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;
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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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
CO
(2 -0.12
o
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
-------
^
o
E
o>
i
o
tt)
^
t-
0>
o
JO
*
?
^
z"
0
ll
o
Q.
UJ
cc
UJ
Jj
o
UJ
N
J
s
o
Z
9.0
8.0
7.0
6.0
5.0
4.0
3.0
2.0
1.0
O
1 1 1 1 • 1 I
LOS ANGELES
TURBINE A
«•
/'®r"^|Lii^=®=^^
If
1
91
1
1
I x P* = 411 MW
j i
®/ 0 P* = 822 MW
//
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
co
o
O.14
> O.12
I
<
0 0.10
a
u
N
U
| 0.08
o
z
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
UJ
til 0.10
o
UJ
N
< 0.08
i
0.06
0.04
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
-------
-0.02
~ -0.04
K
bl
-0.06
o
-0.08
co
ui
CO
CO
u
X
Q
OJ
N
O
-0.10
-0.12
-0.«4
-0.16
-o.ie
-0.20 -
-0.22
0.2
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
-------
-0.02
: -0.04
K
It
u.
-0.06
-0.08
CO
§ -0.10
111
o
Ul
N
-0.12
-0.14
-0.16
-0.18
-0.20
-0.22
0.2
1 III' I
II 1 .'/
O
CD
CC
7/
I
II
o
,
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
-------
-O.O2
: -o.04
ui
u.
L -0.06
8 -0.08
CO
§ -0.10
Ul
-0.12
w -0.14
o
UJ
N
I -0.16
K
-0.18
-050 -
-0.22
II,
•I,
ui
i ii
HI
III
H
Im
1
I
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
1.0
i
1.2
1.4
1.6
1.8 (A.B)
0.2
O.4
0.6
0.8
1.0
1.2
1.4 (C)
L, «
NORMALIZED TOWER LENGTH, L/L*
Figure 27 (c). Normalized excess fuel consumption, Miami
96
-------
-O.O2
~ -0.04
L. -0.06
P-
1-0.0,
-0.1O
111
in
CO
ui
o
x
o
UJ
IE
O
-0.12
-ai4
-0.16
-0.18
-0.20
-0.22
O.2
Ill
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
-------
-iBOOO
aor
6JO
•5 5.0
4.0
•ao
r ao
3.0
•ao
f
1.0
5.0
4.0
9.0
-ao
•fe
§ 3.0
S
N
2.0
• 70
•6.0
W -5X)
0L4X)
CHICAGO
PILE HEIGHT, H
—- 35ft, 10.67 m
— 45ft, 13.72m
——55ft, 16.75m
9000
19000
6000
7000
6000
SOOO
7000
6000
5000
4000 £
i
I
3000 S
2000
KJOO *
8000 -
4000
7000
6000
SOOO
02 0.4 0.6 0.8 1.0 1.2 1.4
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
-------
9.0
00
7.O
&0
|
| 50
T
* 4.0
i
1
p
. 2-0
f
*
g 1X>
tt
5 0
.
•
•
.
-9.0
-ao
: 7.0
•6.0
-5.0
4.0
S
£ 3.0
1
g 2-0
H
1 1.0
§
0
-
.
.
-9.0
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111
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Figure 28(b). Normalized evaporation, Los Angeles
99
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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
-------
(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
-------
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
-------
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
-------
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
-------
WATER
OUTLET
Figure 29. Hyperbolic natural-draft crossflow,
wet cooling tower
122
-------
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
-------
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
-------
o
CM
X
co
o
c
Q.
O
cr
o
LJ
a:
3
co
CO
UJ
or
a.
o
co
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
-------
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
-------
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
-------
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
12.0
11.0
10.0
9.0
-. 8-0
o
X
Vf __
~- 7.0
«
o
o
_I
<
1I
o.
o
oc
Ul
o
6.0
5.0
4.0
3.0
2.0
1.0
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
40<>
UJ
X
UJ
o
300
UJ
tr
UJ
ui 200
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
ul
X
100
75
50
C/>
UJ
o
z
UJ
cc
UJ
u.
UJ
o:
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
-------
C0
o
t
o
<
0.
<
o
0.8
0.7
0.6
0.5
0.4
822 MW
O
UJ
fcj 0.3
2
o:
o
0.2
O.I
0.4
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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0.4
LJ
Q.
