P
•
A
•
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•
T1
POWER GENERATION
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Source: HANDBOOK OF MECHANICAL ENGINEERING CALCULATIONS
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POWER GENERATION
1.3
SECTION 1
MODERN POWER-PLANT
CYCLES AND EQUIPMENT
CYCLE ANALYSES
1.4
Choosing Best Options for Boosting
Combined-Cycle Plant Output
1.4
Selecting Gas-Turbine Heat-Recovery
Boilers
1.10
Gas-Turbine Cycle Efficiency Analysis
and Output Determination
1.13

Test Data
1.45
Determining Turbogenerator Steam
Rate at Various Loads
1.47
Analysis of Reheating-Regenerative
Turbine Cycle
1.48
Steam Rate for Reheat-Regenerative
Cycle
1.49
Binary Cycle Plant Efficiency Analysis
1.51
CONVENTIONAL STEAM CYCLES
1.53
Finding Cogeneration System
Efficiency vs a Conventional Steam
Cycle
1.53
Bleed-Steam Regenerative Cycle
Layout and T-S Plot
1.55
Bleed Regenerative Steam Cycle
Analysis
1.59
Reheat-Steam Cycle Performance
1.62
Mechanical-Drive Steam-Turbine
Power-Output Analysis
1.67

1.95
Constant-Temperature Steam Process
1.97
Constant-Entropy Steam Process
1.99
Irreversible Adiabatic Expansion of
Steam
1.101
Irreversible Adiabatic Steam
Compression
1.103
Throttling Processes for Steam and
Water
1.105
Reversible Heating Process for Steam
1.107
Determining Steam Enthalpy and
Quality Using the Steam Tables
1.109
Maximizing Cogeneration Electric-
Power and Process-Steam Output
1.110
ECONOMIC ANALYSES OF
ALTERNATIVE ENERGY SOURCES
1.112
Choice of Most Economic Energy
Source Using the Total-Annual-Cost
Method
1.112
Seven Comparison Methods for

H-p
economizer
I-p
suprerheater
I-p
evaporator
I-p
economizer
L-p
evaporator
L-p
economizer
I-p pump
I-p pump
Reheater
Hot reheat
Cold
reheat
steam
Feedwater
pumps
L-p
steam
Generator
Cooling tower
Makeup water
Condensate
pumps
Deaerator
FIGURE 1 155-MW natural-gas-fired gas turbine featuring a dry low NO

treatment, consumption, and disposal-related O&M (operating & maintenance)
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.5
TABLE 1
Performance Summary for Enhanced-Output Options
Measured change from
base case
Case 1
Evap.
cooler
Case 2
Mech.
chiller
Case 3
Absorp.
chiller
Case 4
Steam
injection
Case 5
Water
injection
Case 6
1
Supp.-
fired

costs for the zero-discharge facility are assumed to be $3/1000 gal ($3/3.8 m
3
)of
raw water, $6/1000 gal ($6/3.8 m
3
) of treated demineralized water, and $5/1000
gal ($5/3.8 m
3
) of water disposal. The plant is configured to burn liquid distillate
as a backup fuel.
Calculation Procedure:
1. List the options available for boosting output
Seven options can be developed for boosting the output of this theoretical reference
plant. Although plant-specific issues will have a significant effect on selecting an
option, comparing performance based on a reference plant, Fig. 1, can be helpful.
Table 1 shows the various options available in this study for boosting output. The
comparisons shown in this procedure illustrate the characteristics, advantages, and
disadvantages of the major power augmentation technologies now in use.
Amidst the many advantages of gas turbine (GT) combined cycles (CC) popular
today from various standpoints (lower investment than for new greenfield plants,
reduced environmental impact, and faster installation and startup), one drawback is
that the achievable output decreases significantly as the ambient inlet air tempera-
ture increases. The lower density of warm air reduces mass flow through the GT.
And, unfortunately, hot weather typically corresponds to peak power loads in many
areas. So the need to meet peak-load and power-sales contract requirements causes
many power engineers and developers to compensate for ambient-temperature-
output loss.
The three most common methods of increasing output include: (1) injecting
water or steam into the GT, (2) precooling GT inlet air, and/or (3) supplementary
firing of the heat-recovery steam generator (HRSG). All three options require sig-

