EPA-660/2-73-004
September 1973
Environmental Protection Technology Series
omographs For Thermal Pollution
lontrol Systems
Office of Research and Development
U.S. Environmental Protection Agency
Washington, D.C. 20460
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and
Monitoring, 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 Office of Research and
Development, EPA, and approved for publication. Approval
does not signify that the contents necessarily reflect the
views and policies of the Environmental Protection Agency,
nor does mention of trade names or commercial products consti-
tute endorsement or recommendation for use.
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EPA-660/2-73-004
September 1973
NOMOGRAPHS FOR THERMAL
POLLUTION CONTROL SYSTEMS
By
Charles L. Jedlicka
Project 16130 HKK
Program Element 1BB392
Project Officer
Dr. Bruce A. Tichenor
National Environmental Research Center
U.S. Environmental Protection Agency
Corvallis, Oregon 97330
Prepared for
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
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ABSTRACT
Nomographs are presented and described which permit the estimation
of heat rejection system performance, tower or pond capital costs and
the perturbations to power plant efficiency and costs which result
from the incorporation and operation of any one of the following thermal
pollution control systems within a power plant as a substitute for
one e- through c ooling:
® natural draft wet towers
* mechanical draft wet towers
@ spray ponds
© cooling ponds
» natural and m'eeJaSriica4rdr:kft'<>yf>y :tbw.ers
The base case plant for cost comparisons is chosen as having a
nominal turbine back pressuv^of'-Z ih.'.'tH-g 'absolute. The total heat
rejection system with its assocfated'c'DSts is defined to extend out-
ward from the turbine exhaust flange, a common boundary for each
of the systems mentioned above.
Performance and capital costs for the thermal pollution control
systems were compared with data from existing facilities and
theoretical estimates from various sources.
This report was submitted in fulfillment of Contract No. 68-01-0171
by Hittman Associates, Inc. under the sponsorship of the Environ-
mental Protection Agency. The principal author is Mr. Charles
Jedlicka, Hittman Associates, Inc. , Columbia, Maryland 21045.
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CONTENTS
Section Page
I Conclusions 1
II Recommendations 3
III Methodology of Nomograph Preparation 5
IV Natural Draft Wet Towers 11
V Mechanical Draft Wet Towers 21
VI Spray Ponds 29
VII Cooling Ponds 33
VIII Mechanical and Natural Draft Dry Towers 41
IX Steam Turbine Generator Performance 49
X Makeup Water Requirements 55
XI Costs for the Heat Rejection Systems 61
XII Nomograph Examples 69
XIII Acknowledgments 101
XIV References 103
XV Nomenclature 107
XVI Appendix (The Nomographs) 111
ill
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FIGURES
Pape
Number s—
1 Nomograph Utilization Flow 6
2 Types of Natural Draft Wet Towers 12
3 Comparison of Tower Performance
{Research-Cottrell vs Keystone) 14
4 Comparison of Tower Performance
(Research-Cottrell vs PNWL) 15
5 Crossflow Induced Draft Tower 22
6 Types of Heat Rejection System Operation 24
7 Spray Pond 30
8 Cooling Pond Systems 34
9 Indirect, Dry-Type Heat Rejection
System with Natural Draft Tower 42
10 Indirect, Dry-Type Heat Rejection
System with Mechanical Draft Tower 43
11 Natural Draft Wet Towers 163
12 Mechanical Draft Wet Towers 164
13 Spray Ponds 165
14 Cooling Ponds 166
15 Dry Towers 167
16 Turbine Performance 168
17 Water Requirements 169
18 Costs 170
19 Costs (Continued) 17
iv
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TABLES
JNumber Page
1 Comparison of Nomograph Performance to
Existing Plant Design Conditions 16
2 Comparison of Capital Costs for Existing
Natural Draft Towers 19
3 Cooling Pond Performance 38
4 Cooling Pond Evaporative Loss 56
5 Nomograph Example - Natural Draft Wet Tower 70
6 Nomograph Example - Mechanical Draft Wet 72
Tower (Closed Cycle)
7 Nomograph Example - Mechanical Draft Wet
Tower (Open Cycle) 74
8 Nomograph Example - Spray Pond (Closed
Cycle) 77
9 Nomograph Example - Spray Pond (Open
Cycle) 79
10 Nomograph Example - Cooling Pond (Closed
Cycle) 81
11 Nomograph Example - Cooling Pond (Open
Cycle) 83
12 Nomograph Example - Natural Draft Dry Tower 86
13 Nomograph Example - Mechanical Draft Dry 88
Tower
14 Nomograph Example - Water Requirements 9°
(Case 1)
15 Nomograph Example - Water Requirements 92
(Case 2)
16 Nomograph Example - Costs (Case 1)
94
17 Nomograph Example - Average Annual Operating 96
Costs (Case 1)
18 Nomograph Example - Cost of Once-Through 97
Cooling (Case 2)
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SECTION I
CONCLUSIONS
The nomographs developed on this project and presented in this report
provide for the estimation of heat rejection system performance, tower
or pond capital costs and the perturbations to power plant efficiency and
costs due to the presence of a thermal pollution control system at a
power plant site. The nomographs are intended primarily for the use of
regulatory organizations, such as the Environmental Protection Agency
(EPA) for making rapid checks on design cost data generated by contractors
or utilities. They are also intended to provide engineers and managers
concerned with the performance and costs of proposed cooling systems
with a tool for identification of critical factors and for rapid estimation
of their impact on operating efficiencies and costs, capital investment
requirements, and the site environment. The nomographs are not
intended to be used for design optimization purposes.
As a result of developing the nomographs, specific comments can be made
regarding the performance and capital costs of pertinent thermal pollution
control systems. The performance nomograph for natural draft wet
towers is satisfactory for the general application of making performance
estimates following comparisons with several sources. For mechanical
draft wet towers, the capital costs predicted by the nomographs show
good correlation with those from other sources. Due to limits on avail-
abile data the scope of the spray pond nomographs is confined to conven-
tional spray ponds only, excluding powered spray modules (PSM). The
cooling pond performance nomographs (open and closed cycle operation)
provide reasonable estimates of cooling pond size based on comparison
of results from various other sources.
It was assumed in the nomographs that at a given plant site, the rated
output would be required under all site conditions. In so doing, it is
assumed that the generator can take a certain overload steam rate.
However, for existing plants the overload ability may be limiting for
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certain thermal pollution control systems. The nomographs are readily
applicable to new plants where the additional heat capacity required can
be made available.
The turbine performance nomographs are based on a conventional steam
turbine generator modified for operation at higher back pressure. A
new plant employing dry towers will be designed to utilize a high back
pressure turbine, when they become commercially available, whose
performance and costs are different from those of conventional units.
However, the nomographs are satisfactory in treating the utilization of
dry towers in new plants. The use of dry towers on existing plants will
almost always be economically unfeasible.
The nomographs yield performance, water requirements and costs for
heat rejection systems operating under design meteorological conditions
and full load plant operation. Examples are presented to show how
average annual water requirements from evaporation and average annual
operating costs can be estimated.
It is important to evaluate water requirements and the annual operating
costs under the off-design conditions actually occurring during the year
at a given site.
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SECTION II
R ECOMMENDATIONS
Cascaded system designs considering combinations of cooling systems
such as evaporative towers and dry towers, designated wet/dry cooling
towers, could feasibly be nomographed. New spray cooling systems
have been developed such as the powered spray systems (Ceramic, Rockford,
Ashbrook) and the Cherne fixed thermal rotor system. Therefore, it
is recommended that the scope of the nomographs be enlarged to include
these and other new systems.
A technical handbook or data book could be prepared for thermal pollu-
tion control systems. It would include background, detailed descrip-
tions, performance and equations based on the current sources for
these systems. The newest technology on powered spray systems
and dry towers would be included. Actual operating data would be in-
cluded for existing thermal pollution control systems from sources
such as the power plant and Federal Power Commission Form 67. It
is recommended that this handbook be prepared.
There are more recent studies available that consider the application
of dry type towers in new plants. This is also true for the other
thermal pollution control systems. Thus, it is recommended that
the nomographs be updated periodically in order to incorporate new
data on performance and costs.
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SECTION III
MKTHODOLOGY OT NOMOGRAPH PREPARATION
Introduction
The selection of a type of heat rejection system, or a system for thermal
pollution control, for use at an electric utility site depends upon the com-
parisons of many parameters. The purpose of the nomographs developed
and presented in this report is to take input data such as site weather data,
power plant data, and economic conditions in the locale and allow one to
estimate significant output parameters. These are heat rejection system
performance, cooling tower or pond capital costs, and the perturbations
to power plant efficiency and costs. Thus, the key factors and parameters
from the various alternative systems can be quantified and analysed at a
given utility plant site following application of the nomographs.
In the next section, the general procedure to be followed when using the
nomographs is schematically presented. In succeeding major sections,
each type of thermal pollution control system is described. The nomo-
graphs for each system are discussed. The development of the turbine
performance, water requirements, and cost nomographs is discussed.
In general, output parameters were determined from the given input para-
meters based on either direct functional relationships or from available
analytical or experimental data.
Section XII contains illustrative examples for each of the thermal pollu-
tion control systems. All of the nomographs are then presented together
in the Appendix. They are easily referred to in conjunction with the
instructive sample cases preceeding them.
Nomograph Utilization Flow
Utilization of the nomographs for thermal pollution control systems
follows a flow presented schematically in Figure 1. The nomographs
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Site Weather Data
Power Plant Data
Tower or Pond Perfor
mance Nomographs:
Wet Towers
Dry Towers
Spray Ponds
Cooling Ponds
Turbine
Back
Pressure
» Water Flow
Rate
• Auxiliary
Power
• Tower or Pond
Cost
Water
Requirements
Nomographs
Makeup
Water
Requirements^
Heat
Rejection
Rate
Cost
Nomographs
Turbine
Performance
Nomographs
Additional
Heat
Capacity
• Annualized Capital
Cost
• Additional Power Cost
• Additional Fuel Cost
• Incremental Generating
Cost
Plant
Efficiency
Figure 1. Nomograph Utilization Flow
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can be organized into the four basic classifications enclosed in the boxes:
Tower or pond performance nomographs
Turbine performance nomographs
Water requirements nomographs
Cost nomographs
The general procedure one follows to obtain output parameters is ex-
plained in the following paragraphs with the aid of Figure 1.
Performance nomographs were developed for the following heat rejection
systems:
Natural draft wet towers - closed cycle operation
Mechanical draft wet towers - closed and open cycle
operation
Spray ponds - closed and open cycle operation
Cooling ponds - closed and open cycle operation
Mechanical draft and natural draft dry towers -
closed cycle operation
Tower or pond performance is dependent upon the design weather condi-
tions chosen at the site such as wet bulb temperature, dry bulb tempera-
ture, and relative humidity. Steam turbine back pressure is then deter-
mined from the resulting cold water temperature, the range and the
terminal temperature difference (see Section XV for nomenclature).
The turbine performance nomographs take as input the turbine back
pressure and power plant data such as net generating capacity or size,
type (fossil or nuclear), and base plant heat rate. Light water reactor
plants have plant efficiencies ranging from approximately 31 to 33 per-
cent while high temperature gas-cooled reactor plants have plant effi-
ciencies similar to those of fossil-fueled plants. Thus, in the subsequent
discussions, the term nuclear will mean light water reactor plants. For
the purposes of heat dissipation, HTGR plants are similar to fossil-
fueled plants. The heat rejection rate for the cooling system is determined.
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The presence of the cooling tower or pond necessitates the requirement
of an additional heat capacity in order to maintain the rated plant output.
This imposes a cost penalty determined later in the cost nomographs.
The presence of the thermal pollution control system usually results in
an increase of turbine back pressure and thus a lower plant efficiency
for the power plant when compared to the base plant operating at 2 in.
Hg absolute turbine back pressure.
The tower or pond performance nomographs are returned to, with the
heat rejection rate. The water flow rate, auxiliary power requirements,
and the tower or pond capital cost are determined. All costs correspond
to the year 1971 (ENR Construction Cost Index 1570).
The water requirements nomographs estimate the makeup water quantity
required for each type of heat rejection system. The components of
makeup water are attributed to drift, evaporative, and blowdown losses.
In the cost nomographs, "incremental costs" are determined as being
the various additional capital and operating costs required to incorpor-
ate and operate the thermal pollution control system within the power
plant. The base case plant for cost comparisons is chosen as having a
nominal turbine back pressure of 2 in. Hg absolute. Thus, additional heat
capacity would be required for operation at turbine back pressures above
this level. It was assumed that the turbine generator can take a certain
overload steam rate. In computing the cost of the loss of efficiency
from operation above 2 in. Hg absolute, one needs to distinguish between
added fuel costs and capability losses. In the nomographs, added fuel-
costs are computed as a result of the operation of the plant above the
base level of 2 in. Hg absolute. In contrast, capability losses and
their associated cost penalty are considered only when the turbine back
pressure exceeds some maximum value such as 3. 5 in. Hg absolute.
Also capability loss can be made up with base load (assumed in the nomo-
graphs) or peaking units. If it is made up with base load, additional
revenue at turbine back pressures less than 3. 5 in. Hg absolute should
be assessed since it reduces the average annual cost of the capability
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loss. Thus an accurate assessment of all of the various "incremental
costs" is a complex problem which exceeds the scope of the nomographs.
The total heat rejection system with its associated costs is defined to
extend from .the turbine exhaust flange, a common boundary for all of
the thermal pollution control systems. Incremental plant costs are
determined separately in the nomographs for the steam supply (either
fossil or nuclear plants) and for the turbine-generator plant. Installed
capital costs for condensers of different tube materials are determined.
The cost of the water circulation system is estimated including pumps,
motors, piping, and installation. After summing these capital cost
components with the tower or pond cost, the total incremental capital
cost is obtained.
The fixed charge rate depends upon the economic conditions at the site
locale such as interest rate, amortization period, interim replacement,
insurance and various taxes. Then the annualized capital cost is deter-
mined from a nomograph using the fixed charge rate and the total
incremental capital cost.
Additional power cost and additional fuel cost are two "annual"
operating costs determined in the cost nomographs. However, they
are based only on design conditions and are thus not true annual costs.
Operation under off-design conditions must be evaluated in order to
determine true annual costs. These two "annual" costs are summed
with the annualized capital cost yielding the total incremental "annual"
cost. Finally, the incremental generating cost in mills/Kw-hr is
obtained.
Each type of heat rejection system utilizes the turbine performance
nomographs and the water requirements nomographs which are common
to all of the systems. Also, the output of all tower or pond performance
nomographs feeds into the set of cost nomographs which are common to
all systems.
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SECTION IV
NATURAL DRAFT WET TOWERS
System Description
The first natural draft wet tower in the United States was built in late
1962 at the Big Sandy Plant of the Kentucky Power Company. The tower
is 245 feet in diameter and 320 feet high. Currently natural draft wet
towers range in size from 250 feet to 400 feet in diameter with heights
from 320 to nearly 500 feet. They are basically a large chimney that
provides a draft to pull air over a large surface of water.
Natural draft towers are usually constructed from reinforced concrete.
The hyperbolic shape distributed across the great height is optimum for
aerodynamic and structural reasons rather than thermodynamic. The
basic components of counterflow and crossflow tower types are shown
in Figure 2. The tower and packing can be designed to operate with air
flowing upward through the packing (counterflow) or horizontally across
the packing (crossflow).
Among the advantages of natural draft wet towers are long term mainte-
nance free operation, smaller amounts of ground space required for
multiple towers, reduced piping costs when towers can be located adja-
cent to plant, no electricity required for operating fans, fewer electrical
controls and less mechanical equipment. Disadvantages include a
decreased ability to design as precisely as for mechanical draft towers,
and inability to control outlet temperatures as well as with mechanical
draft towers. Also, because of their large size natural draft towers
tend to dominate the landscape.
Discussion of the Nomographs
In the Appendix, the nomographs for natural draft wet towers are found on
pages N-l through N-6. The development of these nomographs and their
underlying assumptions are discussed in the following paragraphs.
11
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to
Hot
Water
Distri-
bution / Eliminator
UUllUM fr/f/f,//,,,,,,,,,,
Cold Water'
Basin
' V • * x •
• •'--•' - •
Hot Water /,' Drift
J4.
•Cold Water
Basin
Counterflow
Crossflow
Figure 2. Types of Natural Draft Wet Towers
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The Tower Performance nomograph, page N-l, is based on a para-
metric study performed by Research-CottrelKRef. 1). Cold water
temperature (CWT) is obtained as a function of dry bulb temperature
(DBT), relative humidity and variations in tower height. A design
condition assumed to be fixed in the performance study was a base
diameter of 300 feet.
The performance data from Research-Cottrell were compared to data
from other sources in order to determine the degree of general appli-
cability of the performance nomograph. In Figure 3, the performance
data for the base diameter of 300 feet and a height of 350 feet is com-
pared to the performance of the Keystone plant towers (Ref. 2) of
247 feet in diameter and 325 feet high. At 100 percent relative humidity,
the curves compare very closely. The curves for 50 percent relative
humidity are close at lower dry bulb temperatures and then diverge from
one another at the higher temperatures. The curves at 20 percent
relative humidity deviate by 1. 5°F at 50°F dry bulb and by 3°F at 80°F
dry bulb.
Data from Research-Cottrell for the base diameter of 300 feet and a
height of 400 feet are compared in Figure 4 to the corresponding data
reported by the Pacific Northwest Water Laboratory (PNWL) in
Reference 3. Generally, a comparison between two curves of equal
relative humidity shows a siingl
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100
65
40
50
60 70 80
Dry Bulb Temperature (°F)
100
Figure 3. Comparison of Tower Performance
(Research-Cottrcll vs. Keystone)
14
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100
65
40
50 60 70 80
Dry Bulb Temperature (°F)
Figure 4r Comparison of Tower Performance
(Research-Cotirell vs PNWL)
100
15
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TABLE 1. COMPARISON OF NOMOGRAPH PERFORMANCE
TO EXISTING PLANT DESIGN CONDITIONS
Tower
Height
Plant Ft
Big Sandy
No. 1 322
Keystone
Nos. 1 & 2 325
Ft. Martin
Nos. 1 & 2 371
Paradise
No s.l. 2, &3 43S
Muskingum
River 371
Big Sandy
No. 2 371
Conemaugh
No. 1 371
Tower Total Tower Design Basis
Base Flow Relative
Diameter Rate Range Approach WBT DBT Humidity
Ft 106 gpm OF OF OF °F %
244 0.12 23 15 72 79.5 70
247 0.56 28 18 72 86.5 50
377 0.50 24 18 72 86.5 50
320 0.26 27.5 22.6 72.6 78 78
394 0.22 24 16 70 77 71
397 0.25 28.7 16 70 77 71
288 0.28 28 18 72 86.5 50
WBT +
Approach
OF
87
90
90
95.2
86
86
90
CWT
From
N-l Error
OF °F
91.5 4.5
92 2
91 1
92 -3. 2
88 2
38.5 2.5
92.3 2.3
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The Tower Performance nomograph predicts the design performance
from these plants to within from 1°F to 4. 5°F. In conclusion, as a
result of the various comparisons presented, the Performance Nomo-
graph is assumed to be satisfactory for the general application of
making performance estimates. However, it is realized that a unique
set of performance curves exists for towers at each plant site.
