW,RANGE,PDESI
 26159  FORMATC5X, 'MOT WATER  TEMPERATURE  = ' ,F8.3 ,5Xt "COLO WATER TEMPERATUR
     IE »',F8.3,/5X,'RANG£  -'(F8.3.5X,•TURBINE BACK PRESSURE  =',F8.3)
64951  CONTINUE
       IF(THB.E0.95  .AND.TUB.EQ.95 I GO  TO 35724
       GO  TO  25814
35724  ITET»TET
       PDESI"(PSA(ITET)+(PSA(lT£T+l)-PSA(ITETH*(TET-ITETI)*l728./848.64
      THW=TET-TTO
                                          360

-------
       TCW-THW-TQ*CONST/EGPM
       RANGE-THW-TCW
       WRIT£<6t357TT»TET-TTO
      COLDWT«HOTHTT-TQ*CONST/FGPM                      »
      p> (PSAUT£T» + -PSAClTET)l*CTET-[TETII/0.49llll
      TOTBLD-TOTRLC+BLCCV«M*PERCEN
                                        361

-------
       TOTHAH»TOTWAW+WAWACO*PEACEN(IWl.IDl.LPlI
       AMANT1»PUMOP1»0.01*B760.*PERCEN(IW1,ID1,LP1)*UENER
       10TMAN«TQTMAN-»AMANT1
       FUECIS*FUECUS*PCRCEN< IWl.IDl.LPl)
       WATCOS»WATCl)3*P(?RCEM( Ilv I , 1 [) I, LP1 )
       WAHACO=»WAWACO*PEHCEN IM
  702  FORMATI180)
 9233  CONTINUE
       GO  TO 901
  902  IFI IHRITE.LT.DGOT0923
       WRITE(6,601)  PL.TWB
  601  FORMAT!1H0.5X,'POWER =«,F5.0i' MW'.IOX.'TWB =',F8.3,«  DEC.  F'l
       WRITE(6i333)TET,HOTWTT,COLDWT,P,TQ
333    FORMAT(/6X,'TURB.TEMP.  = •,F10.4,IXt•DEG.F.  ',
      15Xi«HOT  WATER TEMP. = •,F10.4,1Xt•DEG.F. • t
      25Xt'COLD  WATER  TEMP. =  •,F10.4,IX,'DEG.F.• ,
     3//i6X,'PRESSURE  = '.FS.S.IX.'IN.HG.',
     ASX.'HEAT  REJECTION * •,F8.5,IXt'BTU*10**9',/ I
       HRITE(6,602)
  602  FORMATdHO*IX,'TOB'r3X,'WATER EVA«',3X,•BLOWCOWN*,3X
      1,'PROBABILITY',3X,'FUEL COST',3X,
     2'MATER COST',3X,'WASTE  WATER COST',3X,•SUBS ENERGY LOSSS3X,
     3'OPERATING COST•/3X,'F',
     A7X,'GPH',9X,'GPH',22X,«t/YEAR',6X,
     5'$/YEAR',10X,•I/YEAR'T13X,'S/YEAR',12X,•$/YEAR'/)
       WRITE(6,60TinJ,TWL,BLDOWNfPERCEN(IWl,IDl,LPll,FUECIS.WATCOS,WAWAC
     10,ANUCAP,OPCOS,FPL1
  607  FORMAT(1H ,I 3,Fl5.5.F11.4,F13.6tF13.0,F12.1,F16.1,F20.3,F18.1,
     1F10.3)
       HRITEI6.899I
  899  FORMAT(///1X,1301'*•)////)        ^
  923  CONTINUE
  901  CONTINUE
 1000  CONTINUE
       FUELEX=TOTEI-TEI
       TOTFU1=FUELEX*FC*10CO.*8760.
       TOTOPE=TOTOPE-CWATEO-CBLOWO-CMAINO
       TOTOP=TOTOPE-TEI*FC*1000.*8760.
       TOTEIl=TOTEI/TOTPRO
       TOTWLl = TOTWL/(TQSTAR*1055.0'i/3.6)
       FUELE1=FUELEX/PLMAX
       FPLMAl=FPLMAX/PLMAX
       ENERLl=ENERLS/(PLMAX*8760.)
       FAPLS1=FAPLS/(PLMAX*8760.)
      WRITEI6,12121)
12121 FORMAT
-------
      VEXCESS FUEL COST »',F?6.0,' I/YEAR'/IOX
      4'TOTAL  ANNUAL WATER COST .J.F19.0,' WYEARV10X
      5'TOTAL  ANNUAL WASTE WAFER COST =° F13 o!« $/YEAR'/10X
      6-TOTAL  ANNUAL MAINTENANCE COST »- F 3 0 • !/YEAR-/ «'
      6-TOTAL  ANNUAL CAPACITY LOSS «•.F16.0,• J/YEAR'/HJX
      7'TOTAL  ANNUAL OPERATING COST " .F15.0, • t/YEAR-/10X
      8'EXTRA  ANNUAL OPERATION COST »•  F15 C • i/YE^R')
       TOTFUE'TOTFUE/S                tria.u,  */Yfc*R i