MW
ϭ
6.65 MW, or 3.3 percent. The CC heat rate is improved 0.2 percent, or 15
Btu/kWh (14.2 kJ/kWh). The total installed cost for the evaporative cooling sys-
tem, based on estimates provided by contractors and staff, is $1.2-million. The
incremental cost is $1,200,000/6650 kW
ϭ
$180.45/kW for this ambient condition.
The effectiveness of the same system operating in less-humid conditions—say
95
Њ
F DB (35
Њ
C) and 40 percent RH—is much greater. In this case, the same evap-
orative cooler can reduce inlet-air temperature to 75
Њ
F DB (23.9
Њ
C) by increasing
RH to 88 percent. Here, CC output is increased by 7 percent, heat rate is improved
(reduced) by 1.9 percent, and the incremental installed cost is $85/ kW, computed
as above. As you can clearly see, the effectiveness of evaporative cooling is directly
related to reduced RH.
Water-treatment requirements must also be recognized for this Case, No. 1. Be-
cause demineralized water degrades the integrity of evaporative-cooler film media,
manufacturers may suggest that only raw or filtered water be used for cooling
purposes. However, both GT and evaporative-cooler suppliers specify limits for
turbidity, pH, hardness, and sodium (Na) and potassium (K) concentrations in the
injected water. Thus, a nominal increase in water-treatment costs can be expected.
In particular, the cooling water requires periodic blowdown to limit solids buildup

generator
Cooling
water
Cooling
tower
Condensate
return
25-psia
steam
from
HRSG
Chilled-water loop
2-stage
lithium
bromide
adsorption
chiller
Electric-
driven
centrifugal
chiller
Cooling tower
HRSG
Chilled-
water coils
Circulating
water pump
Chilled
water
FIGURE 2 Inlet-air chilling using either centrifugal or absorption-type chillers, boosts the

/min). Combined with the need for
increased steam condensing capacity, use of a chiller may necessitate a heat sink
25 percent larger than the base case. The total installed cost for the mechanical
chilling system for Case 2 is $3-million, or about $3,000,000 /18,100 kW
ϭ
$165.75/kW of added output. Again, costs come from contractor and staff studies.
Raw-water consumption increase the plant’s overall O&M costs by $35/h when
the chiller is operating. Disposal of additional cooling-tower blowdown costs $17/
h. The compressor used in Case 2 consumes about 4 MW of auxiliary power to
handle the plant’s 68-million Btu/h (19.9 MW) cooling load.
4. Analyze an absorption chilling system
Absorption chilling systems are somewhat more complex than mechanical chillers.
They use steam or hot water as the cooling motive force. To achieve the same inlet-
air conditions as the mechanical chiller (60
Њ
F DB, 100 percent RH) (15.6
Њ
C, 100
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.8
POWER GENERATION
percent RH), an absorption chiller requires about 111,400 lb /h (50,576 kg/h) of
10.3-lb/in
2
(gage) (70.9-kPa) saturated steam, or 6830 gal /min (25.9 m
3
/min) of