The Turbine Back Pressure nomograph, page N-2, allows one to deter-
mine the steam turbine back pressure through the following relationships:
turbine back pressure, in. Hg absolute = f (steam
condensing temperature or saturation temperature) (2)
steam saturation temperature = cold water tempera-
ture + condenser rise + terminal temperature
difference (TTD) (3)
The cold water temperature is an input obtained from the first nomo-
graph. The range is the temperature decrease in the tower. The
range of the natural draft tower is equal to the condenser rise
because only closed cycle operation is assumed for the system.
Ranges from 24°F to 32°F cover those for existing towers. The
terminal temperature difference (TTD) is assumed constant at 6°F
throughout. It can range from 5°F to 10°F. Reference 4 indicates
that TTD must exceed 5°F at design conditions. This is a minimum
level established by the Heat Exchange Institute. Steam tables were
then employed to obtain the absolute turbine back pressure correspon-
ding to a steam saturation temperature.
The Tower Unit Cost nomograph, page N-3, is based on the cost per-
formance curves for budget estimates presented by the Marley Company
(Ref. 4). These data were reduced so that the nomograph yields the unit
tower cost in dollars per thousand Btu/hr versus wet bulb temperature
(WBT), range and approach. The relative humidity was eliminated as
a variable since unit tower costs at 50 percent relative humidity best
represent the design conditions from existing towers. Reference 4
also presented data for 25 percent and 100 percent relative humidities.
17
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The unit costs from Reference 4 were corrected prior to plotting in order
to represent 1971 costs. An annual factor based on the Engineering News
Record was employed. The input wet bulb temperature is determined from
a psychrometric chart and corresponds to the dry bulb temperature and
relative humidity chosen as entry design conditions to N-l. The approach
parameter is the difference between the cold water temperature deter-
mined from N-l and the wet bulb temperature.
The Tower Unit Cost nomograph is based on cost data which will be
shown to estimate capital costs for several existing towers better than
a cost equation presented in Reference 5. This equation is based on the
calculation of capital costs for British Towers:
tower capital cost = $3, 4 x 10^ x (height of tower in ft
times diameter of tower in ft)- ^ (4)
The capital cost comparison for towers at four existing plant sites is
presented in Table 2. The design conditions are shown. The installed
cost for each plant in the year of installation was determined from FPC
Form 67 (Ref. 6). The installed cost excludes only the cost of the con-
denser. Each cost was then corrected to 1971 using factors from the
Engineering News Record.
From the design conditions for each tower, the capital cost was deter-
mined from the Marley cost performance curves. Capital costs from
equation (4) were computed. Before a direct comparison could be made
between the Marley and Reference 5 costs and those of Form 67, an
incremental cost for the water circulation system was added to the former.
This amounted to $0. 23 x 106 for the Keystone Tower and $0. 41 x 106 for
the other towers. Water circulation system cost includes capital costs
for pumps, motors, piping and installation. In all cases, excluding
Conernaugh, the costs based on the Marley data were closer to those
obtained from Form 67. It was observed, in passing, that for Big Sandy
No. 2 the tower unit cost at 50 percent relative humidity was only 7 per-
cent higher than the one at the design condition of 71 percent relative
humidity.
18
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CD
TABLE 2. COMPARISON OF CAPITAL COSTS FOR
EXISTING NATURAL DRAFT TOWERS
WBT
Plant °F
Keystone
No. 2a 72
Ft. Martin
No. 2 72
Big Sandy
No. 2 70
Conemaugh
No. 1 72
Tower Design Basis
Percent Range Approach
RH °F °F
50 28 18
50 24 18
71 28.7 16
50 28 18
Form 67 Installed
Cost Corrected to
1971 - $106
4.04
6.88
5.47
3. 64
1971 Capital Cost 1971 Capital Cost
Based on Marley From Ref. 5
Data - $106 Eon. - $1Q6
2. 98 2. 87
5.13 3.33
5. 96 3. 22
5.87 3.37
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The Tower Cost nomograph,, page N-4, is used to obtain the natural draft
tower cost in millions of dollars. This capital cost is obtained from the
multiplication of the heat rejection rate by the tower unit cost. The heat
rejection rate is an input from the turbine performance nomographs. The
tower unit cost is the output of N-3.
The Flow Rate nomograph, page N-5, yields the water flow rate in mil-
lions of gpm. The following equation is employed:
water flow rate, gpn, = heat rejection rate Btu/hr
&K condenser rise, °F x 500 * '
In this equation, the specific heat of water is 1 Btu/lb°F, and 500 is a
conversion factor. Heat rejection rate is an input from the turbine
performance nomographs. Under closed cycle operation the condenser
rise is equal to the range of the natural draft tower. A detailed explana-
tion of the effects of closed cycle operation versus open cycle operation
is given in Section V.
The Auxiliary Power nomograph, page N-6, yields the auxiliary power
requirements in Mw. The power requirements for the natural draft
tower are due to circulating water pumps only. The pump power require-
ments are obtained from the following equation:
,. water flow rate, gpm x total head, ft
pump power, Mw = ' -p-f -. !
v ^ ^ purnp efficiency
x 1. 88 x 10-7 (g)
The water flow rate is an input from the previous nomograph. The pump
efficiency is assumed to be 0. 85. Total head consists of pumping head
plus head losses such as friction. The range of total head shown in the
nomograph is justified from three sources. In Reference 1, a data sheet
summarizing potential natural draft tower designs at one large plant site
indicated a range of pump heads from 40 to 55 ft. At the Keystone
Plant (Ref. 2), water enters the natural draft towers approximately
42 ft above the basin. A total head of 75 ft was assumed in the cost
cases analysed in Reference 4 considering usage of natural draft towers
at a large nuclear plant site.
20
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SECTION V
MECHANICAL DRAFT WET TOWERS
System Description
Mechanical draft wet towers are divided into two categories, forced air
flow and induced air flow. Induced draft towers are further subdivided
into counterflow and crossflow towers. Induced draft towers are
favored over forced draft towers (Ref. 7). Crossflow induced draft
towers have advantages over counterflow induced draft towers and are
most commonly used. Figure 5 shows the basic arrangement of a cross-
flow induced draft tower.
Crossflow induced draft towers can usually attain better thermal perfor-
mance than counterflow towers, i. e., heavier water loadings, longer
ranges and closer approaches. For a specified applied horsepower a
greater airflow is possible in crossflow towers because of lower static
losses, and thus they are more efficient. Other advantages of the
crossflow induced draft tower include low pumping head, convenient
arrangement of the distribution system, the fill height approximately equal
to the tower height, more air flow per fan horsepower, and the ability
to use fans of larger diameter so that fewer cells are required for a given
capacity. Disadvantages are an insufficient pressure head on the distri-
bution pans to keep the orifices from becoming clogged and the entire
water feed exposed to the air which favors growth of algae. Also a sub-
stantial crossflow correction factor needs to be applied to the driving
force, particularly where long range and close approach performance are
required.
Discussion of the Nomographs
The nomograpns lor the mechanical draft wet towers are found on pages
N-7 through N-12 of the Appendix. The development of each of these
nomographs is discussed in the following paragraphs.
21
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Air Out
Water In
Air In
Water^
Out
Packing
Air In
Figure 5. Crossflow Induced Draft Tower
22
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The Tower Correction Factor nomograph, page N-7, is based on the
rating factor curves for large plants published by the Marley Company
in Reference 4. The tower correction factor (synonymous to Marley's
rating factor) is a function of wet bulb temperature, range and approach.
The limits of these input parameters cover all of the most logical
design conditions relative to the electric utility industry.
The Turbine Back Pressure nomograph, page N-8, yields the condenser
inlet temperature and the steam turbine back pressure. The tempera-
ture of the cold water leaving the tower, or tower effluent temperature,
equals the sum of the wet bulb temperature and the approach. Under
closed cycle, operation, the tower effluent temperature is equal to the
condenser inlet temperature. The turbine back pressure is a function of
the steam saturation temperature which is determined from equation (3).
The Flow Rate nomograph, page N-9, yields the water flow rate from
equation (5). Under closed cycle operation the condenser rise is equal
to the range of the mechanical draft tower. The types of operation for
a heat rejection system are defined with the aid of Figure 6. In the
figure, the closed cycle case shows an example where both the range
and condenser rise are equal to 25°F. The cooling water is totally
recirculated except for a small quantity of makeup water necessary
to replace evaporative, drift and blowdown losses.
Open cycle cooling is also illustrated by an example in Figure 6.
Hot water from the condenser is passed through a supplementary heat
rejection system (wet tower or pond) for cooling prior to discharge
into a natural receiving body (stream, river, bay or ocean). An
allowable temperature difference is defined as being the temperature
of the hot discharge water from the heat rejection system into the
stream minus the temperature of the water available from the stream.
The temperature of the water available from the stream is equal to
the condenser inlet temperature, an input to N-8 for the open cycle case.
The allowable temperature difference usually ranges from 0°F to 5°F
maximum, and depends upon site characteristics and legal requirements.
23
-------
100°F
Heat
Rejection
System
Range = 25°F
100°F
Condenser
Condenser
Rise = 25<>F
Closed Cycle
100°F
Heat
Rejection
System
Range = " 25°F
100°F
Condenser
75°F
75°F
Natural
Receiving
Body
Cond_enser
Rise = 30°F
Open Cycle
Figure 6. Types of Heat Rejection System Operation
24
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The allowable temperature range is discussed further in Reference 8
with respect to streams with cold or warm water fisheries, lakes and
reservoirs. In the figure the discharged water temperature to the
stream (75°F) minus the available water temperature from the stream
(70°F) is equal to 5°F.
Open cycle cooling has its limitations caused by changing meteorological
conditions. It may not work year round. For example, if the wet bulb
temperature is 75°F and the approach is 10°F, then the discharge
water temperature from the heat rejection system would be 85°F.
Water at this temperature would not be allowed to be discharged into the
stream if the available water temperature from the stream was 77°F.
Some power plants can utilize a combination closed cycle and open
cycle system. The plant would try to maximize the time during the
year where open cycle cooling would take place. However, under adverse
meteorological conditions, it would need to close the open cycle loop
when the discharge temperature exceeded that allowed under local water
quality standards. Restriction to closed cycle operation might mean
that the plant would have to cut back on output (partial load operation
to reduce heat rejection).
The Tower .Cost nomograph, Page N-10, provides for the determination
of the number of tower units and the corresponding mechanical draft
tower cost. The number of tower units (in millions) results from the
product of the tower correction factor from N-7 and the water flow rate
determined in the previous nomograph. The tower unit will be recog-
nized as a synthetic square foot of heat transfer hardware used in a
similar manner as a square foot of surface condenser. Thus, the power
plant designer can accumulate a library of known costs per tower unit and
costs per square foot of condenser surface in order to estimate capital
costs. In Reference 4 a library of costs per tower unit was presented
for nine cases representing actual mechanical draft cooling tower
selections for the electric utility industry. The costs per tower unit
ranged from $4 to nearly $5. 5 and the average of the data was $4. 75
25
-------
per tower unit. Therefore, this range of costs per tower unit was
incorporated into the Tower Cost nomograph. Then mechanical draft
tower cost is the product of the number of tower units and the costs per
tower unit.
The nomographs developed up to this point were employed to check, as
an example, the tower cost result for case No. 8 of Reference 4. Design
conditions for this case were:
WBT =.75°F
Range = 25. 8°F
Approach = 18°F
Water flow rate = 0, 305 x 106 gpm
Output results from the nomographs were:
Tower correction factor = 0. 76
Tower effluent Or condenser inlet temperature = 93°F
Turbine back pressure = 3. 95 in.Hg abs
Heat rejection rate = 3. 9 x 109 Btu/hr
Number of tower units = 0. 23 x 106
Mechanical draft tower cost = $1. 2 x 106
A cost per tower unit equal to $5. 26 was used in the Tower Cost nomo-
graph. The mechanical draft tower cost agreed with that of Reference 4,
This capital cost does not include cold water basins, fan motor starters,
controls, and wiring. Comparison of costs predicted by the nomographs
with those from other sources is done in Section XII after introducing the
nomograph example. Good correlation between the costs is shown Based on
these costs, an approximate 15% increment should be added to the value
from the Tower Cost nomograph in order to include the basins and
electrical apparatus-
In the Fan Power nomograph, page N-ll, fan power requirements are
directly proportional to the number of tower units (TU). In Reference 4
26
-------
similar to cost per tower unit, the fan horsepower per tower unit was
presented for nine different cases considering applications of mechanical
draft cooling towers. The average mechanical draft fan power required
was 0. Oil + 25% hp per tower unit. Therefore, the fan power require-
ments in Mw is obtained from the following:
fan power, Mw = 0. Oil x 0. 746 x 10"3 ~- x TU
= 0.82 x ID'5 x TU (8)
The Pump Power nomograph, page N-12, estimates the pump power
requirements for mechanical draft towers in either the closed cycle or
open cycle modes of operation. Equation (6) is employed for either mode
of operation. The pump efficiency is assumed to be 0. 85. The difference
in pump power arises in the total head parameter corresponding to either
mode of operation.
Pumping heads for mechanical draft towers alone in large power station
units range from 50 to 60 ft according to Reference 9. Therefore a
60 ft total pumping head was assumed as a constant in the pump power
equation. Consequently, for the tower operating in the closed cycle
mode, a single straight line relates pump power requirements to the
water flow rate.
Under open cycle operation, water is transported from the source and
then returned to the source after passing through the condenser and the
cooling tower. The pumping head and losses are very dependent upon the
plant site and source of water. Therefore, in the nomograph the total
pumping head is represented by a family of lines. Total pumping head
includes the 60 ft pumping ahead ahead attributed to the tower alone
plus a variable pumping head component whose choice is site dependent.
Finally, the auxiliary power required to operate the mechanical draft
tower equals the fan power determined in the preceding nomograph
plus the pump power resulting from either closed or open cycle
operation.
27
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SECTION VI
SPRAY PONDS
System Description
Spray ponds for utility sites currently are available in two different
configurations, conventional spray ponds and powered spray systems,
including those produced by Ceramic Cooling Tower Co. , Richards
of Rockford and Ashbrook. Also, a spinning disk spray system is being
developed by Cherne. In conventional spray ponds, warm water is
pumped through pipes from the condenser and then out of the spray nozzles.
The nozzles atomize the warm water into fine droplets in the neighbor-
hood of 3/16-inch diameter. The powered spray systems employ
quantities of floating spray modules, with one or more sprays, inde-
pendently deployed in the warm water discharge canal or reservoir.
The modules require mooring and electrical connections to shore.
An attempt was made to include the performance and costs of the
powered spray systems in the nomographs. However, due to
limits on available data, the scope of the nomographs is confined to
conventional spray ponds only.
The basic arrangement of a conventional spray pond is shown in
Figure 7. The spray nozzles are usually located five to 10 ft above the
surface of the pond. Height of the sprays is approximately seven ft.
The drops move irregularly relative to the air medium and are more
or less deformed, while circulation occurs within the droplets. Heat
transfer between the droplets and the medium occurs by the three
mechanisms of conduction, convection and radiation.
Performance of the spray pond is a strong function of the design of the
nozzles. Poor designs require high pressure and power, do not mix
the air and water efficiently, and have excessive water losses. However,
water losses can be decreased with the use of louvered fences. Perfor-
mance is limited by the relatively short contact time between the air and
water spray.
29
-------
Air In
Water In —>
[S
V
Air Out
Figure 7. Spray Pond
An advantage of spray ponds is the requirement for very Little mainte-
nance other than occasional cleaning of the pipes and nozzles and routine
maintenance on the pumps. However, impurities can easily enter the
open water area and be carried into the condenser, increasing mainte-
nance requirements. The disadvantages of the danger of freezing and/or
poor heat transfer due to climatic conditions may also occur.
Discussion of the Nomographs
The nomographs for spray ponds are found on pages N-13 through N-16
of the Appendix. Their development is discussed in the following para-
graphs.
The Spray Pond Performance nomograph, page N-13, is based on data
published by Elgawhary and Rowe (Ref. 10) and Perry's Handbook
(Ref. 11). Pond water temperature after spray is a function of inlet
water temperature, wet bulb temperature, and wind velocity. In
Reference 10, the spray model consisted of an elevated nozzle spraying
hot water above a large pond surface.
In order to utilize the N-13 nomograph, the selected inlet (to the spray
system) water temperature must be greater than the wet bulb temperature
plus condenser rise for a closed cycle system. For example, entry with
30
-------
an inlet water temperature of 80°F and a WBT of 75°F would be an in-
valid set of conditions for a closed cycle system. This is true because
the condenser rise and the approach together are bound to exceed the
5°F required in this impossible case.
The Turbine Back Pressure nomograph, page N-14, yields the steam
turbine back pressure which is a function of the steam saturation
temperature. For a closed cycle system, first, the condenser rise
is determined by subtracting the pond water temperature determined
from N-13 from the inlet water temperature. The pond water tempera-
ture is equal to the condenser inlet temperature (not to be confused with
the inlet water temperature to the spray pond). Then one enters the
Turbine Back Pressure nomograph with the condenser inlet tempera-
ture and the condenser rise in order to obtain the turbine back pressure.
For this system, the steam saturation temperature results from equa-
tion (3). For an open cycle system, the turbine back pressure is
determined from N-14 after entry with a given condenser rise and a
condenser inlet temperature due to the available water from the
natural receiving body.
The Flow Rate nomograph, page N-15, yields the water flow rate from
equation (5). Under closed cycle operation the condenser rise is equal
to the range of the spray pond. Figure 6 can also be employed for
spray ponds to illustrate the magnitude of condenser rise for both
closed and open cycle modes of operation of this heat rejection system.
On page N-16 are found nomographs for Spray Pond Cost and Auxiliary
Power. The spray pond capital cost in dollars is defined as being the
product of the water flow rate in gpm and the pond unit cost in dollars
per gpm. The nominal unit cost value of $9 per gpm is based on the
installed cost for the spray pond at the Canadys Station of the South
Carolina Electric and Gas Company. From Reference 12 data, it was
derived as follows:
m, spray pond capital cost, $/Kw x plant size, Kw
pond unit cost, $/gpm = -*—*-* water flow rate, gpm
$3. 65/Kw x 450, OOP Kw _
= ~ i'SO.OOOgpm
31
-------
The spray pond capital cost in $/Kw includes site preparation, material
and construction labor costs on a 1971 basis.
Auxiliary power requirements in Mw are defined as being the product of
the water flow rate in gpm and the power consumption in Kw per gpm.
The range of values for power consumption are based on Reference 13.
They represent the pumping power requirements of conventional spray
ponds under both closed and open cycle modes of operation. The
pumping power requirements in Mw are due to the spray and to the
distribution piping losses.
32
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SECTION VII
COOLING PONDS
System Description
Heat rejection from power plants through the use of cooling ponds is
highly dependent upon site weather conditions. The heat is rejected
from the pond surface by the natural effects of conduction, convection,
radiation, and evaporation. However, the cooling pond also absorbs
heat through the processes of solar radiation and atmospheric radiation
to the pond, as well as waste heat from the power plant.