UJ
•»
CO
CO
o
o
oc
UJ
UJ
o
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N
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o
0.3
0.2
O.I
1 \ 1
LOS ANGELES
TURBINE A
36% EFF.
PILE HEIGHT, H
42 ft, 12.80m
49 ft ,14.93m
56 ft, 17.07 m
63ft, 19.20 m
822 MW
O
A
O
622 MW
411 MW
•
A
B
g
0.4 0.8 1.2 1.6 2.0
NORMALIZED SHELL HEIGHT, S/S*
Figure 35. Normalized energy loss
2.4
138
-------
LU
O.
«- v/
X
u.u
•
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X
o
IT -0.4
a.
2E
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cc
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1 d* ' i i i
S LOS ANGELES
li Tl/RBINE A
I 36% EFF.
a
j PILE HEIGHT, H 822 MW 411 MW
4 42 ft, 12. 80m O •
1
1 49 ft, 14.93m A A "
j 56 ft, 17.07m D Q
J 63 ft, 19.20m • H -
1
1
9
r
t
I
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1
1
1
1
r
1
I
I
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" 1 "
I i 1 I I
0.4 0.8 1.2 1.6 2.0
NORMALIZED SHELL HEIGHT, S/S*
Figure 36. Normalized excess fuel consumption
2.4
139
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t.
4>
5
^ 8.5
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k.
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IT
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z 7.0
• • — r- 1 1 1 1
LOS ANGELES
TURBINE A
36% EFF.
PILE HEIGHT, H 822 MW 411 MW
42 ft, 12.80m O •
-
49 ft, 14.93m A A
56 ft, 17.07 m D B
- 63 ft, 19.20m • B
t y4ll MW
\« JB
ll -JBT
\fa ^*
•^?-&S«K^
•» H LJBj'^^Ji'^*
822 MW
—
-
MB
*
.
1
*
—
II 1 1 1 1
10,800 '
***
o
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10,400 r
•
35
o
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*
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9200 g
H
$
o
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N
8800 <
a:
o
z
0 0.4 0.8 1.2 1.6 2.0 2.4
NORMALIZED SHELL HEIGHT, S/S*
Figure 37. Normalized evaporation
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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a.
-i
u
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tn
(0
O
>-
H
O
Q.
O
O
UJ
IM
ec
o
SHELL HEIGHT, S (m)
100 150
200
LOS ANGELES
TURBINE A
36% EFF.
PILE HEIGHT, H
42 ft, 12.80 m
49 ft, 14.93 m
56 ft, 17.07 m
63 ft, 19.20 m
100
200 300 400 500
SHELL HEIGHT, S (ft)
600
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.
PILE HEIGHT, H
42 ft, 12.80 m
49 ft, 14.93 m
56 ft, 17.07 m
63 ft, 19.20 m
200
100
200 300 400
SHELL HEIGHT, S (ft)
500
600
Figure 39. Variation of normalized energy
loss with shell height and plant
capacity, 36% turbine efficiency
145
-------
UJ
a.
a.
5
3
to
z
o
o
0.0
-0.2
-0.4
-0.6
-0.8
0
-1.0
-1.2
UJ
u.
CO
CO
UJ
o
X
UJ
o
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* -1.4
a:
o
z -1.6
SHELL HEIGHT, S (m)
50 100 ISO
200
411 MW
LOS ANGELES
TURBINE A
36% EFF.
PILE HEIGHT, H
42 ft, 12.80 m
49 ft, 14.93 m
56 ft, 17.07 m
63 ft, 19.20 m
100 200 300 400 500
SHELL HEIGHT, S (ft)
600
Figure 40. Variation of normalized excess fuel
consumption with shell height and
plant capacity, 36% turbine efficiency
146
-------
SHELL HEIGHT, S (m)
50 100 150
8.5
s
E
«
f
§
w
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LOS ANGELES
TURBINE A
36 % EFF.
••
.
V<^\
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\VV ^ 's'^S
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PILE HEIGHT, H
rt« ft I" }>n m
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63 ft, 19.20 m
i i i ii i -
i 100 200 300 400 500 600
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n
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SHELL HEIGHT, S (ft)
Figure 41. Variation of normalized evaporation
with shell height and plant capacity,
36% turbine efficiency
147
-------
*
Q.
