Handbook of Mechanical Engineering Calculations P1

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 G

P • A • R • T 1

POWER GENERATION

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

Determining Best-Relative-Value of

Industrial Gas Turbines Using a

Life-Cycle Cost Model 1.18

Tube Bundle Vibration and Noise

Cycle Alternatives Analysis 1.37

Turbine Exhaust Steam Enthalpy and

Moisture Content 1.42

Steam Turbine No-Load and

Partial-Load Steam Flow 1.43

Power Plant Performance Based on

Test Data 1.45

Determining Turbogenerator Steam

Rate at Various Loads 1.47

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

Reheat-Regenerative Steam-Turbine Heat Rates 1.74

Steam Turbine-Gas Turbine Cycle Analysis 1.76

Gas Turbine Combustion Chamber Inlet Air Temperature 1.81

Regenerative-Cycle Gas-Turbine Analysis 1.83

Extraction Turbine kW Output 1.86

STEAM PROPERTIES AND PROCESSES

1.112

Choice of Most Economic Energy Source Using the Total-Annual-Cost Method 1.112

Seven Comparison Methods for Energy Source Choice 1.115

Selection of Prime Mover Based on Annual Cost Analyses 1.120

Determining If a Prime Mover Should

Be Overhauled 1.122

H-p turbine

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 NOx combustor (Power).

Cycle Analyses

CHOOSING BEST OPTION FOR BOOSTING

COMBINED-CYCLE PLANT OUTPUT

Select the best option to boost the output of a 230-MW facility based on a

1) The plant has a heat-recovery steam generator (HRSG) which is a triple-pressuredesign with an integral deaerator A reheat condensing steam turbine (ST) is usedand it is coupled to a cooling-tower / surface-condenser heat sink turbine inlet Steam

operation at International Standard Organization (ISO) conditions Evaluate the ious technologies considered for summer peaking conditions with a dry bulb (DB)

RH) The plant heat sink is a four-cell, counterflow, mechanical-draft cooling toweroptimized to achieve a steam-turbine exhaust pressure of 3.75 inHg absolute (9.5cmHg) for all alternatives considered in this evaluation Base circulating-water sys-tem includes a surface condenser and two 50 percent-capacity pumps Water-treatment, consumption, and disposal-related O&M (operating & maintenance)

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

fired HRSG

Supp.-Case 7 2

fired HRSG

1 Partial supplementary firing.

2 Full supplementary firing.

3 Based on lower heating value of fuel.

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 referenceplant Although plant-specific issues will have a significant effect on selecting anoption, 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 Thecomparisons shown in this procedure illustrate the characteristics, advantages, anddisadvantages of the major power augmentation technologies now in use

Amidst the many advantages of gas turbine (GT) combined cycles (CC) populartoday from various standpoints (lower investment than for new greenfield plants,reduced environmental impact, and faster installation and startup), one drawback isthat 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 manyareas So the need to meet peak-load and power-sales contract requirements causesmany power engineers and developers to compensate for ambient-temperature-output loss

The three most common methods of increasing output include: (1) injectingwater or steam into the GT, (2) precooling GT inlet air, and / or (3) supplementaryfiring of the heat-recovery steam generator (HRSG) All three options require sig-nificant capital outlays and affect other performance parameters Further, the options

may uniquely impact the operation and / or selection of other components, includingboiler feedwater and condensate pumps, valves, steam turbine / generators, con-densers, cooling towers, and emissions-control systems.

2. Evaluate and analyze inlet-air precooling

Evaporative cooling, Case 1, Table 1, boosts GT output by increasing the densityand mass flow of the air entering the unit Water sprayed into the inlet-air streamcools the air to a point near the ambient wet-bulb temperature At reference con-

92 percent RH, respectively, using conventional humidity chart calculations, page16.79 This boosts the output of both the GT and—because of energy added to the

GT exhaust—the steam turbine / generator Overall, plant output for Case 1 is

Btu / kWh (14.2 kJ / kWh) The total installed cost for the evaporative cooling tem, based on estimates provided by contractors and staff, is $1.2-million The

The effectiveness of the same system operating in less-humid conditions—say

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 directlyrelated to reduced RH

Water-treatment requirements must also be recognized for this Case, No 1 cause demineralized water degrades the integrity of evaporative-cooler film media,manufacturers may suggest that only raw or filtered water be used for coolingpurposes However, both GT and evaporative-cooler suppliers specify limits forturbidity, pH, hardness, and sodium (Na) and potassium (K) concentrations in theinjected water Thus, a nominal increase in water-treatment costs can be expected