Cooling pond systems in the closed cycle and open cycle modes oi
operation are shown schematically in Figure 8. The closed cycle
system resembles the once-through cooling system with the exception
that the cooling water is recirculated in a cooling pond. If the pond
size is in excess of 2 acres/Mw for a fossil plant or 3 acres/Mw for a
nuclear plant, the surface water temperatures will closely coincide
with once-through cooling systems. However, many cooling lakes
are much smaller and therefore, operate at much higher surface
water temperatures.
Advantages of using cooling pond systems are: reasonable construction
costs where soil conditions permit, their service as a settling basin
for suspended solids, potential operation for extended periods without
makeup water, and benefits from other purposes such as recreation.
Disadvantages of cooling pond systems are: the requirement for large
land area and the requirement for a soil basin of low permeability.
Cooling ponds can be classified, on the basis of circulation pattern
and temperature distribution, as completely mixed ponds and flow-
through ponds. In a completely mixed pond, the flow between the inlet
and outlet locations of the pond combined with wind mixing tend to
keep the pond at a nearly uniform temperature. The drop in the
temperature takes place by mixing in a small portion of the pond. This
33
-------
Pond Inlet
Condenser
Chemicals
Condenser
Rise
Circulating
Water Pumps
Pond Outle
Spillway
Closed Cycle
Chemicals
Circulating
Water Pumps'
Condense
Inlet
Open Cycle
Figure 8. Cooling Pond Systems
34
-------
condition seems to exist in ponds where the surface area is large
compared to the water flow rate from the plant and the pond tempera-
ture is uniformly 1 to 2°F above the equilibrium temperature. The
equilibrium temperature is defined as the pond surface temperature
for which the heat leaving the surface will exactly equal the heat
entering the surface of a body of water.
In a flow-through pond the temperatures decrease continually along the
pond. The pond effluent can either be returned to the plant intake
(closed cycle) or discharged to a natural receiving body (open cycle).
The amount of temperature drop from one end of the pond to the other
depends upon the initial temperature rise, water flow rate, pond
surface area, and meteorological conditions. For a given pond volume
and similar meteorological conditions, a pond with greater surface
area will provide a greater temperature drop. The rate at which
heat is lost decreases from the pond inlet to the pond outlet because
the temperature excess gradually decreases along the pond. Flow-
through ponds are more common.
Discussion of the Nomographs
The nomographs for cooling ponds are presented on pages N-17
through N-21 of the Appendix. Their development and underlying
assumptions are discussed in the following paragraphs.
For a flow-through pond, the one-dimensional, exponential tempera-
ture decay equation is:
k A
where:
T , = pond outlet temperature, °F
T. = pond inlet temperature, °F
E = design equilibrium temperature, °F
35
-------
k = heat exchange coefficient, Btu/ft^ day °F
A = pond area
P
P, Cp= density and specific heat for water
WFR = water flow rate
Under closed cycle operation {see Figure 8),ATC is defined to be the
condenser rise which is equal to T^n - TQut. The residual temperature
rise, AT, is defined as:
AT = Tout - En (10)
It is similar to the "approach" parameter specified for the wet cooling
towers and spray ponds. Following the substitution of these definitions
and the rearrangement of equation (9), one obtains the following equation:
AP _ P°p .,„ , AT x nn
WFR ~ " k ^ (AT +ATC ) (11)
The water flow rate in equation (11) and the plant size are related through
equation (5) and equation (17), for the heat rejection rate presented in
Section IX. In the Cooling Pond Performance nomograph, page N-17, a
family of curves, AT vs. Mw/acre (pond loading) was developed for each
ATC using k as a variable. The heat exchange coefficient, k, describes
the rate of heat lost across the air-water interface per unit area per unit
temperature increase and depends upon the local site meteorology. It
was assumed in the computations that the fossil and nuclear plant effi-
ciencies remained constant at their respective values, 35. 8 percent and
31. 2 percent, corresponding to a turbine back pressure of 2 in. Hg
absolute. This is a reasonable assumption for the range of back pressure
operation applicable to cooling ponds, 2 to 4 in. Hg absolute.
For the open cycle cooling pond system (see Figure 8), equation (9)
again applies for the flow-through pond. However, cooling pond per-
formance also depends upon the temperature of the water available
from the river or the condenser inlet temperature in addition to
36
-------
condenser rise, AT and k. The following parameter, is defined:
ATC = condenser rise - pond outlet temperature (12)
+ condenser inlet temperature
Then equation (9) becomes for the open cycle case:
AP . PCP - , AT . ,,,.
_____ _ - _____ m (AT+ATC.) (13)
Thus, it follows that the same curves can be employed on N-17 for
the open cycle case except for the substitution of ATC for ATC
when one enters the nomograph.
Pond sizes predicted from the curves of N-17 (following interpolation)
are compared in Table 3 with those from several plant cases described
in References 14, 15, and 16. The k values for each site were esti-
mated from the design chart presented by Brady (Ref. 17). Repre-
sents k as a function of windspeed and an average temperature which
is based on the dewpoint temperature, T^, and the water surface
temperature, Ts. For each case, the T
-------
TABLE 3. COOLING POND PERFORMANCE
CO
CO
Site
Location
Southeast
-Miami
Michigan
Southwest
- Yuma
385-Fossil
1000-Fossil
1000-Nuclear
Cooling
Pond
Cycle
Closed
Closed
low -through)
Closed
low-through)
Water
Flow
Rate
cfs
320
950
1300
Condenser
Rise
or Range
OF
24
20
22
Pond
k
Btu/day- En AT Acres
ft2-°F °F °F (Reference)
153 84.6 1 1000
(Rcf. 14
Sta. 2)
162 86 2 1740
(Ref. 15
Case V)
177 83.5 6.5 1140
(Ref. 16)
Size
Acres
(From Curves
of N-17)
895
1890
1695
-------
The Cooling Pond Cost nomograph, page N-19. yields the land and
excavation costs. First the pond size in acres is obtained by dividing
the plant size in Mw by the pond loading parameter, Mw/acre, deter-
mined in the Cooling Pond Performance nomograph. The cooling pond
land and excavation cost in dollars is obtained from the product of the
pond size and the unit cost in dollars per acre.
The range of this unit cost appearing on the nomographs is justified in
several references. In Reference 9, it was pointed out that cooling pond
costs are a very strong function of the amount of land required. A unit
cost of $1000 per acre for land and excavation appears to be reasonable.
However, in the future the cooling pond may prove to be more expensive
as larger amounts of more expensive land are required for big nuclear
plants. Also, in the series of cooling pond cases considered in Reference
15, land costs of $500 per acre and $1000 per acre were employed in the
Lake Michigan area.
The Flow Rate nomograph, page N-20, yields the water flow rate directly
from equation (5).
The Auxiliary Power nomograph, Page N-21, estimates the auxiliary
power due to the pump power requirements for cooling lakes. Equation
(6) is employed for either mode of operation. Pump efficiency, as
before, is assumed to be 0. 85. The difference in pump power arises
in the total head parameter corresponding to either mode of operation.
The pumping head and losses are also very dependent upon the plant
site. Therefore, in the nomograph the total pumping head is represented
by a family of lines whose range is assumed to span cooling pond applica-
tions under the two modes of operation.
39
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SECTION VIII
MECHANICAL AND NATURAL DRAFT DRY TOWERS
System Description
In the mechanical and natural draft dry tower heat rejection systems, the
circulating water never comes into direct contact with the cooling air.
Condensation by air cooling has been used in small industrial power
plants for over 50 years. However, the application of air cooling to
relatively large generating units has been limited. There are two basic
types of air-cooled condensing systems, the indirect system and the
direct system. The indirect system uses a condenser at the turbine
to condense the exhaust steam. It is often referred to as the Heller
system .since the concept to use the indirect system of condensation by
air cooling with a steam turbine generator was presented by Dr. Laszlo
Heller in 1956. In the direct system, steam is condensed in the tower
cooling coils without the use of a condenser or circulating water.
Indirect, dry-type heat rejection systems with a natural draft tower
and with a mechanical draft tower are shown schematically in Figures
9 and 10, respectively. These diagrams present the principal components
for the indirect systems according to Reference 18. Water from the
condenser is pumped to the dry-type tower for cooling. Water from the
tower cooling coils is sprayed into the direct contact steam condenser
and mixes directly with the exhaust steam from the turbine. The
water of condensate purity falls to the bottom where it is removed by cir-
culating and condensate pumps. The greater part of the water flows through
the pipes back to the cooling coils, and an amount equal-to the exhaust
steam from the turbine is directed back to the boiler feedwater circuit.
In the Heller system, the cooling coils are mounted vertically, and the
warm circulating water enters the bottom of the coils, flows upward in
the inner rows of coils to the top water boxes, and then is directed down-
ward through the outer rows of coils. The outer rows of coils come into
contact with the entering air, thereby providing the greatest cooling range
in water temperature.
41
-------
Natural
\ Draft Tower
Steam
Turbine
Exhaust
Steam
CD
Cooling
Coils
Direct Contact
Condenser
to
Circulating
Pump Motor
Water Recovery
Turbine
Circulating
Water Pump
Condensate
to Boiler
Feedwater
Circuit
Figure 9. Indirect, Dry-Type Heat Rejection
System with Natural Draft Tower
-------
v;
Mechanical
Draft Tower
CD
Air
Flow
V
Cooling
Coils
oo
Steam
Turbine
Fxhaust
Steam
Direct Contact
Condenser
Circulating
Pump Motor
O
Water Recovery
Turbine
Circulating
Water Pump
^"Condensate
To Boiler
Feedwater
Circuit
Figure 10. Indirect, Dry-Type Heat Rejection
System with Mechanical Draft Tower
-------
In order to prevent drawing air into the system in case of leaks in the
cooling coils, a positive pressure head of approximately three feet is
imposed at the top of the coils. This is accomplished by means of either
a throttling valve in the circulating water discharge from the tower, or,
if a v/ater recovery turbine is used, by varying the position of the adjust-
able turbine vanes. In order to recover some of the pressure head
between the cooling coils and the condenser, in some installations water
recovery turbines are coupled to the drive shaft of the circulating water
pump to recover the available energy.
After passing through the recovery turbine, the circulating water is
again sprayed into the direct contact condenser and recycled through
the cooling system. Since the circulating water does not come into
direct contact with the cooling air, there is no evaporative loss of water
as with the wet-type towers.
Discussion of the Nomographs
The nomographs for the mechanical draft and natural draft dry towers
are presented on pages N-22 through N-26 of the Appendix. The devel-
opment of each of these nomographs is discussed in the following para-
graphs.
The nomograph on page N-22 entitled Combined Performance - Natural
Draft shows the performance curves for a large natural draft dry tower
superimposed on steam turbine performance curves for power plants
representing several sizes. The performance for this tower was pre-
sented in Reference 18. The tower was dual rated, 4 x 1()9 Btu/hr heat
rejection rate at 50°F ITD (initial temperature difference) and 6 x Id"
Btu/hr at 67. 8°F ITD, corresponding to fossil and nuclear plant appli-
cation, respectively. This natural draft tower represents one of many
applicable tower designs. The derivation of natural draft dry tower
performance and the use of the nomograph is discussed in succeeding
paragraphs.
44
-------
The performance of dry- type towers is governed by the following
equation (Ref.
ITD = AQb (14)
where,
ITD = initial temperature difference, °F
= steam saturation temperature - dry bulb temperature
A = tower constant
Q = heat rejection rate, 106 Btu/hr
b = exponent dependent upon natural or
mechanical draft towers
For the natural draft dry tower, an average value of b is about 0. 75
(Ref. 18). Therefore, the performance equation for the natural draft
tower rated 4 x 109 Btu/hr heat rejection rate and 50° ITD is fully
determined after solving for A in equation (14):
ITD = AQb
50 Ax (40QO)0-75 or
A = 0.1
This performance equation is:
ITD = 0.1 (Q)°-75 (15)
With equation (15) the family of performance curves of turbine back
pressure versus heat rejection rate for various dry bulb temperatures
was developed. First equation (15) was used to compute ITD's corre-
sponding to Q's or heat rejection rates other than 4 x 10^ Btu/hr.
Then a dry bulb temperature was selected, e.g. 90°F. The addition
of 90°F to each ITD yields a corresponding steam saturation tempera-
ture. The steam tables are employed to obtain turbine back pressures
in in. Hg absolute. Thus, a curve of turbine back pressure versus heat
rejection rate at constant dry bulb temperature can be plotted. Following
the same procedure, performance curves for other constant dry bulb
45
-------
temperatures are determined and appear in nomograph N-22. Thus,
the turbine back pressure performance of this natural draft dry tower
is shown for various ambient air temperatures and heat rejection loads.
Turbine performance curves for fossil and nuclear plants of several net
generating capacities are overlaid on the nomograph. The develop-
ment and discussion of these curves, some of which appear in the
turbine performance nomographs, are in Section IX. The curves of
heat rejection rate versus turbine back pressure are based on the
assumption that the specified net generating capacity is maintained
constant as back pressure increases.
The intersection of the turbine performance curve for a plant operating
at a given rated capacity with the tower performance curve at a given
dry bu!b temperature yields operating conditions for the given tower.
Thus, the output of the nomograph is turbine back pressure and heat
rejection rate. The range of net generating capacities displayed is
assumed to correspond to the range of applicability for this tower design.
This tower design is not the optimum one for the range of plant capacities
shown. Reference 18 pointed out that this particular tower design was
dual rated for application to both 800 Mw fossil and nuclear plants. The
optimum tower design results only after the performance and costs are
computed for dry towers having various combinations of Q and ITD
(ranging from 30 to 80°F) in equation (14). Therefore, N-22 is only
applicable for making first estimates of turbine back pressure and heat
rejection rate for the natural draft dry tower with a given plant.
The nomograph on page N-23 entitled Combined Performance- Mechanical
Draft shows the superposition of mechanical draft dry tower performance
curves onto steam turbine performance curves of various power plants.
This mechanical draft tower has a dual rating of 4 x 109 Btu/hr at
50°F ITD and 6 x 109 Btu/hr at 72° ITD corresponding to fossil and
nuclear plant applications, respectively. It represents one of many
applicable tower designs. The Q equal to 4000 and the ITD equal to
50°F are substituted into the dry tower performance equation (14). Also
substituted is b equal to 0. 91, the exponent for mechanical draft dry
towers (Ref. 18). The solution of equation (14) based on these values
46
-------
yields a tower constant, A, equal to . 0263. Therefore, the performance
equation for this mechanical draft dry tower is:
ITD = . 0263(Q)0-91 (16)
With equation (16) the family of performance curves was developed for
various dry bulb temperatures by following the same procedure outlined
for the natural draft dry tower nomograph. Thus, in N-23 the turbine
back pressure performance of the mechanical draft dry tower is shown
versus heat rejection rate and dry bulb temperature.
Turbine performance curves for several fossil and nuclear plant capac-
ities are overlaid onto N-23. Incorporated into these curves is the
assumption that the specified net generating capacity is maintained con-
stant as back pressure increases.
The intersection of the turbine performance curve for a plant operating
at a given rated output with the tower performance curve at a given dry
bulb temperature yields the outputs of turbine back pressure and heat
rejection rate for the given tower. This mechanical draft dry tower
design is assumed to be applicable over the range of net generating
capacities displayed. For the same reasons stated in the natural draft
dry tower discussion, this tower design is also not the optimum one for
the range of plant capacities shown. Therefore, N-23 is only applicable
for making first estimates of turbine back pressure and heat rejection
rate for the mechanical draft dry tower with given plant sizes confined
to a limited size range.
The Initial Temperature Difference nomograph, page N-24, allows the
ITD to be determined, as defined in equation (14), from the turbine back
pressure and the dry bulb temperature. For an input turbine back
pressure from the dry tower performance nomographs, a corresponding
steam saturation temperature is obtained from steam tables. A satu-
ration temperature scale is also displayed for approximate estimates
on the nomograph. The inital temperature difference is the design
approach parameter for dry towers.
-------
The Capital Cost nomograph, page N-25, yields costs of heat rejection
systems employing dry towers versus ITD and plant capacity and type.
The heat rejection system (Figure 9 and 10) is defined as including all
equipment and installation from the turbine flange outward: condenser,
cooling system piping, water storage facilities, pumps, valves, controls,
recovery turbine if used, and the cooling tower with its heat exchanger
equipment. Reference 18 presented data showing that the capital costs
of the natural draft and mechanical draft dry systems (and the physical size)
decrease with increasing ITD for 800 Mw fossil and nuclear-fueled plants
based on 1970 cost levels. These capital cost data were escalated to
1971 cost levels using a factor of 1. 14 based on the Engineering News
Record. Then the 1971 capital cost levels for 800 Mw power plants were
linearly extrapolated to yield capital costs for the plant sizes displayed
in the nomograph. The extrapolation is justified based on Reference jg.
It was stated that the results of their cost analysis, as evaluated on a
cost per Kw basis, should be generally applicable to generating plants
in the size range of 600 Mw to 1000 Mw, or over a somewhat larger
range of sizes.
The Auxiliary Power nomograph, page N-26, yields auxiliary power
requirements in Mw for mechanical draft and natural draft dry towers
versus ITD and the plant capacity and type. These data were tabulated
in the Beck report, Part II (Ref. 18) for 800 Mw fossil and nuclear
fueled plants. The auxiliary power requirements for pumps and fans
decrease with increasing ITD. The data were linearly extrapolated to
yield auxiliary power for the plant sizes displayed in the nomographs.
48
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SECTION IX
STEAM TURBINE GENERATOR PERFORMANCE
Background
In order to obtain performance data on large steam turbine generators,
contacts were made with the Power Generation Sales Division of the
General Electric Company, the Large Turbine Division of Westinghouse
Electric Corporation, Allis-Chalmers Power Systems, Inc., and the
Brown-Boveri Corporation. Requests were made specifically for turbine
heat rate and throttle steam rate versus turbine generator output and high
turbine back pressure. It would have been desirable to obtain these spe-
cific data for standard modified turbine designs and high back pressure
turbine designs for both fossil and nuclear plant applications. A large
quantity of publications was received from Westinghouse and General
Electric covering the heat rate performance of large steam turbine
generators in nuclear and fossil-fueled plant applications. These papers
have been published over the years in the Proceedings of the American
Power Conference and the ASME Journal of Engineering for Power.
Turbine performance at increasing back pressure will be different for
the two cases:
(1) Maintain constant generator output by increasing steam
rate.
(2) Allow generator output to decrease while maintaining
constant steam flow rate (derated plant).
It was assumed in the nomographs that at a given plant site, the rated
output would be required under all site conditions, Case 1. In so doing,
it is assumed that the generator can take a certain overload steam rate.
Discussion of the Nomographs
The Turbine Performance nomographs are presented on pages N-27
through N-32 of the Appendix. Their development and underlying
assumptions are discussed in the following paragraphs.
49
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In the Heat Rejection Rate nomograph, page N-27, the heat rate rejection
rate is found as a function of the turbine back pressure, the net generating
capacity for a fossil-fueled plant and the base load heat rate. Tower or
pond heat rejection rates can be related to thein-plant and plant efficiencies
by the following equation (Ref. 9):
Heat Rejection Rate, Btu/hr = 3413 x (plant size, Kw) x
(17)
l"P J
where:
nj = in-plant or steam supply efficiency, which accounts
for in-plant heat losses. This efficiency is 85 percent
(15 percent in-plant and stack losses) for fossil
plants and 95 percent (5 percent in-plant losses) for
nuclear plants (also Refs-. 8 and 15).
rip = plant efficiency which depends upon the turbine
back pressure. (It is the thermal efficiency of
the total plant.)