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o.
<
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0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
O.I
50
SHELL HEIGHT, S (m)
100 150
200
LOS ANGELES -
TURBINE A
28% EFF.
PILE HEIGHT, H
42 ft, 12.80 m
14.93 m _|
17.07 m
19.20 m
49 ft
56 ft
63 ft
411 MW
100
Figure 42.
200 500 400 500
SHELL HEIGHT, S (ft)
600
Variation of normalized capacity
loss with shell height and plant
capacity, 28% turbine efficiency
148
-------
0.4
*
m
a.
0.3
tO
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2
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a
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0.2
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50
T~
SHELL HEIGHT, S (m)
100
T
150
200
LOS,ANGELES
TURBINE A
28% EFF.
PILE HEIGHT, H
42ft, 12.80 m
49 ft, 14.93 m
56 ft, 17.07 m
63 ft, 19.20 m
100 200 300 400 500
SHELL HEIGHT, S (ft)
600
Figure 43. Variation of normalized energy
loss with shell height and plant
capacity, 28% turbine efficiency
149
-------
tu
a.
0.0
-0.2
x -0.4
z
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-0.6
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-1.2
O -1.4
-1.6
SHELL HEIGHT, S (m)
50 100
150
200
411 MW
LOS ANGELES
TURBINE A
28% EFF.
PILE HEIGHT, H
42 ft, 12.80 m
49 ft, 14.93 m _
56 ft, 17.07 m
63 ft, 19.20 m
100 200 300 400
SHELL HEIGHT, S (ft)
500
600
Figure 44. Variation of normalized excess
fuel consumption with shell
height and plant capacity, 28%
turbine efficiency
150
-------
8.5
o
•>
>.
S 8.0
O
O 7.5
CL
UJ
Ul
I-
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Ul
N
a:
o
7.0
SHELL HEIGHT, S (m)
50 100
T
150
LOS ANGELES
TURBINE A
28% EFF.
PILE HEIGHT, H
42 ft, 12.80 m
49 ft, 14.93 m
56 ft, 17.07 m
63 ft, 19.20 m
10,400 E
«
10,000
9600
9200
8800
z
o
DC
O
CL
UJ
oc
Ul
O
UJ
N
OC
O
100 200 300 400
SHELL HEIGHT, S (ft)
500
8400
600
Figure 45. Variation of normalized evaporation
with shell height and plant capacity,
28% turbine efficiency
151
-------
0.24V
50
0.22
0.20
0.18
0.16
u
8 0.14
_i
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I 0.12
OL
U
£ o.io
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O 0.08
z
0.06
0.04
0.02
SHELL HEIGHT, S (m)
too
200
—I—
CHICAGO
36% EFF.
42
42 ft, 12.80 m
49 ft, 14.93 m
66 ft, 17.07 m
63 ft, 19.20m
49
56
63'
I
200
Figure 46(a).
400
SHELL HEIGHT. S (ft)
600
Normalized capacity loss,
36% turbine efficiency, Chicago
152
-------
0.24
SHELL HEIGHT, S (m)
100 150
0.22
0.20
0.18
0.16
CO
O 0.14
< 0.12
o.
u
S o.io
<
o 0.08
0.06
0.04
0.02
200
LOS ANGELES
36% EFF.
42 ft, 12.8O m
49 ft, 14.93 m
^56 ft, 17.07 m
"-63 ft, 19.20 m
56'
200 400
SHELL HEIGHT, S (ft)
600
Figure 46(b). Normalized capacity loss, 36%
turbine efficiency, Los Angeles
153
-------
Q.
0.24'
0.22
0.20
0.18
0.16
50
40
g 0.14
0.12
o.
<
u
S o.io
O 0.08
0.06
0.04
0.02|-
SHELL HEIGHT, S (m)
IOO ISO
200
MIAMI
36% EFF.
42 ft, 12.80 m
49 ft, 14.93 m
56 ft, 17.07 m
63 ft, 19.20 m
200 400
SHELL HEIGHT,S (ft)
600
Figure 46(c)
Normalized capacity loss, 36%
turbine efficiency, Miami
154
-------
0.24"
50
0.22
0.20
0.18
0.16
u
to
g 0.14
>•
H
« 0.12
o.
o
S 0.10
g 0.08
2
0.06
0.04
0.02
SHELL HEIGHT, S (m)
100 150
ZOO
UJ
42'
ST. LOUIS
36% EFF.