       TOTWAT=TOTWAT/S
       TOTWAW-TOTWAW/S
       TOTMAN=TOTMAN/S
       ANUCAP=ANUCAP/S
       TOTOP=TOTOP/S
       TOTOPE=TOTOPE/S
       WRITE(6,62II TOTFUE,TOTWAT,TOTWAW,TOTMAN,ANUCAP,TOTOPE
      ItTOTOP
  621 FORMAT)1H0.7X,'*** AVERAGE OPERATING COSTS — IN MILLS/KH-HR ***•
      1/10X,'AVERAGE FUEL COST =',F22.6,' MILLS/KW-HR'/10X,
      i'AVERAGE  WATER COST *',F21.6,' MILLS/KW-HR'/10X,
      2'AVERAGE  WASTE WATER COST «',F15.6,« MILLS/KW-HR-/IOX,
      4'AVERAGE  MAINTENANCE COST =',F15.6,« MILLS/KW HR'/lOX,
      5'AVERAGE  CAPACITY LOSS =',F18.6,« MILLS/KW/HR-/10X,
      6«AVERAGE  TOTAL OPERATING COST =',FU.6,«  MILLS/KW-HR' /IOX,
      7«AVERAGE  EXTRA OPERATING COST »',FU.6t'  MILLS/KW-HR'I
       RETURN
 1002   WRITE16.623)
 623    FORMAT(IOX,'SPRAY COOLING SYSTEM IS TOO LARGE TO OPERATE1 I
       TOTCOS«10.**12
       RETURN
       END
       SUBROUTINE MODELW J TOB, TW8, I W,LP, TET.TQ, TWL, 1 1! I ,K, TT, IM)
C  *   THIS SUBROUTINE CALCULATES THE MODELING RELATIONSHIPS FOR POWER  *
C  *    PLANT  AMD SPRAY CANAL .     GIVEN WET AND DRY BULB              *
C  *    TEMPERATURESi  OPERATION LEVELS OF SPRAY CANAL, POWER LEVEL OF    *
C  *    TURBINE OUTPUT, THE RESULTS ARE TURBINE EXHAUST TEMPERATURE AND *
C  *    HEAT REJECTION.                                                 *
C**************** *******************
C
c
       DIMENSION HTRJIN(50,14),IENHTR(14),PSA(250)
       REAL NTU
       COMMON/TURBIN/HTRJIN,IENHTR,TLOW,FINC
       COMMON/NCALA/  PSA, TPS.TS, TWBAL.QH1 ,OH2 ,HA
       COMMON/TURB/ BL1 , BL2 ,BL3,TTD,TTOKO,TTDO
       COMMON/TBPR/ ITPMAX, TETMAX, ICAP
       COMMON/SPRAY /R,MK,N, WINDS? ,FF ,TF I LM
       COMMON/SPRDIS/F(6,3) ,ROI«OIS
       COMMON/PILIC/GPM
       COMMON/CONST A/ CONST 1, DON ST, CONST
       FGPM=GPM

C    IF TWB IS HIGH ENOUGH, THEN COOLING CANNOT TAKE PLACE AT ALL UNTIL
C    TURBINE  CONDENSER TEMPERATURE IS HIGHER. THUS,  WILL SKIP TO
C    HIGHER TURBINE TEMPERATURE.