The heat rejection rate varies as the turbine back pressure changes.
This is due to varying plant efficiency and more heat addition to the
plant in order to keep the electrical output constant.
Plant efficiencies versus turbine back pressures, required in equation
(17), were based on turbine performance data tabulated by Beck Associates
in Reference 18, Part II. They presented plant heat rate versus turbine
back pressure for 800 Mw fossil and nuclear plants which assumed in-
plant efficiencies of 90 percent and 100 percent, respectively. These
plant heat rates were corrected to account for fossil and nuclear in-
plant efficiencies of 85 percent and 95 percent, respectively. There-
fore, at the base back pressure of 2 in. Hg absolute, there resulted
plant heat rates equal to 9541 and 10,937 Btu/Kw-hr, respectively, for
fossil and nuclear plants. The performance data used from Reference ig
were for a conventional turbine modified for operation at high exhaust
pressure. Their source was the General Electric Company.
50
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The family of lines, identified by plant heat rate values ranging from
8000 to 12,OOOBtu/Kw-hr, allow one to determine heat rejection rate
versus increasing turbine back pressure for plants whose base plant heat
rates at 2 in. Hg absolute differ from 9541 Btu/Kw-hr. It is emphasized
that the plant heat rate values indicated on the nomograph are only for
plant operation at a back pressure of 2 in. Hg absolute. Plant heat rates
and efficiency change as back pressure increases. As an example,
consider a plant whose plant heat rate at 2 in. Hg absolute is 9000 Btu/Kw-
hr. If this plant is 800 Mw in capacity and is operating at 4 in. Hg absolute
back pressure, a heat rejection rate of 3. 5 x 109 Btu/hr results from
nomograph N-27. Now, after substitution into equation (17), the plant
efficiency is determined:
.85
- 1
3. 5 x 109 Btu/hr = 3413 x 8 x 105 Kw x
or,
Tip = 37. 3 percent.
Then the plant heat rate = 3413 BKw"hr = 9160 Btu/Kw-hr at 4 in.
Hg absolute instead of 9000 Btu/Kw-hr at 2 in. Hg.
The range of plant heat rates displayed on N-27 is justified from statis-
tics presented in Reference 19. In 1969 the best annual plant heat rates
from coal fired plants were just above 8700 Btu/Kw-hr exhibited by the
Muskingum River plant and the Marshall plant. The best plant heat
rates for gas-fired plants exceeded 9500 Btu/Kw-hr. The national average
of the plant heat rates for FPC regions was 10, 447 Btu/Kw-hr in 1969.
Two regional averages exceeded 11,000 Btu/Kw-hr.
The range of plant net generating capacities up to 10, 000 Mw is displayed
in order to address anticipated future large plant complexes.
In the Heat Rejection Rate nomograph on page N-28, heat rejection rates
for nuclear plants are determined as a function of turbine back pressure,
net generating capacity, and the base load heat rate. The development
51
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of this nomograph is also based on equation (17). The same procedure
was followed here as was done in developing the fossil plant nomo-
graph, N-27. For the nuclear plant, in-plant losses were assumed to
be 5 percent. The base plant heat rate for the nuclear plant is 10, 937
Btu/Kw-hr at 2 in. Hg absolute based on the Beck data (Ref. 18). The
family of plant heat rates ranging from 9000 to 14,000 Btu/Kw-hr allow
one to determine heat rejection rate versus increasing turbine back
pressure for plants whose base plant heat rates differ from 10, 937 Btu/
Kw-hr at 2in. Hg absolute.
The Additional Heat Capacity nomograph, page N-29, for fossil plants
allows the determination of additional heat capacity versus turbine back
pressure and the net generating capacity. As back pressure increases
the plant efficiency decreases. The power output (Mwe) decreases if
the heat input is kept constant. An alternative, which was chosen in
this effort, is to increase the heat input and maintain the power output
at the rated value. In this case, a penalty must be paid for the additional
heat input or additional heat capacity. The derivation for additional
heat capacity follows.
The baseline is at 2 in. Hg absolute which corresponds to plant efficien-
cies for fossil and nuclear plants of 35. 8 percent and 31. 2 percent,
respectively. At the baseline of 2 in. Hg absolute and efficiency, r\p,
the heat input is:
where:
Qin = heat input, Btu/hr, at 2 in. Hg
W = heat equivalent of the rated output, Btu/hr
= plant efficiency = 0.358 (fossil plant) or
0.312 (nuclear plant)
52
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At a certain back pressure other than 2 in. Hg absolute, the plant effi-
ciency is Tip 'and the heat input is:
Qin' = _-- (19)
*p
where:
Qin' = heat input, Btu/hr, at a certain back pressure
r)p' = plant efficiency at a certain back pressure
Finally, the additional heat capacity is:
= Qin - Qin = WU - . (20)
The Additional Heat Capacity nomograph, page N-30, for nuclear plants
allows the determination of additional heat capacity versus turbine back
pressure and the net generating capacity. The additional heat capacities
also result from the use of equation (20) where nuclear plant heat rates
versus back pressures are substituted.
The Plant Efficiency nomograph, page N-31, illustrates the change of
plant efficiency for fossil and nuclear plants as the turbine back pressure
increases. These curves apply only for plants whose base plant heat
rates are 9541 Btu/Kw-hr (fossil)and 10,937 Btu/Kw-hr (nuclear) at
2 in. Hg absolute pressure. The plant efficiency was derived from plant
heat rate data presented in Reference 18.
The Turbine Heat Rate nomograph, page N-32, shows the variation of
turbine heat rate with increasing turbine back pressure. These data are
from Reference 18 and apply to a conventional steam turbine generator
modified for operation at high exhaust pressure. Turbine heat rate is
the product of the plant heat rate and the in- plant efficiency. Nomo-
graphs N-31 and N-32 are not generally applicable to all plants.
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SECTION X
MAKEUP WATER REQUIREMENTS
The nomographs for determining makeup water requirements for the
various thermal pollution control systems are presented on pages N-33
through N-38 of the Appendix. Their development is discussed in the
following paragraphs.
Evaporative Losses Under Design Conditions
The Cooling Pond nomograph, page N-33, yields the evaporative
loss in cfs/Mw as a function of wet bulb temperature and the pond
loading parameter (acre/Mw). Evaporative loss in gal/net Kw-hr
was presented in Reference 20 for nuclear plants only. Thus in
order to obtain this loss for fossil plants under design conditions, it
can be assumed that they reject 50 percent less heat to the cooling
water than the nuclear plants. Therefore the evaporative data given
byHauser and Oleson was divided by 1. 5 to obtain fossil plant evapora-
tive losses. This assumes that the proportion of heat rejected by
evaporation remains constant. Following a straightforward conversion
of units, the evaporative loss in cfs/Mw results and is shown in the
nomograph.
The evaporative losses from N-33 are good for rough estimates only
because they are based on a special set of assumptions made in
Reference 20. These assumptions are a 60 percent relative humidity,
a 70 percent cloud cover, a windspeed of 8 mph and a cooling range of
2QOF.
The input wet bulb temperature to N-33 can be estimated based on the
design meteorological conditions for the cooling pond at the site. If
dry bulb temperatures are not available, an approximation can be made
by assuming DBT is equal to the design equilibrium temperature, En.
55
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Then following the selection of the design relative humidity, WBT can be
established. The pond loading input to N-33 is obtained from the Cooling
Pond Performance nomograph, N-17.
The output of the nomograph, based on Reference 20, was compared to
the evaporative losses predicted using the data of Reference 14. Evapora-
tive losses were compared at 1 and 2 acres/Mw at a New York site location.
The comparison shown in Table 4 is very good.
TABLE 4. COOLING POND EVAPORATIVE LOSS
Pond
Loading Cooling Evaporative Evaporative
Site Nuclear Pond Range E WBT Loss-Ref. 14 Loss-Ref. 20
Location Acre/Mw Cycle °F QF °F 1Q-5 cfs/Kw 1Q-5 cfs/Kw
NE-New
York
NE-New
York
1
2
Closed
Closed
20
20
76
76
66.
66.
3
3
2.
3.
86
7
3.
4.
23
1
The input wet bulb temperature, 66. 3°F, to N-33 was determined from
a psychrometric chart after assuming 1) a 60 percent design relative
humidity and 2) the air temperature or DBT was equal to En.
The nomograph for Evaporative Loss for Wet Systems, Page N-34, pro-
vides for the determination of evaporative loss for natural draft and
mechanical draft wet towers and for spray ponds. Evaporative loss in
gal/net Kw-hr was presented in Reference 20 for these wet systems as
a function of range. Evaporative losses for the wet towers were pre-
sented versus approach also, in addition to range.
N-34 is based on the same assumptions for meteorological conditions as
N-33. Thus it is good for rough estimates only.
Hauser and Oleson performed a sensitivity analysis whereby individual
design parameters were varied to determine the effect on evaporative
losses from cooling towers, spray ponds, and cooling ponds. Evaporative
rates for mechanical draft and natural draft wet towers were very sensitive
56
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to the range and approach parameters. Spray ponds showed a large
increase in evaporative losses for low ranges. Evaporative losses
for cooling ponds were most sensitive to changes in wet bulb tempera-
ture.
Average Annual Evaporative Losses
The rate of overall water usage in actual plant applications will
generally be much less than those calculated for design conditions
for several reasons. Design conditions are generally selected to per-
mit the plant to produce full power 90 to 100 percent of the time during
the year. During the majority of the year, conditions will be more
favorable than the design meteorological conditions. This was
illustrated in a study of a 1000 Mwe fossil-fuel power plant to be
located near Lake Michigan, (Ref. 15). In this case, the basic design
conditions discussed above were used for the plant and the following
adjustments were made to compute evaporative water loss on an aver-
age annual basis.
1. An 82 percent plant capacity factor was assumed
2. Evaporative losses for wet towers and spray ponds
were reduced 20 percent to account for more favor-
able conditions over the year.
3. Evaporative losses from cooling ponds were reduced
to account for the annual average incoming short
wave radiation of 1600 Btu per square foot per day
compared to a design value of about 2800 Btu per
square foot per day with the difference being equi-
valent to 10 cfs per 1000 acres pond surface
averaged over the year when adjusted for reflective
losses. It should be noted again that the evapora-
tion data provided in Reference 20 were based upon a
cloud cover of 70 percent. Thus, the above "correc-
tion" for short wave radiation would not be suitable.
57
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Therefore, the data in N-33 are assumed to be based on
average rather than design short wave radiation.
In addition to the adjustments noted above, the natural evapotranspira-
tion losses should also be considered in the case of cooling ponds.
Natural evapotranspiration is the difference between the average annual
precipitation rate and the average annual runoff rate in a given region.
For the Lake Michigan area, the annual average natural evapotranspira-
tion rate is about 20 inches per year. This is equivalent to a reduction
of 3. 5 cfs for 1500 acre ponds and 4. 6 cfs for 2000 acre ponds. These
data apply only to the Lake Michigan area and should not be directly
applied to other regions.
In the nomograph examples for water requirements found in Section XII.
appropriate factors are used to estimate the average annual evaporative
losses from the design values obtained from the nomographs.
Percent Evaporative Loss, Slowdown and Makeup
Water Nomographs
In the Percent Evaporative Loss nomograph, page N-35, the evapora-
tive loss is determined as a percentage of the water flow rate. Initially,
the nomograph is entered with the evaporative loss input in cfs/Mw
from either N-34 or N-35. Then this evaporative loss parameter is
multiplied by the net generating capacity (Mw) for a given plant in order
to yield evaporative loss in cfs. The input water flow rate, which may
be in gpm, is taken. Before entering the nomograph it is converted to
cfs by the multiplication factor, 2.23 x 10"^ cfs per gpm. Finally,
the evaporative loss is:
,. , a, evaporative loss, cfs inn /01\
evaporative loss, % = f-—TJ 7—'—? x 100 (21)
^ ' water flow rate, cfs
Nomographs on pages N-36 and N-37 are identified as Percent Blowdown.
Slowdown is determined as a percentage of the water flow rate. As
water is lost by evaporation from the cooling water supply of wet
cooling systems, nonevaporating substances are concentrated in the
cooling water remaining. There is a practical limit of concentration of
58
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the substances if corrosion, fouling and general deterioration of the
cooling structures are to be prevented. To avoid such problems, a
certain amount of the cooling water customarily is drained off from the
system for disposal. This water, termed blowdown, is replaced by
fresh makeup water.
The equationfor concentration factor or number of concentrations maybe
given as:
C = E + D+B . }
u D + B (22'
where:
C = factor of concentration in the evaporative system
E = evaporative loss or evaporation, percent
D = drift loss, percent
B = blowdown, percent
The variables, E, D, and B, are all percentages of the water flow rate.
This equation was rearranged to yield the governing equation for nomo-
graphs N-36 and N-37:
K - E - D (C - 1) (23)
a C - I
Nomographs N-36 and N-37 apply only to natural draft and mechanical
draft wet towers and the spray ponds. In the first nomograph, a con-
stant drift loss of °- 005 percent is assumed. In N-37, blowdown is
determined at two other constant levels of drift, 0. 001 percent and 0.01
percent. Drift is the loss of entrained water that is,carried out of the
top of a wet tower or from a spray pond. The typical drift guarantee
of 0. 2 percent of the water flow rate is far in excess of current engi-
neering capability and- practicality for large towers. Drift loss can be
almost completely eliminated by control of air velocity and use of drift
eliminators. Mechanical draft wet towers can be currently purchased
with certification of drift elimination at the 0. 02 percent level.
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Natural draft towers can be certified at the 0. 002 percent level. Also
drift measurements on operating towers show as low as 0. 005 percent
for mechanical draft and 0. 001 percent for natural draft towers. The
percent evaporation is an input from N-35. The number (or cycles)
of concentrations and the drift loss are chosen for a given application.
The blowdown parameter then follows from the nomographs. Note
that the blowdown values from the nomographs for the three drift
levels are essentially equal for cycles of concentration less than about
10.
The Makeup water nomograph, page iN-iSb, yields the makeup water
requirements for the wet systems in either cfs or gpm. They are
assumed to be negligible for the dry cooling towers. The input para-
meter to this nomograph is the makeup water requirements as a
percentage of water flow rate. For cooling ponds this input is assumed
to be the percent evaporative loss, E, from Nomograph N-35. However,
it should also include precipitation and runoff as well as blowdown, if
applicable. For the wet towers and spray ponds, makeup water require-
ments are:
makeup water requirements, percent of water flow rate =
evaporation 4- drift + blowdown = E + D + B (24)
Then, multiplication of the input parameter by the water flow rate in
cfs yields the makeup water requirements in cfs.
Makeup water requirements are determined for two illustrative examples
representing a natural draft wet tower and a cooling pond in Section XII.
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SECTION XI
COSTS FOR THE HEAT REJECTION SYSTEMS
Discussion of the Nomographs
In the cost nomographs, incremental costs are determined as being the
various additional capital and operating costs required to incorporate
and operate the given heat rejection system within the power plant.
These nomographs are presented on pages N-39 through N-49 of the
Appendix. Their development is discussed in the following paragraphs.
The Steam Supply Incremental Cost nomograph, page N-39, estimates
the incremental cost for the steam supply system of either fossil or
nuclear plants due to the presence of a given heat rejection system. This
cost is based on the following approximate equation:
steam supply system incremental cost (SSIC), dollars = (25)
3413 Bt^/Kw-hr X Kl x K2 x Plant unit costs> $/Kw
where:
AQ = additional heat capacity in Btu/hr. This is an
input from the turbine performance nomographs
corresponding to a given cooling system in either
a fossil or nuclear plant
Kj = 0. 358, efficiency of a fossil plant or 0. 312, efficiency
of a nuclear plant (in reality, this varies with turbine
back pressure.)
K2 = Ratio of steam supply system cost to total plant construction
cost
The breakdown of costs for power plants shows that approximately
37 percent of the total construction cost is for the steam supply system
(References 21, 22, and 23). Therefore, K2 is assumed equal to 0.37.
The ranges of unit costs, shown on N-39, for fossil and nuclear plants
are from Reference 24, one of many potential sources.
The Turbine Generator Incremental Cost nomograph, page N-40,
61
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estimates the incremental cost for the turbine generator plant (TGIC) of
either fossil or nuclear plants. This cost is also determined from equa-
tion (25) except that K2 is replaced by K3- K3 is defined as being the
ratio of turbine generator plant cost to the total plant construction cost.
In Reference 23, the co.st breakdown for the power plant showed that
approximately 21 percent of the total cost was for the turbine generator
plant (condenser system excluded). Therefore, K3 is assumed a constant
equal to 0. 21.
These nomographs have limited application. The wet towers, spray ponds
and cooling ponds are assumed to incur no cost penalty for capability
losses unless the turbine back pressures exceed values beyond the range
of roughly 3. 5 in. Hg absolute. However, the nomographs are used to
determine SSIC and TGIC for dry towers operating at high back pressures.
The cost penalty would be computed and apply to the range of back pressure
from 3. 5 in. Hg absolute to the high back pressure value of the plant
using a dry tower. The procedure is shown in the dry tower nomograph
examples in Section XII. It should also be pointed out that the capability
loss can be possibly made up with gas turbine peaking units at a cost of
$100/Kw, as an alternative to increasing the base load. Nomographs
N-39 and N-40 can also serve as auxiliary nomographs to determine costs
of capability loss for derated plant cases. There will be a certain time
of year when a plant won't have a loss of capability. Thus, the capability
loss under design conditions is conservative.
The Condenser Surface Area nomograph, page N-41, yields the area of
the heat transfer surface for the condenser. Two governing equations
for condensers are:
q = WFRx Cp (To - TI) (26)
and
q = rO " TJ (9n\
TT A IT* - T- * v '
UAC n Jig X i
"Vlt^IS
62
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where:
q = total heat transferred in the condenser, Btu/hr
WFR = water flow rate, Ib/hr
U = over-all heat transfer coefficient, Btu/hr-ft2-°F
Ac = area of heat transfer surface, ft2
TQ = water outlet temperature from condenser, °F
T- = water inlet temperature to condenser, °F
TS = steam saturation temperature, °F
C = specific heat for water = 1 Btu/lb-°F
Following the combination of equations (26) and (27) the following
equation for Ac is obtained:
A _ /WFR\, JTS - Ti \ _/WFR\ (condenser rise + TTD 1 .- .
AC - (-JT- r JTT^TO) " (IT) to j - TW - j <28)
If the terminal temperature-difference is assumed to be 6°F and the
water flow rate is in gpm, me final equation for N-41 is:
A cnn/'WFRN,. ( condenser rise + 6 ) (29)
Ac = 500 {—^— ) fa j - g - j
The range of U displayed in the nomograph is partially based on the use
of 630 Btu/hr- ft2-°F in Reference 4.