"*M2 ft, 12.80m
"" 49 ft, 14.93 m
56 If, 17.07 m
63 ft, 19.20m
200
Figure 46(d).
400
SHELL HEIGHT , S (ft)
600
Normalized capacity loss, 36%
turbine efficiency, St. Louis
155
-------
0.24
SHELL HEIGHT, Sim)
100 150
200
CHICAGO
36% EFF.
42 ft, 12.80m
49 f 1,14.93m
56 ft, 17.07m
63 ft, 19.20m
200
400
SHELL HEIGHT , S (ft)
600
Figure 47 (a). Normalized energy loss, 36%
turbine efficiency, Chicago
156
-------
0.24
0.22
0.20
0.18
0.16
in
8 0.14
O
0.12
UJ
HI
8 o.io
N
g 0.08
0.06
0.04
0.02
50
SHELL HEIGHT, S (ml
100 150
200
T
LOS ANGELES
36% EFF.
PUMP ENER6Y LOSS
.42 ft,12.80m
.49 ft ,14.93m
56 ft, 17.07m
•63 ft,19.20m
200 400
SHELL HEIGHT, S (ft)
600
Figure 47(b)
Normalized energy loss, 36%
turbine efficiency, Los Angeles
157
-------
0.24
0.22
0.20
0.18
£ 0.16
<0 Q
O
_l
2 0.12
in
z
ui
S o.io
N
S
g 0.08
O.O6
0.04
0.02
50
SHELL HEIGHT, Sim)
100 ISO
200
o
PUMP ENERGY LOSS
MIAMI
36 % EFF.
TOTAL (INCL. PUMP)
42 ft, 12.80m
49 ft, 14.93m
56 ft,17.07m
63 ft, 19.20m
56'
JL
0
200 400
SHELL HEIGHT. S (ft)
600
Figure 47(c)
Normalized energy loss, 36%
turbine efficiency, Miami
158
-------
0.24
0.22
0.20
50
SHELL HEIGHT, S (ml
100 ISO
200
0.18 -
*
a! 0.16 -
^
•^
ui
0.14 -
S 0.12
ui
ID
3 o.io -
N
§ 0.08
0.06
0.04
0.02 -
ST. LOUIS
36% EFF.
PUMP ENERGY LOSS
T
TOTAL (INCL. PUMP)
,42 ft, 12.80 m
49 (t ,14.95m
56 ft, 17.07m
63 ft,19.20m
42'
49'
56'
63'
200 400
SHELL HEIGHT,S (ft)
600
Figure 47(d)
Normalized energy loss, 36%
turbine efficiency, St. Louis
159
-------
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£ -0.04
\
f
x
uj -0.06
p-
X
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3
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111
-0.08
-0.10
-0.12
tn
w -0.14
o
X
111
S -0.16
-0.18
-0.20
-0.22
-0.24
50
SHELL HEIGHT, S (m)
100 (TURBINE A)
200
100 200 (TURBINE A)
63 ft, 19.20 m
56ft, 17.07m
49 ft ,14.93m
42 ft, 12.80m
ISO
—T—
200 (TURBINE B,C)
CHICAGO
36% EFF.
400
JL
600 (TURBINE B,C)
Figure 48(a).
SHELL HEIGHT, S (ft)
Normalized excess fuel consumption
36% turbine efficiency, Chicago
160
-------
50
SHELL HEIGHT, S (m)
100 (TURBINE A)
50
100
ISO
200 (TURBINE B,C)
-O.O2
-0.04
F-
x
u -0.06
u.
1
a.
m
z
o
u
_J
-0.08
-O.IO
0.12
S -0.14
u
x
I -°J°
I -0.18
-O.2O
-0.22
-0.24,
LOS ANGELES
36% EFF.
63 ft, 19.20 m
56 ft, 17.0 7m
49 ft, 14.93m
42 ft, 12.80m
200
400
JL
600 (TURBINE B,C)
100
200 (TURBINE A)
SHELL HEIGHT, S (ft!