C    IF TWB IS LOW ENOUGH,  COOLING  WATER FREEZES,  WHICH
C    IS NEVER DESIRED.  THUS WHENEVER COOLING WATER  WOULD HAVE BEEN
C    COOLED BELOW FREEZING ANYhHERE  IN THE CYCLE, NC COOLING IS
C    PERFORMED (IMPLYING ALTERNATE SYSTEM USED IN PRACTICE).

C  ASSIGN MODEL PARAMETERS FOR TOWER SECTION
C
       ICAP=0.
       IH'2
       IFR=0
       IFRE»-l
       JFUIII.GT.0.5IGOT01000
       WL'O.
       TPS=0.
       TWBAL«0.
       QH2°0.
       IFUIII.EO.-5)GOT09«n
       TTDO=HTRJIN(1,LPI*TTDKO
       GOT0992
  991  TTDO'TTD

C  ASSIGN  INITIAL  TRIAL TURBINE TEMPERATURE



                                           363

-------
 c
   992 K-0
    99 IFRE-IFRE+1
   201 K»K+1
       TT-TLOH+IK-1I*FINC
       IFJK.GT.tENHTRILPl.AND.TT.GT.< TETMAX+1.95)IGO TO  999
       IF(IIIt.EQ.-5(GOr0404
       TTD=HTRJIN(K,LP)*TTDKO
   404 TT1-TT-TTD
 C
 C  COOL THROUGH COOLING SYSTEM IF POSSIBLE TO GET T01
 C
       IF(TWB.LT.TTl)GOT04J3
       GOT0201
   403 WL2=WL
       TPS2«TPS
       THBAL2'TWBAL
       QH22=QH2
       IF(TT.GT.(TETMAX*l.95))GOT0999
 C
       THI=TTi
       CALL SPRCOL
-------
       TMI-TT1

 c     CALL SPRCOL
       GOT0107
   106 HQ=HTRJIN(K-1,LP)
   107 IF(II1I.GT.-S)GOT0407
       HQ=HQMTHB+TTD-TT + FINC)/FINC*
       GOT0406
   407 HQ=(HQ+(TWB-TT*FINC(/FINC*(HTRJIN9
       TTO=TQ*TTDKO
   409 THL=WL/T01*TQ
       TPS=TPS/TQl*TQ
       THBAL«TWBAL/TQ1*TQ
       QH2=QH2/TQ1*TQ
       TT=TT-FINC
       1F(K.GT.1)K=K-1
       GOT0211
 C
 C  REACH INTERSECTION  BY INCREMENTING TURBINE TEMPERATURE
 C
   100 IF(K.EO.IENHTR{LP))GOT0999
   108 TT=TT+FINC
       K=K+1
       IFdl II.EQ.-SJGOTOAIO
       TTD=HTRJINB,GPM,AFR,RLG,TT2,WLI
 C
       TQ2=(TT1-TT?)*FGPM/CONST
       IF(TQ2.GT.HTRJIN(K,LPIIGOT0101
       IF(K.EO.IENHTRILP)IGOT0999
       T01=TQ2
       GOT0108
 C
 C  INTERPOLATE FOR TOt TET, TfcL

 C 101 HTOIF1=HTRJIN(K,LP»-HTRJIN(K-1,LPI

       TO=tHTRJ?NTK?LP)*HTDIF2-T02*HTOIFl)/|HTDIF2-HTOIFl)
       TET_TT_(TQ2-TQI/HTDIF2*FINC
       IF(IIII.EO.-5)GOT04H
       TTO=TQ*TTDKO
  411  TWL=(WL2+(WL-WL2)/HTDIF2*(TQ-TQ1)I
       TPS = TPS2 + (TPS-TPS2I/HTDIF2*(TO-TOU
       THBAL=THBAL2+(TWBAL-TWBAL2>/MTDIF2*(TQ-TOll
       OH2=OH22<(OH2-OH22)/HTDIF2*(TQ-r01l
       TT=TT-FINC