The Condenser Cost nomograph, page N- 42, estimates capital cost of
condensers employing several types of tube materials, including
90-10 copper-nickel and admiralty. Based on Westinghouse price
lists (Ref. 25),. it was determined that the equipment (or material)
unit cost per surface condensers was $7. 70/ft2 for 90-10 copper-
nickel. The cost includes surface condensers, auxiliaries, and air
ejectors. From Reference 26, the multiplication factor for obtain-
ing field installation cost is found to be approximately 3. Thus, the
condenser capital cost including field installation is $23.10/ft2 for
90-10 copper-nickel. The corresponding cost for condensers with
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admiralty tube materials isn't too far different at $22/ft2. Since admiralty
is the most popular tube material a cost line for it appears in N-42. Two
other cost lines, $15/ft2 and $27/ft2, are displayed in order to cover the
range of condenser tube materials.
The Water Circulation System Cost nomograph, page N-43, estimates
the capital costs for pumps, motors, piping and installation. A cost
equation was derived comprised of contributions from each component
on a cost per gpm basis. The pump cost is estimated as $1. 05/gpm at
100 ft totalhead based on Reference 27. In the estimate, the capacity
per pump was 200, 000 gpm. The motor cost, based on the same refer-
ence, is estimated to be $32/hp. The horsepower required per gpm was
computed to be 0. 0301 from an equation similar to equation (6) assuming
100 ft total head. Cost for piping was estimated as $0. 25/gpm (Ref. 27
and 28) based on a length of piping of 1000 ft. Cost of installation was
estimated to be $0. 4/gpm based on one million gpm. Then the governing
cost equation for N-43 takes the following form:
water circulation system cost (WCSC), dollars = water
flow rate, gpm x (l. 05 x total head, ft + 32 x 0_ 0301
•• i uu
total head, ft , n oc , - .\
x 100 ' +0.25+ 0.4J (30)
The nomograph applies only to the wet towers, spray ponds, and cooling
ponds.
The Cost for Once-Through Cooling nomograph, page N-44, estimates
the intake and outfall structure cost based on FPC Form 67 (Ref. 6) data
for 13 existing power plants. The average cost for intake and outfall
structure was $5. 80/gpm/1000 ft for both once-through fresh water and
salt water systems. As defined in Reference 6, the costs for these once-
through systems include pumps, piping, canals, ducts, intake and dis-
charge structures. Therefore, the cost equation for N-44 is:
64
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cost for once-through cooling (OTCC), dollars = 5. 8 x
water flow rate, gpm x total structural length, ft {31)
The total structural length is from and to the condenser.
In the Capital Recovery Factor nomograph, page N-45, the capital re-
covery factor is a function of interest rate and years amortized. The
curves in the nomograph are from data in interest tables from Refer-
ence 29. Then the fixed charge rate in percent per year can be deter-
mined by adding the capital recovery factor in percent from the
nomograph to the recurring cost percentage. The recurring cost
percentage includes insurance, interim replacements, and various
taxes such as property, state and federal. In Reference 30, represen-
tative values for recurring cost percentage are given as 5 .13 percent
for fossil-fueled plants and 5. 68 percent for nuclear plants. Thus,
the fixed charge rate depends upon the economic conditions at a
particular site locale. Private financing is assumed. Federal
financing results in lower interest rates and nd taxes.
In the Annualized Capital Cost nomograph, page N-46, annualized,
incremental capital cost in dollars per year is obtained from the product
of the fixed charge rate and the total incremental capital cost (TICC).
The input to this nomograph, TICC, will be defined since it depends
upon the type of thermal pollution control system. In general, the total
incremental capital cost, TICC, is equal to the heat rejection system
cost (HRSC) for a given method, plus the component costs from the cost
nomographs.
For wet towers, spray ponds, and cooling ponds:
TICC = HRSC + CC+WCSC (32)
For these systems, HRSC is the capital cost of a natural draft wet
tower, a mechanical draft wet tower, a spray pond, or a cooling pond
from previous nomographs. The CC and WCSC are input capital costs
defined on the respective cost nomographs in this section.
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For the dry towers:
TICC = HRSC + SSIC + TGIC (33)
The heat rejection system cost, HRSC, for the dry towers already in-
cludes cost for the water circulation system and condenser. The pro-
cedure for obtaining SSIC and TGIC is given in the dry tower examples of
Section XII.
For once-through cooling:
TICC = OTCC + CC (34)
The cost for once-through cooling, OTCC, includes the water circula-
tion system.
The Additional Annual Power Cost Nomograph, page N-47, determines
the cost which results from the auxiliary power requirements. First,
the additional annual energy consumption is obtained from the following
equation:
additional annual energy consumption, Kw-hr/yr = (35)
auxiliary power requirements, Mw x plant load
factor x 8. 76 x 106
Finally, the additional annual power cost, in dollars per year, is obtained
from the product of the additional annual energy consumption and the
unit cost for electrical power.
The Additional Annual Fuel Cost Nomograph, page N-48, is based on
the equation:
additional annual fuel cost, $/yr = additional heat (36)
capacity, 10^ Btu/hr x plant load factor x fuel
cost, $/l()6 Btu x 8760
Fossil and nuclear fuel cost variations are covered by the range of fuel
costs presented in the nomograph. The cost is for the additional fuel
required from the increase of steam rate to maintain rated output.
Additional fuel cost is incurred for plant operation above 2 in. Hg
absolute.
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The last nomograph, page N-49, is entitled Incremental Generating Cost.
The input to this nomograph is the resulting summation of costs from the'
last three cost nomographs:
total incremental annual cost, $/yr = annualized
capital cost + additional annual power cost +
additional annual fuel cost /37\
Then the incremental generating cost results from the equation:
incremental generating cost, mills/Kw-hr =
total incremental annual cost. $/yr
8760 x plant load factor x net generating capacity, Mw (38)
It should be emphasized that the costs obtained from the last three
nomographs, N-47, N-48. and N-49, are based on design conditiona.
The true annual costs for additional power and additional fuel based
on off-design conditions would be less than those costs obtained from
JN-47 and N-48.
67
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SECTION XII
NOMOGRAPH EXAMPLES
General
Illustrative cases are presented which consider an 800 Mw fossil-fueled
plant utilizing each of the types of thermal pollution control systems.
The purpose of the examples is an instructive one with respect to their
use. These results should not be used alone to evaluate the merits of
one system versus another. In some cases, results of interest are
pointed out and compared with other sources. Each example is solved
through as far as application of the turbine performance nomographs.
Only the example for the natural draft wet tower is carried through
completely and displayed by the example lines in the turbine performance,
water requirements, and cost nomographs.
Natural Draft Wet Tower
In Table 5, most of the input conditions correspond to the design con-
ditions of Big Sandy, Unit No. 2. The tower cost, calculated in the table
to be $4. 9 million, compares well with that estimated by Wood son in Reference
31» $4.2 million (based on 1970 prices). However, no other assumptions
from Reference 31 are known except for the application to an 800 Mw
fossil-fueled plant.
Mechanical Draft Wet Tower
In Tables 6 and 7, examples are shown for the mechanical draft wet
tower assuming closed cycle and open cycle modes of operation,
respectively. Nomographs N-7 through N-12 show only the example
lines for the closed cycle case.
The mechanical draft tower cost of Table 6 is $1. 55 x 106 and excludes
cold water basins, fan motor starters, controls, and wiring. It can be
compared to capital costs from other sources. For example, Hauser,
69
-------
TABLES. NOMOGRAPH EXAMPLE
NATURAL DRAFT WET TOWER
(sheet 1 of 2)
Net generating capacity, Mw
Type of plant
Plant heat rate, Btu/Kw-hr
Plant load factor, percent
Dry bulb temperature, °F
Wet bulb temperature, °F
Relative humidity, percent
Range, °F
A. Tower Performance (N-l)
Base diameter, ft
Dry bulb temperature, °F (enter)
Relative humidity, percent (enter)
Tower height, ft (enter)
Cold water temperature, °F (read)
B. Turbine Back Pressure (N-2)
Cold water temperature, °F (enter)
Condenser rise, °F (enter)
Terminal temperature
difference, °F
Turbine back pressure, in. Hg abs (read)
C. Tower Unit Cost (N-3)
Wet bulb temperature, °F (enter)
Range, °F (enter)
Approach, °F (enter)
Tower unit cost, $/1000 Btu/hr (read)
D. Tower Cost (N-4)
Heat rejection rate, 109 Btu/hr (enter)
(from Turbine Performance
Nomographs at above plant
capacity and type, heat rate,
and turbine back pressure)
Tower unit cost, $/1000 Btu/hr (enter)
Natural draft tower cost, $106 (read)
E. Flow Rate (N-5)
Heat rejection rate, 109 Btu/hr (enter)
Condenser rise, °F (enter)
Water flow rate, 106 gpm (read)
800
Fossil
9050
60
77
70
71
28.7
300
77
71
400
88.5
88. 5
28. 7
6
3.8
70
28.7
18.5
1.4
3.5
1.4
4.9
3.5
28.7
0.25
70
-------
TABLE 5 (continued)
(sheet 2 of 2)
F. Auxiliary Power (N-6)
Water flow rate, 10^ gpm (enter)
Total head, ft (enter)
Pump power requirements, Mw (read)
G. Plant Efficiency (N-31)
Turbine back pressure, in.Hg abs (enter)
Plant type (enter)
Plant efficiency, percent (read)
H. Additional Heat Capacity (JM-29)
Turbine back pressure, in.Hg abs (enter)
Plant capacity, Mw (enter)
Plant type (enter)
Additional heat capacity,
109 Btu/hr (read)
0.25
50
2. 8
3.8
Fossil
35.2
3. 8
800
Fossil
0. 115
28. 7°F / Cooling
Tower
117. 2°F
Condenser
wvw*-
88. 5°F
~~H 2R. 7°F r*—
71
-------
(sheet 1 of 2)
TABLE 6. NOMOGRAPH EXAMPLE -
MECHANICAL DRAFT WET TOWER
(CLOSED CYCLE)
Net generating capacity, Mw
Type of plant
Plant heat rate, Btu/Kw-hr
Plant load factor, percent
Dry bulb temperature, °F
Wet bulb temperature, °F
Relative humidity, percent
Range, °F
Approach, °F
A. Tower Correction Factor (N-7)
Wet bulb temperature, °F (enter)
Range, °F (enter)
Approach, °F (enter)
Tower correction factor (read)
B. Turbine Back Pressure (N-8)
Wet bulb temperature, °F (enter)
Approach. °F (enter)
Condenser Inlet temperature, °F (read)
Condenser Rise, °F (enter)
Terminal temperature difference,
oF
Turbine back pressure, in.Hg abs (read)
C. Flow Rate (N-9)
Heat rejection rate, 109 Btu/hr (enter)
(from Turbine Performance
Nomographs at above plant
capacity and type, heat rate
and turbine back pressure)
Condenser rise, °F (enter)
Water flow rate, 106 gpm (read)
D. Tower Cost (N-10)
Water flow rate, 106 gpm (enter)
Tower correction factor (enter)
Number of tower units, 106 TU (read)
Cost per tower unit, $/TU (enter)
Mechanical draft tower cost, $106 (read)
800
Fossil
9540
60
70
25
15
70
25
15
1.04
70
15
85
25
6
3. 1
3.9
25
0.32
0.32
1. 04
0.33
4.75
1.55
72
-------
TABLE 6 (continued)
(sheet 2 of 2)
E. Fan Power (N-ll)
Number of tower units, 106 TU
Fan power requirements, Mw
F. Pump Power (N-12)
Type of operation
Water flow rate, 10^ gpm
Total pumping head, ft
Pump power requirement, Mw
Auxiliary power, Mw
G. Plant Efficiency (N-31)
Turbine back pressure, in.Hgabs
Plant type
Plant efficiency, percent
H. Additional Heat Capacity (N-29)
Turbine back pressure, in. Hg abs
Plant capacity, Mw
Plant type
Additional heat capacity,
109 Btu/hr
(enter)
(read)
(enter)
(enter)
(enter)
(read)
(enter)
(enter)
(read)
(enter)
(enter)
(enter)
(read)
0. 33
2.7
Closed
0. 32
60 (constant)
4.2
6.9
3. 1
Fossil
35.5
3.1
800
Fossil
0.058
85°F
85°F
25°F
73
-------
TAELJ? 7. NOMOGRAPH EXAMPLE - '.jhcet 1
MECHANICAL DRAFT WET TOWER
(OPEN CYCLE)
of 2}
Net generating capacity, Mw
Type of plant
Plant heat rate, Btu/Kw-hr
Plant load factor, percent
Condenser inlet temperature, °F
Wet bulb temperature, °F
Relative humidity, percent
Range, °F
Approach, °F
A. Tower Correction Factor (N-7)
Wet bulb temperature, °F (enter)
Range, °F (enter)
Approach, °F (enter)
Tower correction factor (read)
B. Turbine Back Pressure (N-8)
Condenser inlet temperature, °F (enter)
Condenser rise, °F (enter)
Terminal temperature
difference, °F
Turbine back pressure, in. Hg abs (read)
C. Flow Rate (N-9)
Heat rejection rate, 10 Btu/hr (enter)
(from Turbine Performance
Nomographs at above plant
capacity and type, heat rate
and turbine back pressure)
Condenser Rise (Range +Atemp. (enter)
of 50F), °F
Water flow rate, 106 gpm (read)
D. Tower Cost (N-10)
C
Water flow rate, 10 gpm (enter)
Tower correction factor (enter)
Number of tower units, 10^ TU (read)
Cost per tower unit, $/TU (enter)
Mechanical draft tower cost, $106 (read)
800
Fossil
9540
60
80
70
25
15
70
25
15
1. 04
80
30
6
3. 1
3. 9
30
0. 26
0. 26
1. 04
0. 27
4. 75
1. 3
74
-------
TABLE 7 (Continued)
(sheet 2 of 2)
E. Fan Power (N-ll)
Number of tower units, 10^ TU
Fan power requirements, Mw
F. Pump Power (N-12)
Type of operation
Water flow rate, 106 gpm
Total pumping head, ft
Pump power requirements, Mw
Auxiliary power, Mw
G. Plant Efficiency (N-31)
Turbine back pressure, inHg abs
Plant type
Plant efficiency, percent
H. Additional Heat Capacity (N-29)
Turbine back pressure, in, Hg abs
Plant capacity, Mw
Plant type
Additional heat capacity,
109 Btu/hr
(enter)
(read)
(enter)
(enter)
(enter)
(read)
(enter)
(enter)
(read)
(enter)
(enter)
(enter)
(read)
0.27
2.25
Open
0. 26
120
6.9
9. 15
3. 1
Fossil
35. 5
3. 1
800
Fossil
0. 058
Condenser
wvw*
30°F
. 80°F
h»—
75
-------
vn, and >li.-^'.>nhol2;er (V ".. 32} present cur/.3S v/Lic h yield an
estimated cost of $1. 9 x 106 for the range, approach, and plant size
assumed in our example. Their tower cost shouJd be higher since it
includes the basin and eieecricai apparatus. Following the procedure
in a. series of curves presented by Dynatech Co. (Ref. 9), one obtains
a cooling tower cost of $2. 5 x 106 for the conditions in Table 6. How-
ever, they pointed out that the costs from their curves appear to be
50 percent high when compared to other data. Accounting for this fact
and an escalation factor from 1969 to 1971, a corrected cost from
Reference 9 of $2 x 106 is obtained. Woodson (Ref. 31) indicates a
capital cost of $1. 7 x 106 for mechanical draft wet towers and basin
in an 800 Mw fossil-fueled plant. Other design conditions employed
to obtain this result are unknown. As a result of these comparisons,
it is concluded that the nomographs yield good capital cost estimates
for mechanical draft towers. Based on these costs, an approximate
15 percent cost increment should be added to the value from N-10 in
order to include the basins and electrical apparatus.
Spray Pond
Closed cycle and open cycle examples for the spray pond are presented
in Tables 8 and 9, respectively. Nomographs N-13 through N-16
show only the example lines for the closed cycle case.
Cooling Pond
Closed cycle and open cycle examples for the cooling pond are presented
in Tables 10 and 11. Nomographs N-17 through N-21 show only the
example lines for the closed cycle case.
In Reference 31, Woodson reported a cooling lake cost of $2. 6 million
for an 800 Mw fossil-fueled plant. This shows reasonable comparison
with the $2. 2 million value for the closed cycle case in Table 10. The
value from the table is based on a land and excavation unit cost of $2000
per acre.
76
-------
(sheet 1 of 2)
TABLE 8. NOMOGRAPH EXAMPLE -
SPRAY POND
(CLOSED CYCLE)
Net generating capacity, Mw
Type of plant
Plant heat rate, Btu/Kw-hr
Plant load factor, percent
Wet bulb temperature, °F
Condenser rise, °F
Inlet water temperature, °F
Wind velocity, mph
A. Spray Pond Performance (N-13)
Inlet water temperature, °F
Wet bulb temperature, °F
Wind velocity, mph
Pond water temperature, °F
B. Turbine Back Pressure (N-14)
Condenser inlet temperature,
°F
Condenser rise, °F
Terminal temperature
difference, °F
Turbine back pressure,
in. Hg abs
(enter)
(enter)
(enter)
(read)
(enter)
(enter)
(read)
C. Flow Rate (N-15)
Heat rejection rate, 10^ Btu/hr (enter)
(from Turbine Performance
Nomographs at above plant
capacity and type, heat rate
and turbine back pressure)
Condenser rise, °F (enter)
Water flow rate, 10" gpm (read)
D. Spray Pond Cost (N-16)
Water flow rate, 10^ gpm (enter)
Pond unit cost, $/gpm (enter)
Spray pond capital cost, $10^ (read)
E. Auxiliary Power (N-16)
Water flow rate, 10° gpm (enter)
Power consumption, Kw/gpm (enter)
Auxiliary power requirements, (read)
Mw
800
Fossil
9540
60
70
20
110
5
110
70
5
90
90
20
6
3. 1
20
0. 4
0. 4
9
3. 6
0.4
0. 025
10
77
-------
TABLE 8 (Continued)
(sheet 2 of 2)
F. Plant Efficiency (N-31)
Turbine back pressure, in. Hgabs (enter)
Plant type (enter)
Plant efficiency, percent (read)
G. Additional Heat Capacity (N-29)
Turbine back pressure, in. Hg abs (enter)
Plant capacity, Mw (enter)
Plant type (enter)
Additional heat capacity,
109 Btu/hr (read)
3.1
Fossil
35.5
3.1
800
Fossil
0.059
90°F
r-
20°F
Spray
Pond
110°F
Condenser
-A/YVVV*-
20°F
90°F
78
-------
(sheet 1 of 2)
TABLE 9. NOMOGRAPH EXAMPLE -
SPRAY POND
(OPEN CYCLE)
Net generating capacity, Mw
Type of plant
Plant heat rate, Btu/Kw-hr
Plant load factor, percent
Wet bulb temperature, °F
Range, °F
Inlet water temperature, °F
Wind velocity, mph
A. Spray Pond Performance (N-13)
Inlet water temperature, °F (enter)
Wet bulb temperature, °F (enter)
Wind velocity, mph (enter)
Pond water temperature, °F (read)
B. Turbine Back Pressure (N-14)
Condenser inlet temperature, °F (enter)
Condenser rise, °F (enter)
Terminal temperature
difference, °F
Turbine back pressure, in. (read)
Hg abs
C. Flow Rate (N-15)
Heat rejection rate, ICr Btu/hr (enter)
(from Turbine Performance
Nomographs at above plant
capacity and type, heat rate
and turbine back pressure)
Condenser rise (range + A temp.