reduce the compressor load compared to nonhalogenated materials, will be phased
out by the end of the decade because of environmental considerations (destruction
of the ozone layer). Use of nonhalogenated refrigerants is expected to increase both
the cost and parasitic power consumption for mechanical systems, at least in the
near term. However, absorption chillers using either ammonia or lithium bromide
will be unaffected by the new environmental regulations.
Off-peak thermal storage is one way to mitigate the impact of inlet-air chilling’s
major drawback: high parasitic power consumption. A portion of the plant’s elec-
trical or thermal output is used to make ice or cool water during off-peak hours.
During peak hours, the chilling system is turned off and the stored ice and /or cold
water is used to chill the turbine inlet air. A major advantage is that plants can
maximize their output during periods of peak demand when capacity payments are
at the highest level. Thermal storage and its equipment requirements are analyzed
elsewhere in this handbook—namely at page 18.70.
5. Compare steam and water injection alternatives
Injecting steam or water into a GT’s combustor can significantly increase power
output, but either approach also degrades overall CC efficiency. With steam injec-
tion, steam extracted from the bottoming cycle is typically injected directly into the
GT’s combustor, Fig. 3. For advanced GTs, the steam source may be extracted from
either the high-pressure (h-p) turbine exhaust, an h-p extraction, or the heat recovery
steam generator’s (HRSG) h-p section.
Cycle economics and plant-specific considerations determine the steam extrac-
tion point. For example, advanced, large-frame GTs require steam pressures of 410
to 435 lb /in
2
(gage) (2825 to 2997 kPa). This is typically higher than the econom-
ically optimal range of h-p steam turbine exhaust pressures of 285 to 395 lb /in
2
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Injecting steam from the HRSG superheat section into the GT increases unit
output by 21.8 MS, Case 4 Table 1, but decreases the steam turbine /generator’s
output by about 12.8 MW. Net gain to the CC is 8.4 MW. But CC plant heat rate
also suffers by 4 percent, or 270 Btu/kWh (256.5 kJ/kWh).
Because the steam-injection system requires makeup water as pure as boiler
feedwater, some means to treat up to 350 gal/min (22.1 L / s) of additional water
is necessary. A dual-train demineralizer this size could cost up to $1.5-million.
However, treated water could also be bought from a third party and stored. Or
portable treatment equipment could be rented during peak periods to reduce capital
costs. For the latter case, the average expected cost for raw and treated water is
about $130/h of operation.
This analysis assumes that steam- or water-injection equipment is already in
place for NO
x
control during distillate-fuel firing. Thus, no additional capital cost
is incurred.
When water injection is used for power augmentation or NO
x
control, the rec-
ommended water quality may be no more than filtered raw water in some cases,
provided the source meets pH, turbidity, and hardness requirements. Thus, water-
treatment costs may be negligible. Water injection, Case 5 Table 1, can increase
the GT output by 15.5 MW.
In Case 5, the bottoming cycle benefits from increased GT-exhaust mass flow,
increasing steam turbine /generator output by about 3.7 MW. Overall, the CC output
increases by 9.4 percent or 19 MW, but the net plant heat rate suffers by 6.4 percent,
or 435 Btu /kWh (413.3 kJ /kWh). Given the higher increase in the net plant heat
rate and lower operating expenses, water injection is preferred over steam injection
in this case.
6. Evaluate supplementary-fired HRSG for this plant

this option has the highest estimated installed cost ($3-million), and has a relatively
high incremental installed cost.
Water injection, Case 5 Table 1, has the dual advantage of high added net output
and low installed cost for plants already equipped with water-injection skids for
NO
x
control during distillate-fuel firing. Steam injection, Case 4 Table 1, has a
significantly higher installed cost because of water-treatment requirements.
Supplementary firing, Cases 6 and 7 Table 1, proves to be more acceptable for
plants requiring extended periods of increased output, not just seasonal peaking.
This calculation procedure is the work of M. Boswell, R. Tawney, and R. Narula,
all of Bechtel Corporation, as reported in Power magazine, where it was edited by
Steven Collins. SI values were added by the editor of this handbook.
Related Calculations. Use of gas turbines for expanding plant capacity or for
repowering older stations is a popular option today. GT capacity can be installed
quickly and economically, compared to conventional steam turbines and boilers.
Further, the GT is environmentally acceptable in most areas. So long as there is a
supply of combustible gas, the GT is a viable alternative that should be considered
in all plant expansion and repowering today, and especially where environmental
conditions are critical.
SELECTING GAS-TURBINE HEAT-RECOVERY
BOILERS
Choose a suitable heat-recovery boiler equipped with an evaporator and economizer
to serve a gas turbine in a manufacturing plant where the gas flow rate is 150,000
lb/h (68,040 kg/h) at 950
Њ
F (510
Њ
C) and which will generate steam at 205 lb/in
2