       IIII=l
      RETURN

C  RETURN WITH  MESSAGE
C



                                            365

-------
   703 TO—50
       TET»-50.
       THL — 50.
       IIU«0
       1M—50
       RETURN
 C
 C  FIND INTERSECTION WHEN WET-BULB TEMPERATURE INCREASES
 C
 C  REACH INTERSECTION BY INCREMENTING TURBINE TEMPERATURE
 C
  1000 TTD=HTRJ1N(K,LP)*TTDKO
       TT1=TT-TTD
       IFCTT.GT.(TETMAX+1.95))GOT0999
 C
       THI=TT1
       CALL SPRCOL(THItTOB,TWB,NTU,B,GPM,AFR,RLG,TT2,WL)
 C
       TQ1=(TT1-TT2)*FGPM/CONST
  1004 TT=TT+FINC
       IF1TT.LT.IGCT01001
       IFCK.EQ.IENHTR(LP)IGOT0999
       K«K+l
       HQ'HTRJIN(K.LP)
       HTDIF1=HQ-HTRJIN(K-1,LP)
       GOT02070
  1001 HQ=HTRJIN(1,LP)
       HTDIF1«0.
  2070 TTO=HQ*TTDKO
       TT1=TT-TTO
       WL2=WL
       TPS2=TPS
       TWBAL2=TWBAL
       OH22=QH2
       1F(TT.GT.{TETMAX*1.95))GOT0999
 C
       THI=TT1
       CALL SPRCOL(TWI,TDB,TW8,NTUtBtGPM,AFR,RLG,TT2,WL)
 C
       TQ2=(TT1-TT2)*FGPM/CONST
       IF«TQ2.GT.HQIGOT01010
       TQ1=TQ2
       GOTO1004
 C
 C  INTERPOLATE FOR TQt  TET, TV.L
 C
  1010 IFIK.GT.DGOT0412
       TTD=HTRJINI 1-,LP)*TTDKO
       GOT0413
   412 TTO=HTRJIN(K-1,LP)*TTDKO
   413 IF«TWB.LT.(TT-FINC-TTD))GOT01011
       TQ1=TQ2
       GOTO104
  1011 HTOIF2=T02-TQ1
       TQ=(HQ*HTDIF2-TQ2*HTDIF1)/(HTDIF2-HTDIFII
       TET=TT-(T02-TO)/HTOIF2*FINC
       TTO=TO*TTOKO
       THL=(WL2+(WL-WL2)/HTOIF2*(TQ-TQI))
       TPS=TPS2+(TPS-TPS2)/HTDIF2*(TQ-TQ1)
       THBAL=TWBAL2+(TWBAL-TWBAL2I/HTDIF2*(TO-TC1I
       OH2=QH22+(OH2-QH22)/HTDIF2*(TO-TQ1)
       IF(K.GT.l)  K=K-l
       TT=TT-FINC
       RETURN
 999    IF{TT2.LT.32.)GOT0703
       ICAP=l
       TT1=TETMAX-TTD
 C
       TWI=TT1
       CALL  SPRCOU TWI, rDB,TWB,NTUiB,GPM,AFR,RlG,T12,WLI
 C
       TO=(TT1-TT2)*FGPM/CONST
       TET=TETMAX
       1FCIIII.NE.-5)TTD=TQ*TTDKO
       THL°HL
       RETURN
       END
      SUBROUTINE SPRCOLITHI,TDB.TWBiNTU,B,GPM,AFR,RLG,TT2tWL)
c* ***********«*****************.
                                          366