of 5°F), °F (enter)
Water flow rate, 10b gpm (read)
D. Spray Pond Cost (N-16)
Water flow rate, 10^ gpm (enter)
Pond unit cost, $/gpm (enter)
Spray pond capital cost, $106 (read)
E. Auxiliary Power (N-16)
n
Water flow rate, 10° gpm (enter)
Power consumption, Kw/gpm (enter)
Auxiliary power requirements, Mw(read)
800
Fossil
9540
60
70
20
110
5
110
70
5
90
85
25
6
3. 1
25
0.32
0.32
9
2. 9
0.32
0.025
8
79
-------
TABLE 9 (Continued)
(sheet 2 of 2)
F. Plant Efficiency (N-31)
Turbine back pressure, in. Hg abs (enter)
Plant type (enter)
Plant efficiency, percent (read)
G. Additional Heat Capacity (N-29)
Turbine back pressure, in.Hg abs (enter)
Plant capacity, Mw (enter)
Plant type (enter)
Additional heat capacity,
109 Btu/hr (read)
3. 1
Fossil
35.5
3.1
800
Fossil
0.059
90°F
20°F Spray
Pond
110°F
25°F
80
-------
TABLE 10. NOMOGRAPH EXAMPLE*-
COOLING POND
_ (CLOSED CYCLE)
°'
Net generating capacity, Mw
Type of plant
Plant heat rate, Btu/Kw-hr
Plant load factor, percent
Heat exchange coefficient, Btu/day-ft2-°F
Condenser rise, OF
Residual temperature rise, °F
Design equilibrium temperature, °F
A. Pond Performance (N-17)
Condenser rise, °F (enter)
Residual temperature rise, (enter
op-
Heat exchange coefficient, (enter)
Btu/day-ft2-OF
Plant type (enter)
Pond loading, Mw/acre (read)
B. Turbine Back Pressure (N-18)
Condenser inlet temperature, (enter)
OF
Condenser rise, °F (enter)
Terminal temperature
difference, °F
Turbine back pressure, in. (read)
Hg abs
C. Cooling Pond Cost (N-19)
Pond loading, Mw/acre (enter)
Plant capacity, Mw (enter)
Pond size, acres (read)
Land and excavation unit cost,
$/acre (enter)
Pond land and excavation cost,
$106 (read)
D. Flow Rate (N-20)
Heat rejection rate, 109 Btu/hr (enter)
(from Turbine Performance
Nomographs at above plant
capacity and type, heat rate
and turbine back pressure)
Condenser rise, °F !ent ^V
Water flow rate, 106 gpm (read;
800
Fossil
9540
60
150
20
5
80. 6
20
5
150
Fossil
0. 73
85. 6
20
6
2. 72
0.73
800
1100
2000
2.2
3. 9
20
0.39
81
-------
TABLE IG(Continued)
(Sheet 2 of 2)
E. Auxiliary Power (N-21)
Water flow rate, 10^ gpm (enter)
Total head, ft (enter)
Pump power requirements, Mw (read)
F. Plant Efficiency (N-31)
Turbine back pressure, in, Hg abs (enter)
Plant type (enter)
Plant efficiency, percent (read)
G. Additional Heat Capacity (N-29)
Turbine back pressure, in.Hg abs (enter)
Plant capacity, Mw (enter)
Plant type (enter)
Additional heat capacity,
109 Btu/hr (read)
0. 39
20
1.75
2.72
Fossil
35. 6
2.72
800
Fossil
0.031
85. 6°F
20oF ; Cooling
^ * ' Pond
85. 6°F
82
-------
(sheet 1
TABLE 11. NOMOGRAPH EXAMPLE -
COOLING POND
(OPEN CYCLE)
of 2)
Net generating capacity, Mw
Type of plant
Plant heat rate, Btu/Kw-hr
Plant load factor, percent
Heat exchange coefficient, Btu/day-ft2-oF
Condenser rise, °F
Residual temperature rise, °F
Design equilibrium temperature, °F
Condenser inlet temperature, °F
A. Pond Performance (N-17)
ATc, °F (enter)
Residual temperature rise,°F (enter)
Heat exchange coefficient, (enter)
Btu/day-ft2-°F
Plant type (enter)
Pond loading, Mw/acre (read)
B. Turbine Back Pressure (N-18)
Condenser inlet temperature, (enter)
°F
Condenser rise, F (enter)
Terminal temperature
difference, °F
Turbine back pressure, in. (read)
Hg abs
C. Cooling Pond Cost (N-19)
Pond loading, Mw/acre (enter)
Plant capacity, Mw (enter)
Pond size, acres (read)
Land and excavation unit (enter)
cost, $/acre
Pond land and excavation (read)
cost, $106
D. Flow Rate (N-20)
Heat rejection rate, 109 Btu/hr (enter)
(from Turbine Performance
Nomographs at above plant
capacity and type, heat rate
and turbine back pressure)
Condenser rise, °F (enter)
Water flow rate, 106 gpm (read)
800
Fossil
9540
60
150
25
4
84. 6
83. 6
20
4
150
Fossil
0. 64
83. 6
25
6
2.96
0. 64
800
1250
2000
2. 5
3. 9
25
0. 31
83
-------
TABLE 11 (Continued)
(sheet 2 of 2)
E. Auxiliary Power (N-21)
Water flow rate, 106 gpm (enter)
Total head, ft (enter)
Pump power requirements, Mw (read)
F. Plant Efficiency (N-31)
Turbine back pressure, in.Hg abs (enter)
Plant type (enter)
Plant efficiency, percent (read)
G. Additional Heat Capacity (N-29)
Turbine back pressure, in.Hg abs (enter)
Plant capacity, Mw (enter)
Plant type (enter)
Additional heat capacity,
109 Btu/hr (read)
0. 31
50
3.5
2.96
Fossil
35.6
2.96
800
Fossil
0.048
88. 6°F
25°F
84
-------
Natural and Mechanical Draft Dry Towers
["he illustrative examples for the natural and mechanical draft dry
owers are presented in Tables 12 and 13, respectively. The example
ines for each of these cases appear on Nomographs N-22 and N-26.
The presence of the dry towers causes this plant to operate at a turbine
lack pressure of 6 in. Hg absolute. The cost penalty for capability
oss is computed for each case to be approximately $3. 3 x 10^. This
s based on the requirement for supplementary additional heat capacity
tetween 3. 5 in. Hg absolute and 6 in. Hg absolute.. It should be ob-
served that this cost penalty could be reduced if peaking units were
tvailable.
n the nomographs, it is assumed that these plants utilize a conven-
ional turbine modified for operation at high back pressure. In the
uture, plants employing dry towers will be designed to utilize a high
>ack pressure turbine whose performance and costs are different.
low ever, for the present the nomographs may be used for dry towers
n new plants.
85
-------
(sheet 1 of 2)
TABLE 12. NOMOGRAPH EXAMPLE -
NATURAL DRAFT DRY TOWER
Net generating capacity, Mw
Type of plant
Plant heat rate, Btu/Kw-hr
Plant load factor, percent
Dry bulb temperature, °F
A. Combined Performance (N-22)
800
Fossil
9540
60
90
Dry bulb temperature, °F (enter)
Plant capacity, Mw (enter)
Plant type (enter)
Heat rejection, 109 Btu/hr (read)
Turbine back pressure, in. Hg abs (read)
B. Initial Temperature Difference (N-24)
Turbine back pressure, in. Hg abs (enter)
Dry bulb temperature, F (enter)
Initial temperature difference, °F (read)
C. Capital Cost (N-25)
Initial temperature difference, °F (enter)
Plant capacity, Mw (enter)
Plant type (enter)
Heat rejection system cost, $106 (read)
D. Auxiliary Power (N-26)
Initial temperature difference, °F (enter)
Plant capacity, Mw (enter)
Plant type (enter)
Auxiliary power requirements, Mw(read)
E. Plant Efficiency (N-31)
Turbine back pressure, in. Hg abs (enter)
Plant efficiency, percent (read)
F. Additional Heat Capacity (N-29)
Turbine back pressure, in. Hg abs (enter)
Plant capacity, Mw (enter)
Plant type (enter)
Additional heat capacity, 10 Btu/hr (read)
90
800
Fossil
4. 05
6
6
90
50
50
800
Fossil
19.5
50
800
Fossil
7. 1
6
34.?.
6
800
Fossil
0. 37
86
-------
(sheet 2 of 2)
TABLE 12. (Continued)
Steam Supply Incremental Cost (N-29 and N-39)
Additional heat capacity at 3. 5 in. 89
Hg, 106 Btu/hr
Additional heat capacity at 6 in. 365
Hg, 106 Btu/hr
SSIC at 89 x 106 Btu/hr, $10$ la*«onn/K-w °- 67
SSIC at 365 x 1<)6 Btu/hr, $1()6 / at *2Q0'™ 2. 8
.'. A SSIC = (2. 8 - 0. 67) x $106 = $2. 1 x 10°
Turbine Generator Incremental Cost (N-40)
Same input additional heat capacities as in G.
TGIC at 89 x 1Q6 Btu/hr, $10$ } t $200/Kw 0. 38
TGIC at 365 x 106 Btu/hr, $106j * 1. 6
/. ATGIC = (1. 6 - 0. 38) x $106 = $1. 2 x 106
The cost penalty for capability loss for this plant =
(2. 1 + 1. 2) x $106 = $3. 3 x 106
87
-------
TABLE 13. NOMOGRAPH EXAMPLE -
MECHANICAL DRAFT DRY TOWER
Net generating capacity, Mw
Type of plant
Plant heat rate, Btu/Kw-hr
Plant load factor, percent
Dry bulb temperature, °F
A. Combined Performance (N-23)
Dry bulb temperature, °F
Plant capacity, Mw
Plant type
Heat rejection, 10a Btu/hr
(enter)
(enter)
(enter)
(read)
Turbine back pressure, in. Hg abs (read)
B. Initial Temperature Difference (N-24)
Turbine back pressure, In. Hg abs (enter)
Dry bulb temperature, °F (enter)
Initial temperature difference, °F (read)
C. Capital Cost (N-25)
Initial temperature difference, °F (enter)
Plant capacity, Mw (enter)
Plant type (enter)
Heat rejection system cost, $10b (read)
D. Auxiliary Power (N-26)
Initial temperature difference, °F (enter)
Plant capacity, Mw (enter)
Plant type (enter)
Auxiliary power requirements, Mw(read)
E. Plant Efficiency (N-31)
Turbine back pressure, in.Hg abs (enter)
Plant efficiency, percent (read)
F. Additional Heat Capacity (N-29)
Turbine back pressure, in. Hg abs (enter)
Plant capacity, Mw (enter)
Plant type (enter)
Additional heat capacity, 109 Btu/hr (read)
The same procedure is followed as in Table 12 yielding the
penalty for capability loss of $3. 3 x 10^ for this plant.
800
Fossil
9540
60
90
90
800
Fossil
4. 1
6
6
90
50
50
800
Fossil
18.5
50
800
Fossil
21
6
34. 1
6
800
Fossil
0. 37
same cost
88
-------
Makeup Water Requirements
Two examples are presented that utilize the Water Requirements nomo-
graphs. In the first case, the natural draft wet tower introduced in
Table 5 is solved to yield the makeup water requirements. Components
result from N-34 through N-38 for evaporative loss, drift loss, and
blowdown and are shown in Table 14. In Case 2, the makeup water
requirements for the cooling pond (Ref. Table 10) operating in a
closed cycle mode are presented. Table 15 shows the results due to
evaporative losses alone following application of N-33 and N-35.
In Table 14, the average annual evaporative loss is estimated to be
6. 2 cfs following application of the factors introduced in Section X
This can be compared to the design evaporative loss of 13 cfs deter-
mined from the nomographs.
In Table 15, the average annual evaporative loss for the cooling pond
was computed to be 9. 3 cfs after accounting for the evapotranspiration
correction assuming characteristics similar to the Lake Michigan area.
This estimate is much less than the design evaporative loss of 19. 8 cfs.
yet higher than the 6. 2 cfs average water loss from a cooling tower.
89
-------
TABLE 14. NOMOGRAPH EXAMPLE
WATER REQUIREMENTS
(CASE 1)
Net generating capacity, Mw
Type of plant
Type of heat rejection system
Range, °F
Approach, F
Water flow rate, 106 gpm
Drift loss, percent
Number of concentrations
A. Evaporative Loss (N-34)
Range, °F (enter)
Type of cooling system (enter)
Approach, °F (enter)
Evaporative loss, cfs/Mw (read)
B. Percent Evaporative Loss (N-35)
Evaporative loss, cfs/Mw (enter)
Plant capacity, Mw (enter)
Evaporative loss, cfs (read)
Water flow rate, cfs (enter)
Evaporative loss, percent of
flow rate (read)
C. Percent Slowdown (N-36)
Drift loss, percent (enter)
Number of concentrations (enter)
Evaporative loss, percent (enter)
Slowdown, percent (read)
D. Makeup Water (N-38)
Makeup water requirements,
percent (enter)
Water flow rate, cfs (enter)
Makeup water requirements, cfs (read)
Makeup water requirements,
106 gpm (read)
800
Fossil
Natural Draft Wet
28.7
18.5
0. 25
0. 005
3
28. 7
Natural Draft Wet
18. 5
0. 0162
0. 0162
800
13. 0
560
2. 32
0. 005
3
2. 32
1. 16
3. 48
560
19. 5
0. 0087
90
-------
(sheet 2 of 2)
TABLE 14. (Continued)
E. Average Annual Evaporative Loss
Design evaporative loss, cfs 13. 0
x plant capacity factor (. 6)
x off-design conditions factor (. 8)
= Average annual evaporative loss, cfs 6. 2
91
-------
TABLE 15. NOMOGRAPH EXAMPLE -
WATER REQUIREMENTS
(CASE 2)
Net generating capacity, Mw
Type of plant
Type of heat rejection system
Design equilibrium temperature, °F
Wet bulb temperature, °F
Condenser rise, °F
Water flow rate, 10^ gpm
Pond loading, fossil Mw/acre
A. Cooling Pond Evaporation (N-33)
Wet bulb temperature, °F (enter)
Pond loading, fossil acre/Mw (enter)
Evaporative loss, cfs/Mw (read)
800
Fossil
Cooling Pond
(Closed Cycle)
80. 6
70
20
0. 39
0. 73
70
1. 37
0. 0247
B. Percent Evaporative Loss (N-35)
Evaporative loss, cfs/Mw (enter) 0. 0247
Plant capacity, Mw (enter) 800
Evaporative loss, cfs (read) 19. 8
Water flow rate, cfs (enter) 870
Evaporative loss, percent (read) 2. 28
of flow rate
Makeup water requirements, 19. 8
cfs
Makeup water requirements, 0. 0089
106 gpm
C. Average Annual Evaporative Loss
Design evaporative loss, cfs 19. 8
Plant capacity factor (0. 6) x 19. 8 = 11. 9
Evapotranspiration correction* (at 1100 acres) - 2. 6
Average annual evaporative loss, cfs 9. 3
* Assumes characteristics similar to the Lake
Michigan region.
92
-------
Costs
Two examples are presented which utilize the cost nomographs. In
Case 1, the incremental generating cost is determined for the natural
draft wet tower introduced in Table 5. Example lines for this case
appear on Nomographs N-41 through N-49, excluding N-44. Results
for this case are in Table 16 and 17. Table 18 presents the develop-
ment of the incremental generating cost for a once-through cooling
system. In the cost estimation for once-through cooling systems,
only Nomographs N-41, N-42, N-44, N-45, N-46, and N-49 are
employed.
Some of the input quantities selected in the two examples are discussed
in the following paragraphs. The plant load factor was assumed to be
60 percent. This magnitude represents an upper bound of the approxi-
mate average annual plant factors for selected conventional, fossil-
fueled steam-electric generating plants as reported in Reference 19.
Modern, large, fossil-fueled and nuclear-fueled power plants will
be expected to achieve 70 percent and 80 percent, respectively, in
future years.
The unit power cost was assumed at 0. 8 cents/Kw-hr. This value is
a little higher than the reported (Ref. 33) total power plant busbar
energy cost of 0. 72 cents/Kw-hr for stations put into service after
1967. In Table 16, the additional annual power cost has the least
contribution to the total incremental annual cost.
The fuel cost for the fossil plant example was assumed to be $0. 30/
10" Btu. This quantity is representative (at the low end) of the cost
range for the various fossil fuels. In Reference 34, fuel costs in
1971 for the total United States averaged 29. 1 cents/106 Btu for gas,
36. 3 cents/106 Btu for coal and 55. 5 cents/106 Btu for oil consumed.
According to Reference 35, projected nuclear fuel costs up through 1975
will remain nearly constant at 20 cents/10^ Btu. Nuclear fuel costs
are also listed for specific power plants in Reference 19. Fuel costs
for four of these nuclear plants average out to 25 cents/10^ Btu.
93
-------
(sheet 1
TABLE 16. NOMOGRAPH EXAMPLE -
COSTS
(CASE 1)
of 2)
Net generating capacity, Mw
Type of plant
Plant load factor, percent
Type of heat rejection system
Turbine back pressure, in. Hg abs
Additional heat capacity, 10^ Btu/hr
Water flow rate, 10^ gpm
Auxiliary Power requirements, Mw
Natural draft tower cost, $106
800
Fossil
60
Natural Draft Wet
3. 8
115
0. 25
2. 8
4. 9
(enter)
(enter)
(enter)
A. Condenser Surface Area (N-41)
C
Water flow rate, 10° gpm
Condenser rise, °F
Overall heat transfer coefficient,
Btu/hr-ft2-op 6
Area of heat transfer surface, 10 ft2 (read)
B. Condenser Cost (N-42)
Area of heat transfer surface, 10^ ft (enter)
Condenser tube material (enter)
Condenser capital cost, $10^ (read)
(including field installation)
C. Water Circulation System Cost (N-43)
C
Water flow rate, 10 gpm (enter)
Natural draft tower at 50 ft head (enter)
Water circulation system capital (read)
cost, $106
/. The total incremental capital cost =
heat rejection system cost for a given
method + costs from B and C above =
(4. 9 + 8. 2 + 0. 41) x $106 = $13. 51 x 106
0. 25
28. 7
600
0. 37
0. 37
Admiralty
8. 2
0. 25
50
0.41
D. jpapital Recovery Factor (N-45)
Interest rate, percent
Years amortized
Capital recovery factor, percent
Recurring costs, %/year
Fixed charge rate, %/year
(enter)
(enter)
(read)
8
30
8.9
5. 2
14. 1
94
-------
TABLE 16. (Continued)
{sheet 2 of 2)
E. Annualized Capital Cost (N-46)
Total incremental capital cost, (enter)
$106
Fixed charge rate, %/year (enter)
Annualized incremental capital (read)
cost, $106/year
F. Additional Annual Power Cost (N-47)
Auxiliary power requirements, Mw (enter)
Plant load factor, percent (enter)
Additional annual energy (read)
consumption, 10$ Kw-hr/yr
Unit power cost, cents/Kw-hr (enter)
Additional annual power cost, (read)
$106/year
G. Additional Annual Fuel Cost (N-48)
Additional heat capacity, 106 Btu/hr (enter)
Plant load factor, percent (enter)
Fuel cost, $/106 Btu (enter)
Additional annual fuel cost, (read)
$106/year
/, Total incremental annual cost = annual costs
from E, F, and G above = (1. 9 + 0. 12 +
0. 19) x $106/year = 2. 21 x 106/year
H. Incremental Generation Cost (N-49)
Total incremental annual cost, (enter)
$106/year
Plant load factor, percent (enter)
Plant capacity, Mw (enter)
Incremental generating cost, (read)
mills/Kw-hr
13. 5
14. 1
1.9
2. 8
60
15
0. 8
0. 12
115
60
0. 30
0. 19
2. 21
60
800
0. 52
95
-------
TABLE 17. AVERAGE ANNUAL OPERATING
COSTS FOR CASE 1*
Average
Season DBT
OF
Winter
Spring
Summer
Fall
Total
Value
24
43. 5
68
50. 5
77
Average Additional
Relative TBP Auxiliary AQ Annual
Humidity CWT in. Hg Power 106 Fuel Cost
% °F abs Mw Btu/hr $/yr
80
70
70
75
71
- 2 2.