Be-In particular, the cooling water requires periodic blowdown to limit solids buildupand system scaling Overall, the evaporation process can significantly increase aplant’s makeup-water feed rate, treatment, and blowdown requirements Compared

to the base case, water supply costs increase by $15 / h of operation for the firstapproach, and $20 / h for the second, lower RH mode Disposal of evaporative-cooler blowdown costs $1 / h in the first mode, $2 / h in the second Evaporativecooling has little or no effect on the design of the steam turbine

3. Evaluate the economics of inlet-air chilling

The effectiveness of evaporative cooling is limited by the RH of the ambient air.Further, the inlet air cannot be cooled below the wet-bulb (WB) temperature of theinlet air Thus, chillers may be used for further cooling of the inlet air below thewet-bulb temperature To achieve this goal, industrial-grade mechanical or absorp-tion air-conditioning systems are used, Fig 2 Both consist of a cooling medium(water or a refrigerant), an energy source to drive the chiller, a heat exchanger forextracting heat from the inlet air, and a heat-rejection system

A mechanical chilling system, Case 2, Table 1, is based on a compressor-drivenunit The compressor is the most expensive part of the system and consumes asignificant amount of energy In general, chillers rated above 12-million Btu / h (3.5MW) (1000 tons of refrigeration) (3500 kW) employ centrifugal compressors Unitssmaller than this may use either screw-type or reciprocating compressors Overall,

MODERN POWER-PLANT CYCLES AND EQUIPMENT 1.7

Ambient air (95F, 60% RH)

Chilled air (60F, 100% RH)

Gas turbine/

generator Cooling water

Cooling tower

Chilled-Circulating

water pump

Chilled water

FIGURE 2 Inlet-air chilling using either centrifugal or absorption-type chillers, boosts the

achieveable mass flow and power output during warm weather (Power).

compressor-based chillers are highly reliable and can handle rapid load changeswithout difficulty

A centrifugal-compressor-based chiller can easily reduce the temperature of the

ac-cepted as a safe lower limit for preventing icing on compressor inlet blades—and

inlet-air pressure drop because of heat-exchanger equipment located in the inlet-airstream

Cooling requirements of the chilling system increase the plant’s required

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

$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 whenthe 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 tohandle 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-

percent RH), an absorption chiller requires about 111,400 lb / h (50,576 kg / h) of

Cost-effective supply of this steam or hot water requires a redesign of the erence plant Steam is extracted from the low-pressure (l-p) steam turbine at 20.3

absorption chiller increases plant output by 8.7 percent or 17.4 MW but degradesthe plant’s heat rate by 1 percent

Although the capacity of the absorption cooling system’s cooling-water loopmust be twice that of the mechanical chiller’s, the size of the plant’s overall heatsink is identical—25 percent larger than the base case—because the steam extractedfrom the l-p turbine reduces the required cooling capacity Note that this also re-duces steam-turbine output by 2 MW compared to the mechanical chiller, but hasless effect on overall plant output

Cost estimates summarized in Table 1 show that the absorption chilling systemrequired here costs about $4-million, or about $230 / kW of added output Compared

to the base case, raw-water consumption increases O&M costs by $35 / h when thechiller is operating Disposal of additional cooling-water blowdown adds $17 / h.Compared to mechanical chillers, absorption units may not handle load changes

as well; therefore they may not be acceptable for cycling or load-following ation When forced to operate below their rated capacity, absorption chillers suffer

oper-a loss in efficiency oper-and reportedly require more operoper-ator oper-attention thoper-an mechoper-anicoper-alsystems

Refrigerant issues affect the comparison between mechanical and absorptionchilling Mechanical chillers use either halogenated or nonhalogenated fluorocar-bons at this time Halogenated fluorocarbons, preferred by industry because theyreduce the compressor load compared to nonhalogenated materials, will be phasedout by the end of the decade because of environmental considerations (destruction

of the ozone layer) Use of nonhalogenated refrigerants is expected to increase boththe cost and parasitic power consumption for mechanical systems, at least in thenear term However, absorption chillers using either ammonia or lithium bromidewill be unaffected by the new environmental regulations