T
3
317
296
T
w
370
325
T
t
227
227
T
l
390
390
950˚F (510˚C) 1550˚F (843˚C) 390˚F (199˚C) 390˚F (199˚C)
415˚F (213˚C) 440˚F (227˚C) 370˚F (188˚C) 325˚F (163˚C)
317˚F (158˚C) 296˚F (147˚C) 227˚F (108˚C) 227˚F (108˚C)
FIGURE 4 Gas/ steam profile and data (Chemical Engineering).
Calculation Procedure:
1. Determine the critical gas inlet-temperature
Turbine exhaust gas (TEG) typically leaves a gas turbine at 900–1000
Њ
F
(482–538
Њ
C) and has about 13 to 16 percent free oxygen. If steam is injected into
the gas turbine for NO
x

C) and ends at the boiler gas outlet temperature, which is to be
determined by calculation. A pinch-point temperature will be assumed during the
calculation and its suitability determined.
To determine the critical gas inlet-temperature, T
1
, get from the steam tables the
properties of the steam generated by this boiler: t
s
ϭ
390
Њ
F (198.9
Њ
C); h
l
, heat of
saturated liquid
ϭ
364 Btu /lb (846.7 kJ/kg); h
s
, total heat of saturated vapor
ϭ
1199.6 Btu/ lb (2790.3 kJ/kg; h
w
, heat of saturated liquid of feedwater leaving the
economizer at 370
Њ
F (187.8
Њ
C)

s
Ϫ
h
w
)/
ϭ
X, where T
1
ϭ
gas(h
Ϫ
h )
sƒ
temperature in boiler,
Њ
F(
Њ
C); T
2
ϭ
pinch-point gas temperature,
Њ
F(
Њ
C); T
3
ϭ
outlet gas temperature for TEG,
Њ
F(

C);
ϭ
temperature of feedwater,
Њ
F(
Њ
C); othert
ƒ
symbols as before. Using the values determined above, T
1c
ϭ
[390
Ϫ
(0.855)(227)]/(1
Ϫ
0.855)
ϭ
1351
Њ
F (732.8
Њ
C).
2. Determine the system pinch point and gas / steam profile
Up to a gas inlet temperature of approximately 1351
Њ
F (732.8
Њ
C), the pinch point
can be arbitrarily selected. Beyond this, the feedwater inlet temperature limits the
temperature profile. Let’s then select a pinch point of 25

percent and a blowdown of 3 percent, leads to: (1
Ϫ
heat loss)(TEGQ
ϭ
W
evap e
heat capacity, Btu/
Њ
F) (T
1
Ϫ
T
2
), where W
e
ϭ
TEG flow, lb/h; heat capacity of
TEG
ϭ
0.27 Btu /
Њ
F; T
1
ϭ
TEG inlet temperature,
Њ
F(
Њ
C). Substituting,
ϭ

ϫ
10
6
/[(1199.6
Ϫ
342)
ϩ
0.03
ϫ
(364
Ϫ
342)]
ϭ
24,736 lb/h (11,230 kg/h).
Determine the boiler economizer duty from
ϭ
(1
ϩ
blowdown)(W
s
)Q
econ
where symbols are as before. Substituting,
ϭ
1.03(24,736)(342
Ϫ
(h
Ϫ
h ), Q
wƒ econ

0.98
ϫ
0.27)
ϭ
317
Њ
F (158
Њ
C). Figure 4 shows the temperature
profile for this installation.
Related Calculations. Use this procedure for heat-recovery boilers fired by
gas-turbine exhaust in any industry or utility application. Such boilers may be un-
fired, supplementary fired, or exhaust fired, depending on steam requirements.
Typically, the gas pressure drop across the boiler system ranges from 6 to 12 in
(15.2 to 30.5 cm) of water. There is an important tradeoff: a lower pressure drop
means the gas-turbine power output will be higher, while the boiler surface and the
capital cost will be higher, and vice versa. Generally, a lower gas pressure drop
offers a quick payback time.
If
⌬
P
e
is the additional gas pressure in the system, the power, kW, consumed in
overcoming this loss can be shown approximately from P
ϭ
5
ϫ
10
Ϫ
8