72. 5 2. 39 2.
84. 2 3. 35 2.
75. 8 2. 64 2.
88.5 3.8 2.
7
7
8
8
8
0
14
77
27
115
5
30
10
46
190
0
,500
,400
,700
,600
,000
Under
Design
Conditions
Meteorological data for Lake Michigan region.
96
-------
(sheet 1 of 2)
TABLE 18. NOMOGRAPH EXAMPLE -
COST OF ONCE-THROUGH COOLING
(CASE 2)
Net generating capacity, Mw
Type of plant
Plant load factor, percent
Type of heat rejection system
Turbine back pressure, in. Hg abs
Range, °F
Water flow rate, 10b gpm
A. Condenser Surface Area (N-41)
£•
Water flow rate, 10° gpm
Condenser rise, °F
Overall heat transfer coefficient,
Btu/hr-ft2-QF
Area of heat transfer surface,
106 ft2
B. Condenser Cost (N-42)
Area of heat transfer surface,
106 ft2
Condenser tube material
Condenser capital cost, $10°
(including field installation)
C. Cost for Once-Through Cooling (N-44)
£>
Water flow rate, 10° gpm
Total structural length, ft
Intake and outfall structure
cost, $106
(read)
(enter)
(enter)
(read)
(enter)
(enter)
(read)
800
Fossil
60
Once-Through
~ 2
20
0. 38
(enter)
(enter)
(enter)
0. 38
20
600
.*• The total incremental capital cost = costs
from B and C = (10. 6 + 2. 2) x $106 =
$12. 8 x 106
D. Capital Recovery Factor (N-45)
Interest rate, percent
Years amortized
Capital recovery factor, percent
Recurring costs, %/year
Fixed charge rate, %/year
(enter)
(enter)
(read)
0. 48
0. 48
Admiralty
10. 6
0. 38
1000
2. 2
8
30
8. 9
5. 2
14. 1
97
-------
TABLE 18. (Continued)
(sheet 2 of 2)
E. Annualized Capital Cost (N-46)
Total incremental capital cost, (enter)
$106
Fixed charge rate, %/year (enter)
Annualized incremental capital (read)
cost, $106/year
F. Incremental Generating Cost (N-49)
Total incremental annual cost, (enter)
$106/year
Plant load factor, percent (enter)
Plant capacity, Mw (enter)
Incremental generating cost, (read)
mills /Kw-hr
12. 8
14. 1
1. 8
1. 8
60
800
0. 42
98
-------
Based on the end results found in Tables 16 and 18, the differential
busbar cost due to closed cycle cooling is:
0. 52 - 0.42 = 0. 10 mills/Kw-hr
These values are valid assuming operation under design conditions.
The additional annual power cost and the additional annual fuel cost
will be less than the design values presented in Table 16 when the plant
operates under off-design conditions through the year. Average annual
operating costs were estimated for the natural draft wet tower of
Case 1. The results of Table 17 follow after applying several of the
nomographs using off-design meteorological input conditions. In this
table, discrete quantities appear for the four seasons of the year.
The seasonal values can then be compared to the corresponding one
under design conditions presented at the bottom of the table.
The dry bulb temperatures and relative humidities are average,
seasonal, meteorological conditions for the Lake Michigan region
from Reference 15. The data from this reference provided an ex-
cellent example. This reference also discussed and stressed the
importance of annual operating costs under the more favorable off-
design conditions.
Cold water temperatures (CWT) were determined from the Tower
Performance nomograph, N-l. Then turbine back pressure was deter-
mined from N-2 for each season. The design condenser rise for this
natural draft wet tower was 28. 7°F. The TBP for the summer season
is the value closest to the design value.
The values in Table 17 for auxiliary power depend upon water flow
rate which in turn depends upon heat rejection rate (see Nomographs
N-5 and N-6). Heat rejection rate as determined from the Turbine
Performance nomographs, assumes performance of the turbine-
generator at full load. In reality, the turbine-generator operates
during the year at part-load (i. e. , at capacities less than 100 percent).
Under part-load operation, the turbine heat rate at a given turbine back
pressure is higher than the corresponding value under full-load operation.
99
-------
Thus, turbine performance under part-load operation is reduced, and
there is a loss of power plant efficiency under part-load operation. The
values of auxiliary power only reflect the effect of off-design meteoro-
logical conditions and differ little from the design value. Lower auxiliary
power requirements and the corresponding costs will result under actual
part-load operation over the year. Accurate determination of auxiliary
power requirements under part-load operation requires the generation
of additional turbine performance nomographs which are beyond the scope
of this report.
Additional heat capacities (AQ) are also shown only for the effect of
varying meteorological conditions. Full load turbine performance was
assumed. Additional annual fuel costs were determined for each season
after employing an equation similar to equation (36). A plant load factor
of 60 percent was assumed in order to be consistent with Table 16.
The total additional annual fuel cost, $46, 600/year, under off-design
meteorological conditions is significantly less than the value under
design conditions^ $190, 000/year. The additional annual cost contri-
butions due to auxiliary power and fuel are small compared to the
annualized capital cost contribution in Table 16. Thus the incremental
generating cost in mills/Kw-hr is primarily made up by the annualized
capital cost contribution.
100
-------
SECTION XIII
ACKNOWLEDGMENTS
The support of the Environmental Protection Agency, and Dr. Bruce
A. Tichenor, Project Officer, National Environmental Research
Center - Corvallis, Pacific Northwest Environmental Research
Laboratory, is gratefully appreciated.
We are also grateful for the cooperation from individuals and companies,
some cited in the references, who, in response to our contacts, supplied
invaluable data and information.
101
-------
SECTION XIV
REFERENCES
1. Stangeby, J. , Research-Cottrell, private communication,
May 12, 1972.
2. Morgenweck, F. E., "Performance Testing of Large Natural
Draft Cooling Towers, " A. S. M. E. Paper No. 68-WA/PTC-4,
December 1968, p. 3.
3. Winiarski, L.D., B. A. Tichenor, and K. V. Byram, "A Method
for Predicting the Performance of Natural Draft Cooling Towers, "
Project No. 16130 GKF, Pacific Northwest Water Laboratory,
December 1970, p. 32.
4. Dickey, J. B., Jr. and R. E. Gates, "Managing Waste Heat With
the Water Cooling Tower, " The Marley Company, 1970.
5. Smith, N. and J. S. Maulbetsch, "A Survey of Alternate Methods
for Cooling Condenser Discharge Water— System Selection,
Design, and Optimization," Dynatech R/D Company, EPA
Contract No. 12-14-477, January 1971, p. 56.
6. "Report to the Federal Power Commission — Steam-Electric
Plant Air and Water Quality Control Data for the Year Ended
December 31, , " FPC Form 67, submitted annually.
7. Parker, F. L., and P. A. Krenkel, CRC Physical and Engineering
Aspects of Thermal Pollution, Chemical Rubber Co., 1970,
pp. 70-72.
8. Jimeson, R. M. and G. G. Adkins, "Waste Heat Disposal in Power
Plants,"Chemical Engineering Progress, Annual Heat Transfer
Issue, July 1971, pp. 64-69.
9. Carey, J. H. , J. T. Ganley, and J. S. Maulbetsch, "A Survey of
Alternate Methods for Cooling Condenser Discharge Water — Large-
Scale Heat Rejection Equipment, " Dynatech R/D Company, EPA
Contract No. 14-12-477, July 1969.
10. Elgawhary, .A.M. and A.M. Rowe, "Spray Pond Mathematical
Model for Cooling Fresh Water and Brine, " A. S. M. E. Publi-
cation HTD-Vol. 4 entitled Environmental and Geophysical
Heat Transfer, 1971, pp. 1-8.
11. Perry's Chemical Engineer's Handbook, Fourth Edition, McGraw-
Hill, New York, 1963, p. 15-21.
103
-------
12. Malkin, S., "Converting to Spray Pond Cooling. " Power
Engineering, January 1972, pp. 48-49.
13. "Survey of Cooling Methods for Electrical Power Plants, " Hittman
Nuclear and Development Corporation, Report HITN-107, May
1970, p. 23.
14. Patterson, W.D., J. L. Leporati, and M. J. Scarpa, "The
Capacity of Cooling Ponds to Dissipate Heat, " Ebasco Services
Incorporated, Presented at the 33rd Annual American Power
Conference Meeting, April 1971.
15. "Feasibility of Alternative Means of Cooling for Thermal Power
Plants Near Lake Michigan," Pacific Northwest Water Laboratory
and Great Lakes Regional Office of EPA, August 1970.
16. Winiarski, L.D. and K. V. Byram, "Reflective Cooling Ponds, "
A.S.M.E. Paper No. 70-WA/PWR-4, July 1970.
17. Brady, D. K. , "Heat Dissipation at Power Plant Cooling Lakes,"
Proceedings of the American Power Conference, Volume 32,
1970, pp. 528-536.
18. Rossie, J. P. and E. A. Cecil, "Research on Dry-Type Codling
Towers for Thermal Electric Generation, " Parts I and II, R. W.
Beck and Associates, EPA Contract No. 14-12-823, November
1970.
19. "Steam-Electric Plant Construction Cost and Annual Production
Expenses - Twenty Second Annual Supplement - 1969," Federal
Power Commission Report FPC S-209, January 1971.
20. Hauser, L. G. and K. A. Oleson, "Comparison of Evaporative
Losses in Various Condenser Cooling Water Systems," Westing-
house Electric Corporation, Presented at the 32nd Annual American
Power Conference Meeting, April 1970.
21. "Trends in the Cost of Light Water Reactor Power Plants for
Utilities/1 WASH-1150, U.S.A.E.G., May 1970, p. 24.
22. "Final Report on Nuclear Power Plant Siting in the Pacific
Northwest for the Bonneville Power Administration, " Pacific
Northwest Laboratories of Batelle Memorial Institute. Contract
No. 14-03-67868, July 1967.
23. George, H,, "Cost Breakdown of a 1050 Mw Steam Electric
Generating Station," reprinted from Power Engineering, 1956.
24. Roe, K. A. and W. H. Young, "Trends in Capital Costs of
Generating Plants, " Power Engineering, June 1972, pp. 40-43.
104
-------
25. Price List for Surface Condensers for Land Installation,
Westinghouse Electric Corporation, PL 1312, July 19, 1971.
26. Popper, H. , ed. , Modern Cost-Engineering Techniques, McGraw-
Hill, New York, N.Y., 1970, pp. 88-89.
27. Buchanan, S. C. , Allis-Chalmers Manufacturing Company, private
communication, April 14, 1972.
28. Dodge Estimating Guide for Public Works Construction, McGraw-
Hill, New York, N. Y. 1970.
29. Grant, E. L. , Principles of Engineering Economy, Third Edition,
Ronald Press Co. , New York, N.Y., 1950.
30. "Hydroelectric Power Evaluation, " Supplement No. 1, Federal
Power Commission, FPC P-38. Washington, DC, November 1969.
31. Woodson, R. D. , "Cooling Towers, " Scientific American, May
1971, pp. 70-78.
32. Hauser, L. G. , K. A. Oleson, and R. J. Budenholzer, "An
Advanced Optimization Technique for Turbine, Condenser,
Cooling System Combinations, " Westinghouse Electric
Corporation, Presented at the American Power Conference,
April 1971.
33. "17th Steam Station Cost Survey Reveals Steep Rise for Busbar
Energy. " Electrical World. November 1, 1971, p. 41.
34. "Statistical Year Book of the Electric Utility Industry for 1971, "
Edison Electric Institute, No. 39, Publication No. 72-25,
October 1972, p. 50.
35. Hauser, L. G. and R. F. Potter, "The Effect of Escalation on
Future Electric Utility Fuel Costs, " Westinghouse Electric
Corporation, Nuclear Fuel Division, 1971, p. 22.
105
-------
SECTION XV
NOMENCLATURE
The following parameters are defined in this report:
range the water temperature decrease in the tower
or pond
approach
terminal
temperature
difference
the difference between the cold water tempera-
ture out of the tower and the wet bulb temperature
the difference between the steam saturation
temperature and the hot water leaving the
condenser
cold water
temperature
completely
mixed pond
flow-through
pond
equilibrium
temperature
initial
temperature
difference
plant heat
rate
in-plant
efficiency
temperature of the water being supplied to
the power plant
the flow between the inlet and outlet locations
of the pond combined with wind mixing tend to
keep the pond at a nearly uniform temperature
a pond in which the temperatures decrease
continually along the pond length
the pond surface temperature for which the
heat leaving the surface will exactly equal
the heat entering the surface of a body of water
the steam saturation temperature minus the
dry bulb temperature (dry tower only)
heat energy required for production of
electricity expressed in Btu/Kw-hr
the steam supply efficiency for fossil or
nuclear plants
107
-------
turbine heat
rate
drift
blow down
the product of the plant heat rate and the
in-plant efficiency
the loss of entrained water that is carried
out of the top of a wet tower or from a
spray pond
the amount of cooling water drained off
for disposal and replaced by fresh makeup
water
The following symbols are used in this report:
tower constant for dry towers
2
area of heat transfer surface, ft
pond area
blowdown, percent
exponent for dry towers
number of concentrations of the makeup water
condenser cost, dollars
cold water temperature, °F
specific heat for water, Btu/lb-°F
drift loss, percent
dry bulb temperature, °F
evaporative loss, percent
design equilibrium temperature, °F
nonlinear functions of parameters
heat rejection system cost, dollars
initial temperature difference, °F
heat exchange coefficient, Btu/ft2-day-°F
SSIC equation constants
once-through cooling cost, dollars
heat rejection rate, 10° Btu/hr
heat input to plant, Btu/hr
additional heat capacity, Btu/hr
A
AC
A
P
B
b
C
CC
CWT
S
D
DBT
"C^ •—
En
f, fi,f2 =
HRSC
ITD
k
K1'K2 =
OTCC =
Q
Qin
AQ
q
total heat transferred in the condenser, Btu/hr
108
-------
SSIC
TBP
TGIC
TICC
TTD
TU
in
TO
Tout
Ts
AT
ATC
u
w
WBT
WCSC
WFR
steam supply system incremental costs, dollars
turbine back pressure, in. Hg absolute
turbine generator incremental cost, dollars
total incremental capital cost, dollars
terminal temperature difference, °F
mechanical draft wet tower units
dewpoint temperature, °F
water inlet temperature to condenser, °F
pond inlet temperature, °F
water outlet temperature from condenser, °F
pond outlet temperature, °F
steam saturation temperature or water
surface temperature, °F
residual temperature rise, °F
condenser rise, °F (closed cycle)
overall heat transfer coefficient, Btu/hr-ft^- F
heat equivalent of the rated output, Btu/hr
wet bulb temperature, °F
water circulation system cost, dollars
water flow rate, Ib/hr
in-plant or steam supply efficiency
thermal efficiency of the total plant
density of water
109
-------
SECTION XVI
APPENDIX
The nomographs follow on the pages numbered N-l through JN-49.. it
desired the nomographs could be made a separate entity themselves.
In either case, they can be identified in sequence, for example, as
page N-l, or as Nomograph -1 or as simply the abbreviated form,
N-l.
Following the nomographs is a series of figures indicating how the
individual nomographs should be combined to incorporate the entire
series for a given thermal pollution control system into a single
oversize page if desired.
Ill
-------
TOWER PERFORMANCE
100
70
NATURAL DRAFT WET TOWERS
N- I
-------
TURBINE BACK PRESSURE
80 90
COLO WATER TEMPERATURE
100
NATURAL DRAFT WET TOWERS (CONTINUED)
N- 2
-------
TOWER UNIT COST
Ul
(E
CC
UJ
CL
I-
LJ
en
O
I
IE
LJ
CL
in
IE
O
Q
tn
o
o
tr
UJ
z
3
-------
TOWER COST
ae
yj
$
r
o
ui
UJ
X
.3 ,4 .5 .6 .8 I 2 3 4 5 6 8 10 20 30 40 60 80 100
NATURAL DRAFT TOWER COST (MILLIONS OF DOLLARS)
NATURAL DRAFT WET TOWERS (CONTINUED)
-------
FLOW RATE
00
z
o
OQ
2
O
J-
o
UJ
-3
UJ
cc
READ ANSWER HERE
.1
2
.3 .4 5 .6 .8 I 2 3 4 5 6 8 10
WATER FLOW RATE IM1LLIOIMS OF GPM)
NATURAL DRAFT WET TOWERS (CONTINUED)
N- 5
-------
AUXILIARY POWER
100
80
RfiAO
ANSWER
HEM.
.2 .3 A .5 .6 .8 I 2
WATER FLOW RATE (MILLIONS OF GPM)
NATURAL DRAFT WET TOWERS (CONTINUED)
N - 6
-------
TOWER CORRECTION FACTOR
90
MECHANICAL DRAFT WET TOWERS
N - 7
-------
TURBINE BACK PRESSURE
READ
ANSWER
WEftE
MECHANICAL DRAFT WET TOWERS (CONTINUED)
N - 8
-------
FLOW RATE
100
OC
X
m
z
o
t-
u
LU
-9
LJJ
X
ERE- ,
FROM
CLOSED CYCLE:
CONDENSER ;RlS
OPEN CYCLE
ALLOWABLE
DIFFERENCE BETWEEN '. DIS-
CHARGE WATER AND NAT-
URAL RECEIVING' T
D ANSWER
.3 .4 .5 .6 .8 I 2 3 4 5 € 8 10
WATER FLOW RATE (MILL)OWS OF 6PM )
20
MECHAIMICAL DRAFT WET TOWERS (CONTINUED)
N- 9
-------
TOWER COST
i
6
30
.2 .3 .4.5 .6 .8 I 2 3456810 .4.5 .6 .8 I 2 3 4 5 6 8 10 20 30 40 60 80 100
WATER FLOW RATE (MILLIONS OF GPM) MECHANICAL DRAFT TOWER COST (MILLIONS OF DOLLARS)
MECHANICAL DRAFT WET TOWERS (CONTINUED)
-------
FAN POWER
in
g
IT
UJ
o
u.
o
I
D
3 4 5 6 8 10 EO 30 40 60 80 10*
FAN POWER REQUIREMENTS (MW)
MECHANICAL DRAFT WET TOWERS (CONTINUED)
N- II
-------
PUMP POWER
20 -
o
8
a
o
CLOSED...CYCLE
6
x
POWER* PUMP POWER
(CLOSED. OR OPEN CYCLE)
AUXILIARY POWER - FAN
READ.ANSWER HERE
^
2 3 4 5 6 8 10 20 30 40 60 80 IOZ
PUMP POWER REQUIREMENTS (MW)
2 3 3456
INCLUDES 60 FT HEAD
FOR COOLING TOWER
PUMPING
10 20 30 40 60 80 10'
PUMP POWER REQUIREMENTS (MW)
.