Off-peak thermal storage is one way to mitigate the impact of inlet-air chilling’smajor 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 coldwater is used to chill the turbine inlet air A major advantage is that plants canmaximize their output during periods of peak demand when capacity payments are

at the highest level Thermal storage and its equipment requirements are analyzedelsewhere 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 poweroutput, but either approach also degrades overall CC efficiency With steam injec-tion, steam extracted from the bottoming cycle is typically injected directly into theGT’s combustor, Fig 3 For advanced GTs, the steam source may be extracted fromeither the high-pressure (h-p) turbine exhaust, an h-p extraction, or the heat recoverysteam generator’s (HRSG) h-p section

Cycle economics and plant-specific considerations determine the steam tion point For example, advanced, large-frame GTs require steam pressures of 410

MODERN POWER-PLANT CYCLES AND EQUIPMENT 1.9

Water-injection

power sugmentation Attemperating

station Water

injection skid

(gage) (1964 to 2722 kPa) Thus, steam must be supplied from either the HRSG

or an h-p turbine extraction ahead of the reheat section

Based on installed-cost considerations alone, extracting steam from the HRSG

is favored for peaking service and may be accomplished without altering the reheatsteam turbine But if a plant operates in the steam-injection mode for extendedperiods, extracting steam from the turbine or increasing the h-p turbine exhaustpressure becomes more cost-effective

Injecting steam from the HRSG superheat section into the GT increases unitoutput by 21.8 MS, Case 4 Table 1, but decreases the steam turbine / generator’soutput by about 12.8 MW Net gain to the CC is 8.4 MW But CC plant heat ratealso suffers by 4 percent, or 270 Btu / kWh (256.5 kJ / kWh)

Because the steam-injection system requires makeup water as pure as boilerfeedwater, 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 Orportable treatment equipment could be rented during peak periods to reduce capitalcosts For the latter case, the average expected cost for raw and treated water isabout $130 / h of operation

This analysis assumes that steam- or water-injection equipment is already in

is incurred

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 increasethe 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 outputincreases 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 heatrate and lower operating expenses, water injection is preferred over steam injection

in this case

6. Evaluate supplementary-fired HRSG for this plant

of gaseous and liquid fuels upstream of the HRSG, thereby increasing the output

from the steam bottoming cycle For this study, two types of supplementary firingare considered—(1) partial supplementary firing, Case 6 Table 1, and (2) full sup-plementary firing, Case 7 Table 1.

There are three main drawbacks to supplementary firing for peak power

(3) higher costs for the larger plant equipment required

For this plant, each 100-million Btu / h (29.3 MW) of added supplementary firingcapacity increases the net plant output by 5.5 percent, but increases the heat rate

by 2 percent The installed cost for supplementary firing can be significant becauseall the following equipment is affected: (1) boiler feed pumps, (2) condensatepumps, (3) steam turbine / generator, (4) steam and water piping and valves, and (5)selective-catalytic reduction (SCR) system Thus, a plant designed for supplemen-tary firing to meet peak-load requirements will operate in an inefficient, off-designcondition for most of the year

7. Compare the options studied and evaluate results

Comparing the results in Table 1 shows that mechanical chilling, Case 2, gives the

largest increase in plant output for the least penalty on plant heat rate—i.e., 18.1

MW output for a net heat rate increase of 55 Btu / kWh (52.3 kJ / kWh) However,this option has the highest estimated installed cost ($3-million), and has a relativelyhigh incremental installed cost

Water injection, Case 5 Table 1, has the dual advantage of high added net outputand low installed cost for plants already equipped with water-injection skids for

significantly higher installed cost because of water-treatment requirements

Supplementary firing, Cases 6 and 7 Table 1, proves to be more acceptable forplants 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 forrepowering older stations is a popular option today GT capacity can be installedquickly and economically, compared to conventional steam turbines and boilers.Further, the GT is environmentally acceptable in most areas So long as there is asupply of combustible gas, the GT is a viable alternative that should be considered

in all plant expansion and repowering today, and especially where environmentalconditions 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

supplementary firing of the exhaust is required to generate the needed steam Use

leav-ing the economizer

MODERN POWER-PLANT CYCLES AND EQUIPMENT 1.11

Top Numbers: Example 1 Bottom Numbers: Example 2

T w

370 325

T t

227 227

T l

390 390

1. Determine the critical gas inlet-temperature

by volume To evaluate whether supplementary firing of the exhaust is required togenerate needed steam, a knowledge of the temperature profiles in the boiler isneeded

Prepare a gas / steam profile for this heat-recovery boiler as shown in Fig 4

For steam to be generated in the boiler, two conditions must be met: (1) The ‘‘pinch

econ-omizer must be greater than that of the feedwater The pinch point occurs where along the TEG temperature line, Fig 4, which starts at the inlet temperature

determined by calculation A pinch-point temperature will be assumed during thecalculation and its suitability determined