Ϫ
8
(150,000
ϫ
4
ϫ
1000/0.7)
ϭ
42 kW.
If the gas turbine output is 4000 kW, nearly 1 percent of the power is lost due
to the 4-in (10.2-cm) pressure drop. If electricity costs 7 cent /kWh, and the gas
turbine runs 8000 h /yr, the annual loss will be 8000
ϫ
0.07
ϫ
42
ϭ
$23,520. If
the incremental cost of a boiler having a 4-in (10.2-cm) lower pressure drop is, say
$22,000, the payback period is about one year.
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.13
Burner
Fuel
TEG
W

flow and gas-pressure drop. For example, Boiler A generates 24,000 lb/h (10,896
kg/h), while Boiler B provides 25,000 lb /h (11,350 kg/h) for the same gas pres-
sure-drop but costs $30,000 more. Is Boiler B worth the extra expense?
To answer this question, look at the annual differential gain in steam flow. As-
suming steam costs $3.50 /1000 lb (3.50/454 kg), the annual differential gain in
steam flow
ϭ
1000
ϫ
3.5
ϫ
8000/1000
ϭ
$28,000. Thus, the simple payback is
about a year ($30,000 vs $28,000), which is attractive. You must, however, be
certain you assess payback time against the actual amount of time the boiler will
operate. If the boiler is likely to be used for only half this period, then the payback
time is actually two years.
The general procedure presented here can be used for any type industry using
gas-turbine heat-recovery boilers—chemical, petroleum, power, textile, food, etc.
This procedure is the work of V. Ganapathy, Heat-Transfer Specialist, ABCO In-
dustries, Inc., and was presented in Chemical Engineering magazine.
When supplementary fuel is added to the turbine exhaust gas before it enters
the boiler, or between boiler surfaces, to increase steam production, one has to
perform an energy balance around the burner, Fig. 5, to evaluate accurately the gas
temperature increase that can be obtained.
V. Ganapathy, cited above, has a computer program he developed to speed this
calculation.
GAS-TURBINE CYCLE EFFICIENCY ANALYSIS
AND OUTPUT DETERMINATION

value of 200 Btu /lb (466 kJ/kg). Assume complete combustion of the fuel. The
expander reduces the flow pressure to 14.9 lb/in
2
(abs), with an engine efficiency
of 85 percent. Assuming that the combustion products have the same thermody-
namic properties as air, c
p
ϭ
0.24, and is constant. The isentropic exponent may
be taken as 1.4. (a) Find the temperature after compression, after combustion, and
at the exhaust. (b) Determine the Btu /lb (kJ/kg) of air supplied, the work delivered
by the expander, the net work produced by the gas turbine, and its thermal effi-
ciency.
Calculation Procedure:
1. Plot the ideal and actual cycles
Draw the ideal cycle as 1-2-3-4-1, Figs. 6 and 7. Actual compression takes place
along 1-2
Ј
. Actual heat added lies along 2
Ј
-3
Ј
. The ideal expansion process path is
3
Ј
-4
Ј
. Ideal work
ϭ
c

ϭ
temperature after adiabatic compression,
Њ
R; P
1
ϭ
entering air pressure, in
units given above; P
2
ϭ
pressure after compression, in units given above; k
ϭ
isentropic exponent
ϭ
1.4. With an entering air temperature, T
1
of 60
Њ
F (15.6
Њ
C),
or 60
ϩ
460
ϭ
520
Њ
R, and using the data given,
ϭ
(1.4