-------
c
C    THIS SUBROUTINE CALCULATES THE COOLING BY A SPRAY CANAL
C
c* *»************«»*»****«»*»**,
      DIMENSION PSAC250)
      REAL NTU
      COMMON/NCALA/ PSA, TPS.TSt TWBAL.QHl ,QH2,HA
      COMMON/SPRAY/R,MK,N,WINDSP,FF,TFILM
      COMMON/SPROI S/F< 6, 3 ) ,ROhDl S
      COMMON/ATMOS/ PATH
C
      IFIROWD1S.LT.AO.OR.RQWOIS.GT.60> FF=0.18
      KLM=IFIX«ROWDIS-40)/10+1)
      M«MK
      FF=FtM,KLM)
      CW-l.OO
      N1U=0.036*WINOSP+0.156
      HV=1087.-0.54*TWI
      1FLAG=1
      TFILM=0. 5*(THI+TWBA)
      TWF1»TFILH-0.5
 111   TWF=TWFI
      IT»THF
      PVSAT=PSA(IT1+(PSA1IT*1)-PSA(IT))*(TWF-IT)
      PV«PVSAT-0.000367*PATM*(TDB-TWF) *(!.+ ( JTWF-32. ) /1 571 ) )
      S«PV/(1.608*(PATM-PVI 1
      SIGMA=(0.2A+0.*«t*S)*TDB*S*( 1093.8-TWFI
       IFt IFLAG.EQ.2)  GO  TO  121
       IFLAG«IFLAG+1
      TWFI=TWFI+1.
      SAVSIG=SIGMA
      GO TO 111
 121   ARGUM=SIGMA-SAVSIG
      B=ABS(ARGUM)
      X=NTU*B
      TT21=THI-(TWI-TWBA)*«1.-EXP(-X) I
      NN°M*N
       TT2=TWB+(TWI-TWB)*EXP((-NN*R*(1.-FF))*C1.-EXP(-X»))
         BOWEN  RATIO IS ASSUMED   « 0  *****
      WL = (CW/HV)*(TWI-TT2)*GPM
       RETURN
       END
       SUBROUTINE POWERS (TEH.Q.TTSTAR)


       See Appendix  III  for  listing.
                                         367

-------
    APPENDIX VII





 RANGE OF VALUES OF



VARIOUS ECONOMIC AND



  OTHER PARAMETERS
         368

-------
 General
 • '" 	  <	—                       rf
    Unit cost of replacement capacity,
    Unit cost of "short term" replacement
      energy during downtime,
    Unit cost of "long term" replacement
      energy, after backfitting
    Unit cost of fuel,
    Unit cost of water,

    Unit cost of land,

    Unit cost of new condenser,


    Unit cost of blowdown treatment

    Open-cycle maintenance cost
    Open-cycle blowdown cost
    Open-cycle water cost,
    Downtime for hook-up and testing


Mechanical-Draft Cooling Towers
   Unit cost of towers,
   Unit cost of maintenance,
c  =  $90-200/kW
 Jj
     $0.007/kW-hr
                  [2]
                  [2]
   = $0.01/kW-hr       [2]
   = $0.30-0.98/106Btu [6]
c  =
 w
cL /i """
c  =
$0.0-1.0/1000 gal
(highly variable)
$500-5000/acre
(highly variable)
$6.50-23.10/ft2
   = $4.00/f1:          [16]
   = $0.0-0.50/1000 gal
     (highly variable)
M1 =
B' =
W =
DT =
=
0
0
0
5-10 days
30-90 days



[**1
[6]
   =  $7.50/TU          [16]
   -  $200/cell/year    [2]
* Comment by J.P. Chasse  (E.P.A.)
** Private communication, Commonwealth Edison & Iowa-Illinois, Quad
   Cities Nuclear Power Plant
                                 369

-------
   Cost of pump and pipe system





Natural-Draft Cooling Towers



   Cost of towers,



   Maintenance cost,



   Cost of pump and pipe system





Cooling Ponds



   Unit cost of ponds,


      (including land cost)



   Unit pump and pipe system cost,



   Unit maintenance cost
C   = Figure 13
 PP
C   = Figure 32
 cs
[16]
[16]
 C  = $1000-3000/tower/year
  m
C   = Figure 13
 PP
[16]
C   = $500-5000/acre    [26]
 cs
c   = $1.50/gpm
 PP
[26]
 c  = $2.00/acre/year   [26]
  m
Spray Canals



   Unit cost of spray modules,





   Pump and pipe system cost,



   Maintenance cost.