1199.6 Btu / lb (2790.3 kJ / kg; hw, heat of saturated liquid of feedwater leaving the

Writing an energy balance across the evaporator neglecting heat and blowdown

2. Determine the system pinch point and gas / steam profile

can be arbitrarily selected Beyond this, the feedwater inlet temperature limits the

Setting up an energy balance across the evaporator, assuming a heat loss of 2

(hl ⫺ hw)], where the symbols are as given earlier Substituting, Ws ⫽ 21.23 ⫻

profile for this installation

Related Calculations. Use this procedure for heat-recovery boilers fired bygas-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 dropmeans the gas-turbine power output will be higher, while the boiler surface and thecapital cost will be higher, and vice versa Generally, a lower gas pressure dropoffers a quick payback time

/ E, where E⫽efficiency of compression)

To show the application of this equation and the related payback period, assume

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

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

MODERN POWER-PLANT CYCLES AND EQUIPMENT 1.13

Burner Fuel

TEG

(W e h1´ LHV  W t) (W e  W f )h1

F, W f

FIGURE 5 Gas / steam profile for fired mode (Chemical Engineering).

If steam requirements are not stated for a particular gas inlet condition, andmaximum steaming rate is desired, a boiler can be designed with a low pinch point,

a large evaporator, and an economizer Check the economizer for steaming Such

a choice results in a low gas exit temperature and a high steam flow

Then, the incremental boiler cost must be evaluated against the additional steamflow 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 sure-drop but costs $30,000 more Is Boiler B worth the extra expense?

pres-To answer this question, look at the annual differential gain in steam flow suming steam costs $3.50 / 1000 lb (3.50 / 454 kg), the annual differential gain in

about a year ($30,000 vs $28,000), which is attractive You must, however, becertain you assess payback time against the actual amount of time the boiler willoperate If the boiler is likely to be used for only half this period, then the paybacktime is actually two years

The general procedure presented here can be used for any type industry usinggas-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 entersthe boiler, or between boiler surfaces, to increase steam production, one has toperform an energy balance around the burner, Fig 5, to evaluate accurately the gastemperature increase that can be obtained

V Ganapathy, cited above, has a computer program he developed to speed thiscalculation

GAS-TURBINE CYCLE EFFICIENCY ANALYSIS

AND OUTPUT DETERMINATION

A gas turbine consisting of a compressor, combustor, and an expander has air

FIGURE 6 Ideal gas-turbine cycle, 1-2-3-4-1 Actual compression takes place along 1-2  ; actual heat added 2-3; ideal expansion 3-4.

percent Sufficient fuel is injected to give the mixture of fuel vapor and air a heatingvalue of 200 Btu / lb (466 kJ / kg) Assume complete combustion of the fuel The

of 85 percent Assuming that the combustion products have the same

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 ciency

effi-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

temperature difference)

2. Find the temperature after compression

(a) Here we have isentropic compression in the compressor with an

is the temperature after compression

3. Determine the temperature after combustion

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; cycle gas turbine shown below the T-S diagram.

complete-4. Find the temperature at the exhaust of the gas turbine

cp (T3⫺T ) / c (T4ⴖ p 3⫺T )4 ⫽0.85, and solve forT ,4ⴖ the temperature after

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

J)

106.32 Btu (112.16 J)

FIGURE 8 With further gas-turbine cycle refinement, the specific fuel consumption declines.

These curves are based on assumed efficiencies with T3 ⫽ 1400 F (760 C).

Further, as aircraft engines become larger—such as those for the Boeing 777and the Airbus 340—the power output of aeroderivative machines increases at littlecost to the power industry The result is further application of gas turbines fortopping, expansion, cogeneration and a variety of other key services throughout theworld 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

Two recent developments in gas-turbine plants promise much for the future Thefirst of these developments is the single-shaft combined-cycle gas and steam turbine,Fig 9 In this cycle, the gas turbine exhausts into a heat-recovery steam generator(HRSG) that supplies steam to the turbine This cycle is the most significant electricgenerating system available today Further, its capital costs are significantly lowerthan competing nuclear, fossil-fired steam, and renewable-energy stations Otheradvantages include low air emissions, low water consumption, smaller space re-quirements, and a reduced physical profile, Fig 10 All these advantages are im-portant in today’s strict permitting and siting processes

MODERN POWER-PLANT CYCLES AND EQUIPMENT 1.17

Fuel

Synchronous clutch

FIGURE 9 Single-shaft combined-cycle technology can reduce costs and increase thermal

effi-ciency over multi-shaft arrangements This concept is popular in Europe (Power).

engineering work (Power).