Figure 48(b). Normalized excess fuel consumption
36% turbine efficiency, Los Angeles
161
-------
-0.02
-0.04
P-
X
UJ
-0.06
o
O
u
UJ
(O
c/>
UJ
u
x
U)
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Z
K
O
-0.08
-0.10
-0.12
-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'
I
I
111
i
1
1
"
1 '
1 '
II
I '
1
11
1
1 1
CD
CO
OL
150
200 (TURBINE B,C)
200
200 (TURBINE A)
MIAMI
36 % EFF.
'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
-------
SHELL HEIGHT, S (m)
-0.02
-0.04
1/-0.06
O
o.
to
z.
-0.08
-0.10
uj -0.12
-0.14
CO
u
o
X
U
g -0..6
-0.18
-0.20
-0.22
-0.24
100
50
100 (TURBINE A)
200
200 (TURBINE A)
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
u
z
CD
or
E
I 8
i
2
5
?
>»
••
i
S 6
v
<
*0
v.
_i
9
*
i
oc
o
a.
i
o
Ul
N
_ 63 ft, 19.20 m —/ '/
56 ft, 17.07
49ft, 14.93m
42 ft, 12.80m
I -
CHICAGO
36% EFF.
J_
200 400
SHELL HEIGHT, Sift)
m
ui
12,000
10,000
8000
6000
ui
5
K
3
12,000
12,000
10,000
10,000 o
8000
800O
6000
6000
4000
4000
Q
K
O
O.
<
UI
o
ui
N
2000
600
Figure 49(a). Normalized evaporation, 36%
turbine efficiency, Chicago
164
-------
50
SHELL HEIGHT, S (m)
100 ISO
ui
5
5
I
o
ec.
O
o.
o
111
1st
£C
§
LOS ANGELES
36% EFF.
- 42 fl, 12.80m
12,000
10,000
8000
6000
12,000
10,000
8000
6000
4000
o
O
4000 <
ui
UI
i
o
UI
i
o
2000
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
oc
3
£ 8
O
S 6
<
g
5 4
K
>
UI
,K
£
a
w
N
U
rr
o
MIAMI
36% EFF.
200 400
SHELL HEIGHT, S (ft)
12,000
10,000
8000
6000
12,000
10,000 o
E
8000 5
«
6000
4000
4000
o
ec
o
01
oa
ui
o
ui
N
1
2000
Figure 49(c). Normalized evaporation, 36%
turbine efficiency, Miami
166
-------
50
SHELL HEIGHT, S (mi
100 ISO
8
S 7
o
•x.
_l
a:
o
a.
<
id
I
Ul
N
(T
ST LOUIS
36% EFF.
63 ft, 19.20m
56 fI, 17.07m
49 f t, 14.93 n>—,
. 42 ft, 12.80m —
12,000
10,000
8000
600O
12,000
10,000 o
3
8000
6000
O
40OO
2
4000 <
til
Ul
i
o
Ul
N
13
cc
o
2000
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)
100 ISO
200
o
0.22
0.20
0.16
0.16
in
8 0.14
>
t
£ 0.12
£L
O
S o.io
N
I
g 0.08
0.06
0.04
0.02
LOS ANGELES
28% EFF.
49'
200
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
-------
0.24
0.22
0.20
0.18
0.16 -
m
o 0.14
< 0.12
a.
o
S 0.10
_i
<
z
O 0.06
0.06 -
0.04 -
0.02
50
SHELL HEIGHT, S (m)
100 ISO
o
200
—I—
MIAMI
28 % EFF.
56'
42 ft, 12.80 m
49 ft, 14.93 m
56 ft, 17.07 m
63 ft, 19.20 m
_L
200
Figure 50(c)
400
SHELL HEIGHT, S (ft)
600
Normalized capacity loss, 28%
turbine efficiency, Miami
170
-------
0.24
50
SHELL HEIGHT, S (m)
100 ISO
200
0.22
0.20
0.18
\ 0.16
_i
o
w
8 0.14
>•
H
S£ O.I2
Q.
O
S O.IO
N
g
g 0.08
0.06
0.04
0.02
I,
to
ul
"!
ST. LOUIS
28% EFF.