) and solve for the temperature after isentropic compression. Solv-(T
Ϫ
T ), T ,
2
Ј
12
Ј
ing,
ϭ
0.82
ϭ
0.24(772.7
Ϫ
520)/0.24
ϭ
828.4
Њ
R, or 368
Њ
F. ThisT (T
Ϫ
520)
2
Ј
2
Ј
is the temperature after compression.
3. Determine the temperature after combustion
To find the temperature after combustion, use the relation Heating value of fuel
ϭ

3
Ј
3
Ј
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.15
FIGURE 7 Ideal gas-turbine cycle T-S diagram with the same processes as in Fig. 6; complete-
cycle gas turbine shown below the T-S diagram.
4. Find the temperature at the exhaust of the gas turbine
Using an approach similar to that above, determine T
4
from
ϭ
(T / T )
4
Ј
3
Ј
Substituting and solving for
ϭ
1661
ϭ
k
Ϫ
1/k. (1.4
Ϫ

Ј
4
Ј
4
؆
sion, at the exhaust. Substituting as earlier,
ϭ
1218.2
Њ
R, 758.2
Њ
F (403.4
Њ
C). ThisT
4
؆
is the temperature after expansion, i.e., at the exhaust of the gas turbine.
5. Determine the work of compression, expander work, and thermal efficiency
(b) The work of compression
ϭ
c
p
ϭ
0.24(828
Ϫ
520)
ϭ
74.16 Btu (78.23(T
Ϫ
T )

ϭ
32.1/200
ϭ
0.1605, 16.6 percent thermal
efficiency.
Related Calculations. With the widespread use today of gas turbines in a va-
riety of cycles in industrial and central-station plants, it is important that an engineer
be able to analyze this important prime mover. Because gas turbines can be quickly
installed and easily hooked to heat-recovery steam generators (HRSG), they are
more popular than ever before in history.
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.16
POWER GENERATION
FIGURE 8 With further gas-turbine cycle refinement, the specific fuel consumption declines.
These curves are based on assumed efficiencies with T
3
ϭ
1400 F (760 C).
Further, as aircraft engines become larger—such as those for the Boeing 777
and the Airbus 340—the power output of aeroderivative machines increases at little
cost to the power industry. The result is further application of gas turbines for
topping, expansion, cogeneration and a variety of other key services throughout the
world of power generation and energy conservation.
With further refinement in gas-turbine cycles, specific fuel consumption, Fig. 8,
declines. Thus, the complete cycle gas turbine has the lowest specific fuel con-
sumption, with the regenerative cycle a close second in the 6-to-1 compression-
ratio range.

170.6 ft
29.5 ft 95 ft
152 ft
(8.99 m) (46.33 m) (28.95 m)
FIGURE 10 Steam turbine, electric generator, and gas turbine fit into one compact building when
all three machines are arranged on a single shaft. Net result: Reduced site footprint and civil-
engineering work (Power).
Having the gas turbine, steam turbine, and generator all on one shaft simplifies
plant design and operation, and may lower first costs. When used for large reheat
cycles, as shown here, separate high-pressure (h-p), intermediate-pressure (i-p), and
low-pressure (l-p) turbine elements are all on the same shaft as the gas turbine and
generator. Modern high-technology combined-cycle single-shaft units deliver a
simple-cycle net efficiency of 38.5 percent for a combine-cycle net efficiency of
58 percent on a lower heating value (LHV) basis.
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.18
POWER GENERATION
The second important gas-turbine development worth noting is the dual-fueled
turbine located at the intersection of both gas and oil pipelines. Being able to use
either fuel gives the gas turbine greater opportunity to increase its economy by
switching to the lowest-cost fuel whenever necessary. Further developments along
these lines is expected in the future.
The data in the last three paragraphs and the two illustrations are from Power
magazine.
DETERMINING BEST-RELATIVE-VALUE OF
INDUSTRIAL GAS TURBINES USING A
LIFE-CYCLE COST MODEL

p
; (2) annual fuel cost, (3) annual maintenanceC ;
ƒ
cost, C
m
. Summing these three annual costs, all of which are expressed in mils /
kWh, gives C
T
, the life-cycle cost model. The equations for each of the three
components are given below, along with the life-cycle working model, C
T
:
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.19
The life-cycle cost model (C
T
) consists of annual investment cost (C
p
)
ϩ
annual
fuel cost
ϩ
annual maintenance cost (C
m
). Equations for these values are:(C )