Having the gas turbine, steam turbine, and generator all on one shaft simplifiesplant design and operation, and may lower first costs When used for large reheatcycles, as shown here, separate high-pressure (h-p), intermediate-pressure (i-p), andlow-pressure (l-p) turbine elements are all on the same shaft as the gas turbine andgenerator Modern high-technology combined-cycle single-shaft units deliver asimple-cycle net efficiency of 38.5 percent for a combine-cycle net efficiency of

58 percent on a lower heating value (LHV) basis

The second important gas-turbine development worth noting is the dual-fueledturbine located at the intersection of both gas and oil pipelines Being able to useeither fuel gives the gas turbine greater opportunity to increase its economy byswitching to the lowest-cost fuel whenever necessary Further developments alongthese 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

An industrial application requires a 21-MW continuous electrical output year-round.Five different gas turbines are under consideration Determine which of these fiveturbines is the best choice, using a suitable life-cycle cost analysis

Calculation Procedure:

1. Assemble the cost data for each gas turbine being considered

Assemble the cost data as shown below for each of the five gas turbines identified

by the letters A through E Contact the gas-turbine manufacturers for the initialcost, $ / kW, thermal efficiency, availability, fuel consumption, generator efficiency,and maintenance cost, $ / kWh List these data as shown below

The loan period, years, will be the same for all the gas turbines being considered,and is based on an equipment life-expectancy of 20 years Interest rate on the capitalinvestment for each turbine will vary, depending on the amount invested and theway in which the loan must be repaid and will be provided by the accountingdepartment of the firm considering gas-turbine purchase

Equipment Attributes for Typical Candidates*

*Assuming an equipment life of 20 years, an output of 21 MW.

2. Select a life-cycle cost model for the gas turbines being considered

A popular and widely used life-cycle cost model for gas turbines has three parts:

cost, Cm Summing these three annual costs, all of which are expressed in mils /

MODERN POWER-PLANT CYCLES AND EQUIPMENT 1.19

C ƒ⫽E(293)

Thus, the life-cycle working model can be expressed as

⫺n

l {i / [1⫺(1⫺i ) ]}

(A )(kW)(8760)(G )

To evaluate the comparative capital cost of a gas-turbine electrical generatingpackage the above model uses the capital-recovery factor technique This approachspreads the initial investment and interest costs for the repayment period into anequal annual expense using the time value of money The approach also allows forthe comparison of other periodic expenses, like fuel and maintenance costs

3. Perform the computation for each of the gas turbines being considered

sum the results List for each of the units as shown below

Results from Cost Model

4. Analyze the findings of the life-cycle model

Note that the initial investment cost for the turbines being considered ranges tween $200 and $320 / kW On a $ / kW basis, only unit E at the $200 level, would

be-be considered However, the life-cycle cost model, above, shows the cost per kWh

produced for each of the gas-turbine units being considered This gives a muchdifferent 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

was rounded to $975,000 Since the difference in the initial cost between units D

life span of the equipment

Also, note that the 20-year differential in cost / kWh produced between units Dand E is equivalent to over 4.6 times the initial equipment cost of unit E Whenconsidering the values output of a life-cycle model, remember that such values areonly as valid as the data input So take precautions to input both reasonable andaccurate data to the life-cycle cost model Be careful in attempting to distinguishmodel outputs that vary less than 0.5 mil from one another

Since the predictions of this life-cycle cost model cannot be compared to actualmeasurements at this time, a potential shortcoming of the model lies with the va-lidity of the data and assumptions used for input For this reason, the model is bestapplied to establish comparisons to differentiate between several pieces of com-peting equipment

Related Calculations. The first gas turbines to enter industrial service in theearly 1950s represented a blend of steam-turbine and aerothermodynamic design

In the late 1950s / early-1960s, lightweight industrial gas turbines derived directlyfrom aircraft engines were introduced into electric power generation, pipeline com-pression, industrial power generation, and a variety of other applications Thesemachines had performance characteristics similar to their steam-turbine counter-