, 12.80m
49ft, 14.93 m
56ft, 17,07 m
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)
0.24
0.22
0.20
0.18
0.16
Ul
-------
*
111
a.
tel
-------
SHELL HEIGHT, S (m)
0.24
100
150
200
TOTAL (INCL. PUMP)
56 f t, 17.07 m
63ft, I9.£0m
42'
200
400
SHELL HEIGHT , S (ft)
600
Figure 51(c). Normalized energy loss, 28%
turbine efficiency, Miami
174
-------
SHELL HEIGHT, S (m)
0.24
0.22
0.20
0.18
0.16
0.14
«c
UI
z
UI
S 0.10
N
50
0.06
0.04
0.02
100
150
PUMP ENERGY LOSS
200
1
ST. LOUIS
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
-------
-0
-0.02
Z -0.04
x
,"-0.06
P-
x
z
o
-0.08
g -°-'°
z
o
u
uj -0.12
u.
u>
S -0.14
x
o
111
I
-0.16
-0.18
-0.20
-0.22
,-0.240-
100
50
50
SHELL HEIGHT. S (m)
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
-------
-0.02
-0.04
uT -0.06
•>
p-
X
z -0.08
o
t-
o.
o
u
w -0.12
u.
in
v>
S -0.14
x
u
o
bl
H -0.16
<
ee
o
z -0.18
-0.20
-0.22 -
-0.24,
I
100
50
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
-------
-0.02
ut -o.04
ui-0.06
P-
K
-O.O8
Q.
§ -0.10
m
O
u
UJ
-0.12
-0.14
o
X
UJ
«K
I -0.18
-0.20
-0.22
-0.24
100
SO
—T~
SHELL HEIGHT, S (m)
100 (TURBINE A)
50
100
ISO
200 (TURBINE B,C)
T
ST. LOUIS
28% EFF.
63 ft, 19.20m
66 ft, 17.07m
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
-------
*
ffi
03 I
O
I
«
£
i
2 5
o
S
o
p
K
O
0.
tc..
UI
i
o
ut
1ST
SO
SHELL HEIGHT, S (ml
100 ISO
T
CHICAGO
28% EFF.
o
111
m
K
sf-
63ft
56 ft, 17.07 m
h 49ft, 14.93m
42
ft, 12.80m -/
200 400
St€LL HEIGHT,S (ft)
CD
UJ
m
cr
UJ
ffi
-------
SHELL HEIGHT, S (m)
100 ISO
200
400
SHELL HEIGHT, S (ff)
- 12,000
- 10,000
LOS ANGELES
EFF.
o>
Ul
cc
ut
2
a:
12,000
10,000
12,000
8000
i
*
10,000
8000
6000
4000
2000
6000
4000
i
at
o
a.
bl
S
N
600
Figure 53(b).
Normalized evaporation, 28%
turbine efficiency, Los Angeles
181
-------
50
SHELL HEIGHT, S (m)
100 ISO
56 II, 17.07m
49 ft, 14.93 m
UJ
z
00
12,000
- 12,000
- 10,000
- 8000
- 6000
- 4000
10,000 o
E
w
«
£
i
z
»»
8000 |
>-
6000
-------
50
SHELL HEIGHT, Sim)
100 150
u
w
m
cc.
ST LOUIS
28% EFF.
o
E
0
I
o
5
*
•
1
O
Q.
<
111
K
Ul
i
o
111
N
K
i
63ft, 19.20 m
56 fl, 17.07m—'
49ft, 14.93 m —
42 f 1,12.80m —
200
111
m
K.
cn
(C
12,000
10,000
8000
6000
12,000
{10,000
2,000
o
k.
•
J8000 *
10,000
>-
•»»
*>
^6000 ,-~
8000
-HOOO
6000
4000
4000
O
o.
ui
K
UJ
I-
o
M1
N
_J
«t
2000
Figure 53(d)
400 600
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
-------
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
O
8 *— •
*
O
<
-------
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
*
el-
's.
_l
UJ
co"
CO
o
0.10
O.08
o
a:
UJ
z
w 0.06
O
UJ
N
< 0.04
2
O
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
UJ
»
CO
tn
0.12
0.10
QL
U
Z
UJ
s
N
0.08
0.06
(E
O
z
0.04
0.02
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
Z
8 -o.io
UJ
(0
(O
UJ
O
UJ
Nl
o:
o
-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
o 20
E
18
S 16
u
o
*
O
12
O 10
ec
o
UJ
DC
UJ e
O
UJ
N
-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
•x.