G
ϭ
efficiency of electric generator
C
ϭ
E(293)
ƒ
where E
ϭ
thermal efficiency of gas turbine
293
ϭ
conversion of Btu to kWh
C
ϭ
M/kW
m
where M
ϭ
maintenance cost, dollars per operating (fired) hour.
Thus, the life-cycle working model can be expressed as
Ϫ
n
l{i/[1
Ϫ
(1
Ϫ
i)]}
C
ϭϩ

tween $200 and $320 /kW. On a $/ kW basis, only unit E at the $200 level, would
be considered. However, the life-cycle cost model, above, shows the cost per kWh
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1.20
POWER GENERATION
produced for each of the gas-turbine units being considered. This gives a much
different perspective of the units.
From a life-cycle standpoint, the choice of unit E over unit D would result in
an added expenditure of about $975,000 annually during the life span of the equip-
ment, found from [(51.9
Ϫ
46.6)/1000](8760 hr/yr)(21,000 kW)
ϭ
$974,988; this
was rounded to $975,000. Since the difference in the initial cost between units D
and E is $6,720,000
Ϫ
$4,200,000
ϭ
$2,520,000, this cost difference will be re-
covered in $2,520,000 /974,988
ϭ
2.58 years, or about one-eighth of the 20-year
life span of the equipment.
Also, note that the 20-year differential in cost/ kWh produced between units D
and E is equivalent to over 4.6 times the initial equipment cost of unit E. When
considering the values output of a life-cycle model, remember that such values are

Traditionally, the major focus has been on first cost of industrial gas-turbine
units, not on operating cost. Experience with higher-technology equipment, how-
ever, reveals that a low first cost does not mean a lower total cost during the
expected life of the equipment. Conversely, reliable, high-quality equipment with
demonstrated availability will be remembered long after the emotional distress as-
sociated with high initial cost is forgotten.
The life-cycle cost model presented here uses 10 independent variables. A sin-
gle-point solution can easily be obtained, but multiple solutions require repeated
calculations. Although curves depicting simultaneous variations in all variables
would be difficult to interpret, simplified diagrams can be constructed to illustrate
the relative importance of different variables.
Thus, the simplified diagrams shown in Fig. 11, all plot production cost, mils/
kWh, versus investment cost. All the plots are based on continuous operation of
8760 h/yr at 21-MW capacity with an equipment life expectancy of 20 years.
The curves shown depict the variation in production cost of electricity as a
function of initial investment cost for various levels of thermal efficiency, loan
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.21
FIGURE 11 Economic study plots for life-cycle costs (Power).
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.22
POWER GENERATION
repayment period, gas-turbine availability, and fuel cost. Each of these factors is
an element in the life-cycle cost model presented here.

and tube length observed in only gases and vapors. This occurs when the vortex
shedding frequency is close to the acoustic frequency. Excessive noise is generated,
leading to large gas pressure drops and bundle and casing damage. The starting
point in the evaluation for noise and vibration is the estimation of various frequen-
cies.
Use the listing of C values shown below to determine the mode of vibration.
Note that C is a factor determined by the end conditions of the tube bundle.
End conditions
Mode of vibration
123
Both ends clamped 22.37 61.67 120.9
One end clamped, one end hinged 15.42 49.97 104.2
Both hinged 9.87 39.48 88.8
Since the tubes are fixed at both ends, i.e., clamped, select the mode of vibration
as 1, with C
ϭ
22.37. For most situations, Mode 1 is the most important case.
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.23
FIGURE 12 Strouhl number, S, for inline tube banks. Each curve
represents a different longitudinal pitch / diameter ratio (Chen).
2. Find the natural frequency of the tube bundle
Use the relation, ƒ
n
ϭ
90C[ Substituting, with C