In the 1970s, a new breed of aeroderivative gas turbines entered industrial vice These units, with simple-cycle thermal efficiencies in the 32–37 percentbracket, represented a new technological approach to aerothermodynamic design.Today, these second-generation units are joined by hybrid designs that incor-porate some of the aeroderivative design advances but still maintain the basic struc-tural concepts of the heavy-frame machines These hybrid units are not approachingthe simple-cycle thermal-efficiency levels reached by some of the early second-generation aeroderivative units first earmarked for industrial use

ser-Traditionally, the major focus has been on first cost of industrial gas-turbineunits, 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 theexpected life of the equipment Conversely, reliable, high-quality equipment withdemonstrated 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 gle-point solution can easily be obtained, but multiple solutions require repeatedcalculations Although curves depicting simultaneous variations in all variableswould be difficult to interpret, simplified diagrams can be constructed to illustratethe relative importance of different variables

sin-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 afunction of initial investment cost for various levels of thermal efficiency, loan

repayment period, gas-turbine availability, and fuel cost Each of these factors is

an element in the life-cycle cost model presented here

This procedure is the work of R B Spector, General Electric Co., as reported

in (8.89 cm) and a longitudinal pitch of 3 in (7.62 m) There are 40 tubes wideand 60 tubes deep in the heater; 300,000 lb (136,200 kg) of air flows across the

for possible tube vibration problems

Calculation Procedure:

1. Determine the mode of vibration for the tube bundle

Whenever a fluid flows across a tube bundle such as boiler tubes in an evaporator,economizer, HRSG, superheater, or air heater, vortices are formed and shed in thewake beyond the tubes This shedding on alternate sides of the tubes causes aharmonically varying force on the tubes perpendicular to the normal flow of thefluid It is a self-excited vibration If the frequency of the Von Karman vortices, asthey are termed, coincides with the natural frequency of vibration of the tubes, thenresonance occurs and the tubes vibrate, leading to possible damage of the tubes.Vortex shedding is most prevalent in the range of Reynolds numbers from 300

to 200,000, the range in which most boilers operate Another problem encounteredwith vortex shedding is acoustic vibration, which is normal to both the fluid flowand tube length observed in only gases and vapors This occurs when the vortexshedding frequency is close to the acoustic frequency Excessive noise is generated,leading to large gas pressure drops and bundle and casing damage The startingpoint 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

Since the tubes are fixed at both ends, i.e., clamped, select the mode of vibration

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

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

21 ft / s (6.4 m / s)

vortex shedding frequency, cps

4. Determine the acoustic frequency

As with vortex frequency, we must first determine several variables, namely:

ft (7.13 m)

2 are summarized in the tabulation below

Moment-connected corners

Main wall beams

Main roof beams Roof cross-tie beams

Gas flo w

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

in combined-cycle units makes this consideration even more important (Power).

The tube natural frequency and the vortex shedding frequency are far apart.Hence, the tube bundle vibration problem is unlikely to occur However, the vortexshedding and acoustic frequencies are close If the air flow increases slightly, thetwo frequencies will be close By inserting a baffle in the tube bundle (dividing theductwork into two along the gas flow direction) we can double the acoustic fre-quency as the width of the gas path is now halved This increases the differencebetween vortex shedding and acoustic frequencies and prevents noise problems.Noise problems arise when the acoustic and vortex shedding frequencies areclose—usually within 20 percent Tube bundle vibration problems arise when thevortex shedding frequency and natural frequency of the bundle are close—within

20 percent Potential noise problems must also be considered at various turndownconditions of the equipment

Related Calculations. For a thorough analysis of a plant or its components,evaluate the performance of heat-transfer equipment as a function of load Analyze

at various loads the possible vibration problems that might occur At low loads inthe above case, tube bundle vibration is likely, while at high loads acoustic vibration

is likely without baffles Hence, a wide range of performance must be reviewedbefore finalizing any tube bundle design, Fig 13

This procedure is the work of V Ganapathy, Heat Transfer Specialist, ABCOIndustries, Inc

MODERN POWER-PLANT CYCLES AND EQUIPMENT 1.25

DETERMINING OXYGEN AND FUEL INPUT IN

GAS-TURBINE PLANTS

In a gas-turbine HRSG (heat-recovery steam generator) it is desired to raise the

exhaust gases contain 15 percent oxygen by volume, determine the fuel input andoxygen 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 ically, the gas-turbine exhaust gas contains 14 to 15 percent oxygen by volume Sothe question arises: How much fuel can be fired to generate more steam? Wouldthe oxygen in the exhaust gases run out if we fired to a desired temperature? Thesequestions are addressed in this procedure

to a weight basis by multiplying by its molecular weight of 32 and dividing by themolecular weight of the exhaust gases, namely 29.5 Then multiplying by (100 /23) gives the air equivalent as air contains 23 percent by weight of oxygen

2. Relate the air required with the fuel fired using the MM Btu (kJ ) method

Each MM Btu (kJ) of fuel fired (HHV basis) requires a certain amount of air, A.