   Lining cost of canal,



   Excavation of canal,
 c  = $16,000-26,250 /module

  S                [49,56,57]
c   = $1.50/gpm
 PP
[26]
 c  = 1% of pump and module
  m

      operating cost


 c  = $0.93/ft2         [*]
  Ll


 c_ = $2.50/yd3         [*]
   * Private communicaton with local industry
                                  370

-------
 4. TITLE AND SUBTITLE
Economic Assessment of Backfitting Power Plants
with Closed-Cycle Cooling Systems
                                                      5. REPORT DATE
                                                       March 1976
                                                      6. PERFORMING ORGANIZATION CODE
 ,.AUTH  R< 'A.R.Giaquinta, T.E.Croley II, V.C.Patel,
 J.G.Melville, M.S.Cheng, and A.S.Uzuner
                                                     8. PERFORMING ORGANIZATION REPORT NO.
 . P        ORANIZATION NAME AND ADDRESS
 University of Iowa
 Iowa Institute of Hydraulic Research
 Iowa City, Iowa  52242
                                                     10. PROGRAM ELEMENT NO.
                                                      1BB392; ROAP 21AZU-019
                                                     11. CONTRACT/GRANT NO.
                                                      68-03-0430
 12. SPONSORING AGENCY NAME AND ADDRESS      ——	
 EPA, Office of Research and Development
 Industrial Environmental Research Laboratory
 Research Triangle Park, NC  27711
                                                     13. TYPE OF REPORT AND PERIOD COVERED
            13. TYPE OF REPORT AND I
            Final; 4/74-10/75
                                                     14. SPONSORING AGENCY CODE
                                                      EPA-ORD
 is. SUPPLEMENTARY NOTE
                  Sproject officer for ^jg report is James P. Chasse, Environmental
 Research Laboratory, Corvallis, Oregon 97330.
 16. ABSTRACT rphe repor£ gives jjj Detail B. method for assessing the economic consequen-
 ces of backfitting electric power plants (currently operating on open-cycle or once-
 through cooling systems) with conventional closed-cycle cooling systems.  Four
 types of closed-cycle systems were investigated: mechanical- and natural-draft
 crossflow wet cooling towers, cooling ponds, and spray canals.  To estimate oper-
 ational penalties  associated with backfitting, thermodynamic models were used to
 reproduce the operating characteristics of different types  of turbines, condensers,
 and cooling systems.  Capital and operating cost information  was compiled and
 used, in conjunction with the levelized annual cost accounting method, to evaluate
 the total differential cost of power production resulting from the backfit.  Computer
 programs were developed and are presented.  Many  representative calculations were
 performed and are presented graphically. The results for three types of conventional
 turbines and four geographical sites were obtained for a range of cooling system
 sizes: they are plotted visually. Once the various unit costs of replacement
 capacity, energy loss, fuel, and water are known, these results can be used to
 evaluate the cost to be assessed against backfitting.  Representative unit cost
 values are  included in the report.
 7.
                             KEY WORDS AND DOCUMENT ANALYSIS
                 DESCRIPTORS
 Air Pollution
 Electric Power Plants
 Cooling
 Economic Analysis
 Capitalized Costs
 Operating Costs
                          Computer Pro
                           gramming
                          Thermody-
                           namics
                                          b.lDENTIFIERS/OPEN ENDED TERMS
Air Pollution Control
Stationary Sources
Closed-Cycle Cooling
 Backfitting
                                                                 c.  COSATi Field/Group
13B
10B
13A
05C
14A
09B
20M
 8. DISTRIBUTION STATEMENT

 Unlimited
                                          19. SECURITY CLASS (This Report)
                                          Unclassified
                        21. NO. OF PAGES
                             384
                                         20. SECURITY CLASS IThh rtavr)
                                          Unclassified
                                                                  22. PRICE
EPA Form 2220-1 (9-73)
                                        371

-------