V.
O
% 1
i
2
141
O
•s.
_j
101
(C
o
Q.
UJ
>
•^
n£
16 'o
-------
22
o 20
I
I 18
,c
>» .16
i
o>
8 14
*
O
12
O
cc
o
I s
UJ
(T
UJ
I
O
UJ
N
22 7
55
20 i
ID
10
O
16
*
O
12
o:
10
8
UJ
8 K
0 UJ
.«
UJ
N
4 ^
2
cc
2 i
_L
_L
_L
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
-------
22
o 2O
E
5 18
2
-X
O
2. 16
*-
**•
t
£
°, 14
*
o
Of.
o
a.
oc.
UJ
N 4
<
5
a:
§ 2
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
a>
18
PO
O
16
O
12
10
CL
|
Ul
cr
6 a
UJ
N
a;
2
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
-------
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
-------
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
-------
UJ
2
5
m
UJ
z
m
tr
o
UJ
z
CO
I- H
0.12-1 0.16-1 0.18
0.10-
O.O8 -
UJ
to O.O6 -
CO
O
0.04 -
a:
UJ
-z.
UJ
0 0.02 -
N
a:
o
0.14-
0.12-
0.10-
0.08 -
0.06 -
0 J 0.04 -
0.02-
O.16
0.14
0.12
0.1O
O.O8
O.O6
0.04
0 J 0.02
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
-------
< CO o
tU LU
00
UJ
_ 2
CD CD
01 CC QC
r> ^ n>
b t fc
O.08-1 0.16-1 0.18
0.06-
UJ 0.04 -
UJ
en
-------
LU
z
CD
QL
GO U
UJ
z
CO
DC
0.06-1 .014 -i O.18 -
0.04-
0.02-
UJ
to
§
I
UJ
Q
UJ
M
cc
o
0J
.012-
.010-
0.08-
0.06-
0.04-
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
UJ
z
m
o:
o
LJ
Z
m
o:
0.10-, 0.16-, 0.18
0.08 J
UJ
of 0.04 H
CO
o
0.02
CC
o
0.14-
0.12-
0.10-
0.08-
tr
UJ
UJ
Q 0J0.06-|0.08
UJ
NI
0.04-
0.02-
0.16
0.14
0.12
0.10
0.06
0.04
0J0.02 -
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
-------
*UJ
Q.
UJ
li.
1-0.02
-0.04
Q.
5
z
o
o
CO
CO
UJ
o
X
UJ
o
UJ
N
DC
O
-0.06
-0.08
-0.10
-0.12
-0.14
LOS ANGELES
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
u!"
:. -0.02
p -0.04
a.
to
•z.
o
o
O
-0.06
-0.08
V)
C/>
S -0.10
X
lli
o
lil -0.12
r"J
-0.14
0.2
0.4 0.6 0.8 1.0 1.2
(TURBINE A,B)
0 0.2 0.4 0.6 0.8 1.0
(TURBINE C)
NORMALIZED CANAL SIZE, N/N*
Figure 70(d). Normalized excess fuel
consumption, St. Louis
260
-------
o
§
QJ
10 -
8 -
5
O
OC
UJ
(E
UJ
I
UJ
M
o:
o
0 J Z- 4 -
0.2 0.4 0.6 0.8 1.0 1.2
NORMALIZED CANAL SIZE, N/N*
- 12000
- 10000
- 8000
- 6000
- 4000
- 200O
1.4
m
UJ
z
m
cc.
o
« r12000 £
a: I |
i
s
12000
- 100OO
10000
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8000
6000
4000
2000 L 0
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4OOO g
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- 2000 a;
UJ
a
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Nl
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Figure 71(a). Normalized evaporation, Chicago
261
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<
— * III
o ~r
£*£
_*
w ff^
£ z> £
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•x 12 -i
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-
-
m = ) TURBINE A
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(-
12000
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8000
6000
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-6000
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Lo g
4.
0
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
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
UJ
£
o:
t-
r12000
m
cc.
r 12000
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E
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- 10000
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-6000
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Figure 71 (c). Normalized evaporation, Miami
263
-------
6
8 -
o 4 H
a.