(calcu-lations for turbine exhaust gases fuel input are done on a low-heating-value basis)

3. Simplify the gas relations further

from the exhaust gases to the burner fuel consumption

4. Find the fuel input to the HRSG

FIGURE 14 Steam injection systems offer substantial improvement in both capacity and

ef-ficiency (Power).

The relation above requires enthalpies of the gases before and after the burner,which entails detailed combustion calculations However, considering that the mass

of fuel is a small fraction of the total gas flow through the HRSG, the fuel flow

percent That is, only 3.32 percent oxygen by volume is consumed and we still

fired and the gases will not run out of oxygen for combustion

Typically, the final oxygen content of the gases can go as low as 2 to 3 percent

through an HRSG simulation program (contact the author for more information)that all of the fuel energy goes into steam Thus, if the unfired HRSG were gen-erating 23,000 lb / h (10,442 kg / h) of steam with an energy absorption of 23 MMBtu / h (24.3 MM J / h), approximately, the amount of steam that can be generated

128,000 lb / h (58,112 kg / h) of steam This is close to a firing temperature of 3000

Related Calculations. Using the methods given elsewhere in this handbook,one may make detailed combustion calculations and obtain a flue-gas analysis aftercombustion Then compute the enthalpies of the exhaust gas before and after theburner Using this approach, you can check the burner duty more accurately thanusing the gas specific-heat method presented above This procedure is the work of

V Ganapathy, Heat Transfer Specialist, ABCO Industries, Inc

Power magazine recently commented on the place of gas turbines in today’s

modern power cycles thus: Using an HRSG with a gas turbine enhances the overallefficiency of the cycle by recovering heat in the gas-turbine’s hot exhaust gases.The recovered heat can be used to generate steam in the HRSG for either (1)injection back into the gas turbine, Fig 14, (2) use in district heating or an industrialprocess, (3) driving a steam turbine-generator in a combined-cycle arrangement, or(4) any combination of the first three

MODERN POWER-PLANT CYCLES AND EQUIPMENT 1.27

L-p steam H-p steam

Condenser

Deaerator Boiler feed pump

H-p drum

L-p drum

Stack L-p economizer H-p economizer L-p superheater

FIGURE 15 HRSG and gas turbine used in repowering (Power).

Steam injection into the gas turbine has many benefits, including: (1) achievableoutput is increased by 25 percent or more, depending on the gas-turbine design,(2) part-load gas-turbine efficiency can be significantly improved, (3) gas-fired NOxemissions can be markedly reduced—up to the 15–45 ppm range in many cases,(4) operating flexibility is improved for cogeneration plants because electrical andthermal outputs can be balanced to optimize overall plant efficiency and profit-ability

Combined-cycle gas-turbine plants are inherently more efficient than cycle plants employing steam injection Further, combined-cycle plants may also

simple-be considered more adaptable to cogeneration compared to steam-injected gas bines The reason for this is that the maximum achievable electrical output de-creases significantly for steam-injected units in the cogeneration mode because lesssteam is available for use in the gas turbine In contrast, the impact of cogeneration

tur-on electrical output is much less for combined-cycle plants

Repowering in the utility industry can use any of several plant-revitalizationschemes One of the most common repowering options employed or consideredtoday by utilities consists of replacing an aging steam generator with a gas-turbine / generator and HRSG, Fig 15 It is estimated that within the next few years,more than 3500 utility power plants will have reached their 30th birthdays Asignificant number of these facilities—more than 20 GW of capacity by someestimates—are candidates for repowering, an option that can cut emissions andboost plant efficiency, reliability, output, and service life

And repowering often proves to be more economical, per cost of kilowatt erated, compared to other options for adding capacity Further, compared to building

gen-a new power plgen-ant, the permitting process for repowering its typicgen-ally much shorterand less complex The HRSG will often have a separate firing capability such asthat discussed in this calculation procedure

To steam turbine H-p drum

L-p evaporator H-p economizer

H-p feedwater pump

L-p drum

To steam turbine

L-p economizer

Condensate pump

FIGURE 16 HRSG circuit shown is used by at least one manufacturer to

prevent steaming in the economizer during startup and low-load operation

(Power).