2 345689
MECHANICAL DRAFT WET TOWERS (CONTINUED)
-------
SPRAY POND PERFORMANCE
u.
i.
LU
cr
cr
LU
O,
2
LJ
EK
LJ
H
I-
LJ
K
3
LU
n
2
UJ
v-
LJ
h-
?
Q
Z
o
Q
.. ...IN LET WATER.
j TEMPERATURE.:
READ
ANSWER
HERE.
SPRAY PONDS
N - 13
-------
TURBINE BACK PRESSURE
CO
on
DC.
I
UJ
2
U)
LU
I
U
2
K
3
UJ
TO
-------
FLOW RATE
ir
CD
on
UJ
5
cc
o
UJ
-3
LU
a:
UJ
IOOQ
CLOSED i
CONDENSER R1SE-RAN
OPEN CYCLED
CONDENSER RfSE • «A-NG€
ALLOWABLE TEMPERATURE
DIFFERENCE ' BETWEEN
DISCHARGE WATER AND
NAT-y R AL
— 5"F MAX)
.3 .4 .5 .6 .8 I 2 3 4 5 6 8 10
WATER FLOW RATE (MILLIONS OF GPM)
20
SPRAY PONDS (CONTINUED)
N - 15
-------
SPRAY POND COST
AUXILIARY POWER
i
cr>
X
a_
en
f.
O
*
O
-J
cc
UI
M"-n- i •:•.;-;;
.7.8 I 3 4 5 6 8 10 20 30 40 60 80 10
SPRAY POND CAPITAL COST (MILLIONS OF DOLLARS)
O
to
Z
*
O
ct
UI
-SpHpf
1
3 4 5 6 8 10 20 30 40 60 80 IO
AUXILIARY POWER REQUIREMENTS (MW)
SPRAY PONDS (CONTINUED)
-------
COOLING POND PERFORMANCE
LLJ
CL
3
tt:
LJ
CL
5
LU
Q
co
UJ
cc
CLOSED CYCLED ATC = CONDENSER RISE
OPEN CYCLE= ATC= CONDENSER RISE-POND OUTLET TEMPERATURE +CONDENSER INLET TEMPERATURE
READ ANSWER
HERE
.5 1.0
FOSSIL CMW/ACRE }
J_
:
J_
_L
.5
NUCLEAR (MW/ACRE)
1.5
I.O
iO
ATC«30"F
.5 1.0
FOSSIL (MW/ACRE)
J t_ L_ _j L
1.5
1.0
NUCLEAR (MW/ACRE)
COOLING PONDS
-------
TURBINE BACK PRESSURE
'. „.
- , '• .< • - - - ;
i
75 80 85
CONDENSER INLET TEMPERATURE (»F)
COOLING PONDS (CONTINUED)
N - is
-------
z
I
COOLING POND COST
\
I
. ^- --. -—;--
' I ' — ^ • __ '- • • - " ",~T~.jf-'~r"~r.~:\-.f .
-Sr.- -—-
-
ENTER HERE
.3 .4 .5 .6 .8 t
MW /ACRE
2 .01 .02 .03 .04 .06 .08 .1 .2 .3 .4 .5 .6 .8 I 2 34568 10 15
LAND AND EXCAVATION COST (MILLIONS OF DOLLARS)
COOLING PONDS (CONTINUED)
-------
FLOW RATE
CT
I
*«s
D
t-
m
O
J
cc
LLJ
<
tr
o
o
LLJ
"J
LU
CE
h-
-------
AUXILIARY POWER
READ
ANSWER
HERE
.
;
,
.3 .4 .5 .6 .8 1
3 4
WATER FLOW RATE (MILLIONS OF GPM )
COOLING PONDS {CONTINUED)
N - 21
-------
COMBINED PERFORMANCE-NATURAL DRAFT
DQ
a
3
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a
IVI
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u.
o
to
ill
1
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UJ
Q
i
C/5
OT
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--
O
•r
in
.-
03
!>-
3
READ ANSWER
HERE
45678
HEAT REJECTION RATE (BILLION BTU / HR)
DRY TOWERS
N- 22
-------
COMBINLO PERFORMANCE: -MECHANICAL DRAFT
en
rn
•'
:.
13
-------
INITIAL TEMPERATURE DIFFERENCE
187
180
170
UJ
K
at
u
0.
5 160
z
o
i-
<
OT
150
140
130
120
110
100
80
UJ
3
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IE
UJ
U.
o
it:
r
o
U
(T
^J
M
(A
Ul
ft
ft.
u
CXI
.u
iE
K
40 50 60 70
INITIAL TEMPERATURE DIFFERENCE (°F)
80
DRY TOWERS (CONTINUED)
N- 24
-------
CAPITAL COST
«
•-
'&
<
J
J
o
Cl
LL
O
(0
I
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I
s
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ANSWER
HERE
,0
TO
LME1CHAN1CAL DRAFT
FOSSIL
:~ ~ NUCLEAR
READ
ANSWER
HERE
40 50 60 70 80
INITIAL TEMPERATURE DIFFERENCE («F)
30 40 50 to 70 80
INITIAL TEMPERATURE DIFFERENCE ("F]
DRY TOWERS (CONTINUED)
-------
AUXILIARY POWER
i
no
30;
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- ~ NUCLEAR.
.
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V.
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30 40 50 60 70 80
INITIAL TEMPERATURE DIFFERENCE (»F)
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Z)
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X\;:--\,;- -?
S'-
> - -
SO 40 50 60 70 80
INITIAL TEMPERATURE DIFFERENCE CF)
DRY TOWERS (CONTINUED)
-------
HEAT REJECTION RATE
ENTER
HERE
.
TURBINE PERFORMANCE
N- 27
-------
HEAT REJECTION RATE
! I I
VALUES INDICATED ARE
ONLY FOR PLANT
OPERATION AT BACK
PRESSURE OF Z IN. Hg A8S.
-
TURBINE PERFORMANCE (CONTINUED)
N- 28
-------
ADDITIONAL HEAT CAPACITY
z
t
ro
<£
16
20 30 40 60 80 I02
3 456 8 10
ADDITIONAL HEAT CAPACITY (MILLION STU/HR)
TURBINE PERFORMANCE (CONTINUED)
-------
ADDITIONAL HEAT CAPACITY
i
tw
o
:
~
I !
20 30 40 60 80 10
ADDITIONAL HEAT CAPACITY (MILLION BTU/HR)
TURBINE PERFORMANCE (CONTINUED)
-------
PLANT EFFICIENCY
to
no
o
K
UJ
I
o
UJ
(T
3
07
W
UJ
cr
D_
o
a
UJ
z
cr
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>-
X
PLANT
ER HERE
ANSWER
HER£ :
26 27 28 29 3O 31 32 33 34 35 36
PLANT EFFICIENCY (%)
24 25
TURBINE PERFORMANCE (CONTINUED)
N- 31
-------
ro
TURBINE HEAT RATE
I4POO r
13,000
a
r
3
go
UJ
;-l
r-
111
12,000
i 1,000
10,000
9,000
8,000
10 I! 12 13 14 15 16 17 18
TURBINE BACK PRESSURE (INCHES OF MERCURY ABS. )
TURBINE PERFORMANCE (CONTINUED)
-------
COOLING POND EVAPORATION
,0333.
OJ
01
.030 -
READ
ANSWER
HERE
.050
.020
65 70
WET BULB TEMPERTURE (°F)
80
WATER REQUIREMENTS
-------
0267
.0250 -
020 -
.040rr--7
EVAPORATIVE LOSS FOR WET SYSTEMS
«
015 -
.0153 '—
\
;r.;il":-:-
i:-:-^--
READ ANSWER HERE
. :::: i •. .
^•::i:i;::-:-'-'
WATER REQUIREMENTS (CONTINUED)
N- 34
-------
% EVAPORATIVE LOSS
TPTrmni •
.
H§i
WWr!
BJCAQ ; ANSWER
'
' •>
2 .3 .4 ,5 ,6 .8 I
.OZ .03 .04 ,06 .08 .1
,01
EVAPORATIVE LOSS (CF3/MW>
2 3 4 5 6 8 10
EVAPORATIVE LOSS {% OF WATER FLOW RATE)
WATER REQUIREMENTS (CONTINUED)
N- 35
-------
% SLOWDOWN
20
10
fflffltt
W r—T- -
-
. . i+J-U*
...i—
READ
ANSWER
HERE
• ; - • \ t. '• i t:'
\
. .
m
;••;:;:: - -
Bfe:
. - "-:;:: \
3456 789 10 II 12 ' 13 14 15 16 17 16 19 20
NUMBER OF CONCENTRATIONS
WATER REQUIREMENTS
N- 36
-------
% SLOWDOWN
•
00) % DRJFt LOSS
20
2 3 4 5 6 7 6 9 10 II 12 13 14 15
NUMBER OF CONCENTRATIONS
.06 a
I 2 3 4 5 6 7 8 9 10 II 12 13 14 15
NUMBER OF CONCENTRATIONS
WATER REQUIREMENTS (CONTINUED)
-------
MAKEUP WATER
,o5
8
f
UJ
o
UJ
£C
tr
LU
8
3 .1
3
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io3
e
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MAKEUP WATER FOR
WET TOWERS AND
SPRAY POND = EVAPOR-
ATION + DRIFT + BLOW-
DOWN.
.5 .6 8 I 2 3
MAKEUP WATER REQUIREMENTS (% OF FLOW RATE)
WATER REQUIREMENTS (CONTINUED)
N- 38
-------
I
04
STEAM SUPPLY INCREMENTAL COST
(SSIC)
8
X
X
0)
6 FOSSIL. PLANT
4
,
3
z 10
~, L^_IX: :4_-,.~4::^',~J_i-,; ,
>
>
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.
.1 2 .3 .4 .5.6 8 I 2 3 4 5 6 8 10 20 30 40 6O K>
STEAM SUPPLY SYSTEM INCREMENTAL COST (MILLIONS Of DOLLARS)
•:
l^i^— • •
-'
* —
6..: MUCLEAR PLANT.
5
.1 Z .3 456 .81 Z 3 4 56 8 10 20 JO 40 60
STEAM SUPPLY SYSTEM INCREMENTAL COST (MILLIONS OF DOLLARS!
COSTS
-------
z
I
TURBINE
o*-
8
e ' FOSSIL PLANT
5
.
3
'
GENERATOR INCREMENTAL COST
(TGIC)
///
2
m
u
O
8:-
tf
•/.
r ----t-|,~t-—r-i-.-4—; -•
.1 .2 .3 .4.5.6 .81 2 3 4 5 6 - 8 10 20 3040 60 10'
TURBINE GENERATOR PLANT INCREMENTAL COST (MILLIONS OF DOLLARS)
10'
8
G
5
-4
-,
--
m
« 10
O
i NUCLEAR PLANT
'
I
i
.
1 ;iii
2 3 456 81 2 3 4 5 6 8 10 20 3O 40 6O 10
TURBINE GENERATOR PLANT INCREMENTAL COST (MILLIONS OF DOLLARS)
COSTS (CONTINUED)
-------
CONDENSER SURFACE AREA
O
in
o
10
8
6
I
<
-------
01
z
o
cc
I-
UJ
X
UJ
o:
CONDENSER COST
(CO
• /
2 34568/0 20 30 40 5060 80 IQ2 2 3 4 5 6 8 10s
CONDENSER CAPITAL COST (MILLIONS OF DOLLARS)
COSTS (CONTINUED)
-------
WATER CIRCULATION SYSTEM COST
(WCSC)
/ / So
/ / / s
ONLY TO THE WEf
RiEAO ^ "ANSWER HERE
__.
.2 .3 .4 5 6 .8 I 2 3 4 5 6 8 tO 20
WATER CIRCULATION SYSTEM CAPITAL COST (MILLIONS OF DOLLARS)
COSTS (CONTINUED)
N- 43
-------
COST FOR ONCE THROUGH COOLING
(OTCC)
Ob
ID
a
w
z
o
'Is
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s
cc
CJ
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or
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m / iH
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i MF^
.5 .6 ,8 I 2 3 4 5 6 8 10 20 30 4O 5060 80 10
INTAKE AND OUTFALL STRUCTURE COST (MILLIONS .OF DOLLARS)
COSTS (CONTINUED)
N - 44
-------
CAPITAL RECOVERY FACTOR
INTEREST RATE (%)
COSTS (CONTINUED)
N- 45
-------
ANNUALIZED CAPITAL COST
hu
O
:
•~
M
U
T«J
-------
ADDITIONAL ANNUAL POWER COST
>
READ ANSWER HERE
1
r
.2 3 456 .81 2 3 4 5 6 8 10 20 3040 608010^ .002 .004 .00701 .02 .03.04 .06.08.1 .2 .3 .4.5.6 .81 2 3 4 5 6 8 10
AUXILIARY POWER REQUIREMENTS (MW) ADDITIONAL ANNUAL POWER COST (MILLION DOLLARS/YR)
COSTS (CONTINUED)
-------
ADDITIONAL ANNUAL FUEL COST
D
t-
D
Z
o
V
h
o
s
UJ
rr
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0)
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13
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,
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; : ^ : : . '»
i: _ : •. J_ yjiMMal
'; • ' • • . -";. CrvlTl
•
„ v •• '
E
,02
01
•
COSTS (CONTINUED)
N - 48
-------
INCREMENTAL GENERATING COST
{ft
rr
O
Q
_J
a
in
o
o
a
z.
UJ
cr
U
DC
I
X
X
Ifl
in
o
O
a:
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IT
O
80
TOTAL INCREMENTAL ANNUAL
ANNUALIZED CAPITAL COST + ADDITIONAL
30 ANNUAL POWER COST**
ANNUAL FUEL
20
:
CENTER HERE
888 KB i
COSTS (CONTINUED)
N- 49
-------
Tower
Performance
N-l
From
TPN's
(N-27
or
N-28)
Tower Cost
N-4
Turbine Back
Pressure
To
TPN's
N-2
Flow Rate
From
TPN's
N-5
Tower Unit Cost
N-3
Auxiliary Power
N-6
Figure 11. Natural Draft Wet Towers
-------
Tower
Correction
Factor
Turbine Back
Pressure
Flow Rate
N-7
To
TPN' s
05
Tower Cost
N-10
From
TPN's
(N-27
or
N-28)
N-9
Pan Power
N-ll
Pump Power
Figure 12. Mechanical Draft Wet Towers
-------
en
en
Spray Pond
Performance
N-13
Turbine Back
Pressure
To
TPN1 s
N-14
Flow Rate
Spray Pond
Cost
Auxiliary Power
From ^
TPN's
(N-27
or
N-28)
N-15
1
N-16
i
N-16
Figure 13. Spray Ponds
-------
Cooling Pond
Performance
(Clo
sed anc
Cycle;
N-17
Open
Turbine Back
Pressure
To
TPN's
N-18
cr>
Cooling Pond Cost
N-19
Flow Rate
Auxiliary
Power
N-21
From
TPN's
(N-27
or
N-28)
N-20
Figure 14. Cooling Ponds
-------
Combined Performance-
Natural Draft
Combined Performance
Mechanical Draft
N-22
N-23
Initial
Temperature
Difference
N-24
Capital Cost
N-25
Natural
Draft
N-25
Mechanical
_ Draft
Auxiliary Power
N-26
Natural
Draft
N-26
Mechanical
Draft
Figure 15. Dry Towers
-------
to
CO
Heat Rejection
Rate
Fossil
Plant
N-27
Plant Efficiency
N-31
Heat Rejection
Rate
Additional Heat Capacity
Nuclear
Plant
N-28
N-29
Fossil Plant
Additional Heat Capacity
N-30
Nuclear Plant
Turbine Heat Rate
N-32
Figure 16. Turbine Performance
-------
Cooling Pond Evaporation
CD
N-33
Percent
Slowdown
.005 Percent
Drift
N-36
Evaporative Loss
For
Wet Systems
N-34
Percent Slowdown
IN-3 7
Q.Q1 Percent
DrifJ,
. 01 Percent
Drift x
„ if
Percent
Evaporative Loss
N-35
Makeup
Water
N-38
Figure 17, Water Requirements
-------
Steam Supply
Incremental Cost
Fossil
Plant
N-39
Nuclear
Plant
Turbine Generator
Incremental Cost
N-40
Fossil
Plant
Nuclear
Plant
Condenser
Surface Area
-3
o
Condenser
Cost
Water Circulation
System Cost
Cost For
Once-Through
Cooling
N-42
N-43
N-44
Figure 18. Costs
-------
Capital
Recovery
Factor
Annualized
Capital Cost
N-45
N-46
Additional Annual Power Cost
N-47
Additional Annual
Fuel Cost
Incremental
Generating Cost
N-48
N-49
Figure 19. Costs (Continued)
-------
SELECTED WATER
RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
w
Nomographs for Thermal Pollution Control Systems
16130 HKK
Hittman Associates, Inc.
9190 Red Branch Road
Columbia, MD 21045
U.S. Environmental Protection Agency
U.S. Environmental Protection Agency
Report No. EPA-660/2-73-004, September 1973.
68-01-0171
Nomographs are presented and described which permit the estimation of heat
rejection system performance, tower or pond capital costs and the perturbations to
power plant efficiency and costs which result from the incorporation and operation
of any one of the following thermal pollution control systems within a power plant as
a substitute for once-through cooling: natural draft wet towers, mechanical draft
wet towers, spray ponds, cooling ponds, and natural and mechanical draft dry
towers. The base case plant for cost comparisons is chosen as having a nominal
turbine back pressure of 2 in. Hg absolute. The total heat rejection system with its
associated costs is defined to extend outward from the turbine exhaust flange, a
common boundary for each of the systems mentioned above.
Performance and capital costs for the thermal pollution control systems were
compared with data from exisitng facilities and theoretical estimates from various
sources. The nomographs yield performance, water requirements and costs for
heat rejection systems operating under design meteorological conditions and full
load plant operation. Examples are presented to show how average annual water
requirements from evaporation and average annual operating costs can be estimated.
Thermal pollution,* thermal power plants, economics,* water cooling,* cooling towers,*
cooling water, costs, annual costs, capital costs, cost analysis, electric power
costs, water consumption, water loss, graphical methods,* curves, mathematical studies,
Cooling systems, heat rejection systems, closed cycle cooling,* thermal pollution
control costs,* cooling tower performance.*
05D
s
Rvpi
•
No. t)i
Send To:
WATER RESOURCES SCIENTIFIC INFORMATION CENTER
U S DEPARTMENT OF THE 1 NTERIOR
WASHINGTON D C. 2Q24O
Charles
Jedlicka,
Hittman Associates, Inc..
-------
ENVIRONMENTAL PROTECTION AGENCY
Forms and Publications Center
Route 8, Box 116. Hwy. 7O, West
Raleigh, North Carolina 27612
4
ENVIRON*
S3 PAID
ICTION AOCNCY
EPA-335
Official Business
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BOOK
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