Q 0 J
UJ
M
- 8000
-6OOO
-400O
O
a.
-2000
1.4
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a:
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I
a
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S
cr
O
z
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
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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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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, $/kW-hr or mills/kW-hr
288
-------
APPENDIX II
LIST OF INPUTS TO COMPUTER PROGRAMS
289
-------
POWER PLANT CHARACTERISTICS
(1) Turbine Characteristics
9
(a) HR, Heat rejection rate matrix (10 Btu/hr)
(b) IHR and IPMAX, Number of rows of heat rejection rate matrix
(c) NPL, Number of columns of heat rejection rate matrix
(d) TBP, Design turbine back pressure (in. Hg abs)
(e) TPMAX, Maximum turbine back pressure (in. Hg abs)
(f) TLOW, Lowest turbine temperature in heat rejection rate
matrix (°F)
(g) FINC, Increment of temperature in heat rejection rate
matrix, (°F)
(h) EF, Base turbine efficiency for HR matrix
(i) EN, Alternative base turbine efficiency
(2) Plant Capacity
(a) PLMAX, Maximum plant capacity (MW)
(b) DPL, Power interval (=1/10 maximum plant capacity (MW)
(c) PLMIN, Minimum plant capacity (MW)
(d) LP, Power level
(e) TTDD, Design terminal temperature difference (°F)
(f) IPLI, Initial power level index
(g) IPLF, Final power level index
(h) MM, Interval of power level index
(i) CF, Fraction of full load
(j) EFI, in-plant efficiency
(k) NYEAR, Remaining life of plant (years)
SITE CHARACTERISTICS
(1) TDBD, Design Dry-Bulb Temperature (°F)
(2) TWBD, Design Wet-Bulb Temperature (°F)
(3) TDB10, Extreme Dry-Bulb Temperature (°F)
(4) TWBlO, Extreme Wet-Bulb Temperature (°F)
(5) PERCEN, Temperature Distribution (Fraction)
290
-------
(6) ITWBI, Initial Wet-Bulb Temperature (°F)
(7) ITWBF, Final Wet-Bulb Temperature (°F)
(8) ITDBF, Final Dry-Bulb Temperature (°F)
(9) ITBD, Temperature Interval (°F)
(10) TWBREF, Reference Wet-Bulb Temperature (°F)
•(11) FOGL, Upper Limit of Medium Fogging (°F-lb H 0/lb air)
(12) FOGM, Upper Limit of Medium Fogging (°F-lb H 0/lb air)
ECONOMIC PARAMETERS
(1) Unit Costs
(a) UNCOND, Condenser ($/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 ($/1000 Btu)
(d) DRH, Relative humidity in unit cost matrix
(e) NOITT, Number of iterations in NTU calculations
(f) FRIFAC, Smooth pipe curve from Moody chart
(g) Tower size
(i) WIDTHW, Pile width (ft)
(ii) BASEDI, Base diameter (ft)
(iii) HTND, Total tower height (ft)
(iv) FILLHT, Pile .height (ft)
(h) ELEV, Elevation of site from sea level (ft)
(i) Tower parameters
(i) AW, Proprietary pile coefficient
(ii) BW, Proprietary pile coefficient
293
-------
(j) EFFICW, Water pump efficiency
(k) HEIGHT, Pumping height (ft)
2
(1) AFRL, Air flow rate loading (Ib/hr/ft -face area)
2
(m) WFRL, Water flow rate loading (gpm/ft -plan area)
(n) SLANDA, Specific land area (acres/MW)
2
(o) UO, Overall heat transfer coefficient (Btu/hr/ft /°F)
(3) Cooling Ponds
(a) NNOTSI, NNOTS, Parameter for different water loadings
(b) NOWTSI, NOWTS, Parameter for different pond areas
(c) RHO, Specific weight of water (Ib/ft )
(d) C, Specific heat of water
(e) MONTH, Index for month of year
(f) W2, Wind speed at 2 meters above ground (miles/hr)
(g) QSC, Clear sky solar radiation (Btu/ft /day)
(h) AMR, Average monthly reflection (fraction)
(i) UPOND, Unit cost of pond ($/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
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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
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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
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