50.2, as C
ϭ
61.67.
3. Compute the vortex shedding frequency
To compute the vortex shedding frequency we must know several factors, the first
of which is the Strouhl Number, S. Using Fig. 12 with a transverse pitch /diameter
of 1.75 and a longitudinal pitch diameter of 1.5 we find S
ϭ
0.33. Then, the air
density
ϭ
40/(460
Ϫ
219)
ϭ
0.059 lb /ft
3
(0.95 kg /m
3
); free gas area
ϭ
40(3.5
Ϫ
2)(13.5/12)
ϭ
67.5 ft
2
(6.3 m
2
); gas velocity, V

ϭ
49(679)
0.5
ϭ
1277 ft/s (389.2 m/s); wave length,
␭
ϭ
2(w)/n, where w
ϭ
width of tube bank,
ft (m); n
ϭ
mode of vibration
ϭ
1 for this tube bank; then
␭
ϭ
2(11.7)/1
ϭ
23.4
ft (7.13 m).
The acoustic frequency, ƒ
a
ϭ
(V
s
)/
␭
, where V
s

a
ϭ
1277/
23.4
ϭ
54.5 cps. For n
ϭ
2; ƒ
a
ϭ
54.4(2)
ϭ
109 cps. The results for Modes 1 and
2 are summarized in the tabulation below.
Mode of vibration
n
12
ƒ
n
, cps 18.2 50.2
ƒ
c
, cps 41.6 41.6
ƒ
a
(without baffles) 54.5 109
ƒ
a
(with baffles) 109 218
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Upper header
Tube restraint
Tubes
Lower header
Lower header
cradle
Floor
pressure-part
supports
Main floor
beams
Floor cross-tie
beams
Moment-connected corners
Gas flow
Wall cross-tie
beams
1
/
2
-in. dia.
liner stud
Tube
restraint
supports
1
/
4
-in. casing
FIGURE 13 Tube bundles in HRSGs require appropriate support mechanisms; thermal cycling

temperature of 150,000 lb/h (68,100 kg /h) of exhaust gases from 950
Њ
F (510
Њ
C)
to 1575
Њ
F (857.2
Њ
C) in order to nearly double the output of the HRSG. If the
exhaust gases contain 15 percent oxygen by volume, determine the fuel input and
oxygen consumed, using the gas specific-heat method.
Calculation Procedure:
1. Determine the air equivalent in the exhaust gases
In gas-turbine based cogeneration/combined-cycle projects the HRSG may be fired
to generate more steam than that produced by the gas-turbine exhaust gases. Typ-
ically, the gas-turbine exhaust gas contains 14 to 15 percent oxygen by volume. So
the question arises: How much fuel can be fired to generate more steam? Would
the oxygen in the exhaust gases run out if we fired to a desired temperature? These
questions are addressed in this procedure.
If 0 percent oxygen is available in W
g
lb/h (kg/h) of exhaust gases, the air-
equivalent W
a
in lb /h (kg/h) is given by: W
a
ϭ
100(W
g

W
ƒ
Btu/h (kJ/ h). Air required lb/h (kg /h)
ϭ
(Q /LHV)(HHV)(A), using the MM Btu,
where A
ϭ
amount of air required, lb (kg) per MM Btu (kJ) fired. The above
quantity
ϭ
air available in the exhaust gases, W
a
ϭ
0.0417 W
g
(O).
3. Simplify the gas relations further
From the data in step 2, (Q / LHV)(HHV)(A)/10
6
ϭ
0.0417 W
g
(O). For natural gas
and fuel oils it can be shown that (LHV/A
x
HHV)
ϭ
0.00124. For example, LHV
of methane
ϭ

g
ϩ
)(h
g 2
), where h
g 1
and h
g 2
W
ƒ
are the enthalpies of the exhaust gas before and after the fuel burner;
ϭ
fuelW
ƒ
input, lb/h (kg/h); Q
ϭ
fuel input in Btu/h (kJ /h).
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MODERN POWER-PLANT CYCLES AND EQUIPMENT