These comments from Power magazine were prepared by Steven Collins,

As-sistant Editor of the publication

HEAT-RECOVERY STEAM GENERATOR (HRSG)

SIMULATION

the steam-generation and design-temperature profiles if the feedwater temperature

approach point and 1 percent heat loss Evaluate the evaporator duty, steam flow,economizer duty, and exit-gas temperature for normal load conditions Then deter-mine how the HRSG off-design temperature profile changes when the gas-turbine

tem-perature remaining the same

Calculation Procedure:

1. Compute the evaporator duty and steam flow

Engineers should be able to predict both the design and off-design performance of

an HRSG, such as that in Fig 16, under different conditions of exhaust flow, perature, and auxiliary firing without delving into the mechanical design aspects oftube size, length, or fin configuration This procedure shows how to make suchpredictions for HRSGs of various sizes by using simulation techniques

tem-MODERN POWER-PLANT CYCLES AND EQUIPMENT 1.29

HRSGs operate at different exhaust-gas conditions For example, variations inambient temperature or gas-turbine load affect exhaust-gas flow and temperature.This, in turn, affects HRSG performance, temperature profiles, efficiency, and steamgeneration The tool consultants use for evaluating HRSG performance under dif-ferent operating conditions is simulation With this tool you can: (1) Predict off-design performance of an HRSG; (2) Predict auxiliary fuel consumption for periodswhen the gas-turbine exhaust-gas flow is insufficient to generate the required steamflow; (3) Evaluate options for improving an HRSG system; (4) Evaluate field datafor validating an HRSG design; (5) Evaluate different HRSG configurations formaximizing efficiency

by the evaporator, Btu / h) / (enthalpy absorbed by the steam in the evaporator, Btu

2. Determine the economizer duty and exit gas temperature

MW)

3. Calculate the constant K for evaporator performance

condition

4. Compute the revised evaporator performance

Under the revised performance conditions, using the given data and the above value

duty, using the same equation as in step 1 above⫽ (165,000)(0.99)(0.27)(880 ⫺

In this calculation, we assumed that the exhaust-gas analysis had not changed

If there are changes in the exhaust-gas analysis, then the gas properties must beevaluated and corrections made for variations in the exhaust-gas temperature See

Waste Heat Boiler Deskbook by V Ganapathy for ways to do this.

5. Find the assumed duty, Q a , for the economizer

6. Determine the UA value for the economizer in both design and off-design conditions

7. Calculate the economizer duty

Since the assumed and transferred duty do not match, i.e., 3.52 MM Btu / h vs.

4.01 MM Btu / h, another iteration is required Continued iteration will show that

Related Calculations. Studying the effect of gas inlet temperature and gasflows on HRSG performance will show that at lower steam generation rates or atlower pressures that the economizer water temperature approaches saturation tem-perature, a situation called ‘‘steaming’’ in the economizer This steaming conditionshould be avoided by generating more steam by increasing the inlet gas temperature

or through supplementary firing, or by reducing exhaust-gas flow

Supplementary firing in an HRSG also improves the efficiency of the HRSG intwo ways: (1) The economizer acts as a bigger heat sink as more steam and hencemore feedwater flows through the economizer This reduces the exit gas tempera-ture So with a higher gas inlet temperature to the HRSG we have a lower exit gastemperature, thanks to the economizer (2) Additional fuel burned in the HRSGreduces the excess air as more air is not added; instead, the excess oxygen is used

In conventional boilers we know that the higher the excess air, the lower the boilerefficiency Similarly, in the HRSG, the efficiency increases with more supplemen-tary firing HRSGs used in combined-cycle steam cycles, Fig 17, may use multiplepressure levels, gas-turbine steam injection, reheat, selective-catalytic-reduction

Reheater 2 H-p superheater 2

H-p evapor ator

I-p superheater H-p economizer 1 L-p superheater

I-p evapor ator

H-p economizer 2 I-p economizer 3 H-p economizer 3

L-p evapor ator

Feedw ater heater

MODERN POWER-PLANT CYCLES AND EQUIPMENT 1.33

tensive analysis to determine the best arrangement of the various heat-absorbingsurfaces

For example, an HRSG generates 22,780 lb / h (10.342 kg / h) of steam in theunfired mode The various parameters are shown in Table 2 Studying this tableshows that as the steam generation rate increases, more and more of the fuel energygoes into making steam Fuel utilization is typically 100 percent in an HRSG TheASME efficiency is also shown in the table

This simulation was done using the HRSG simulation software developed bythe author, V Ganapathy, Heat Transfer Specialist, ABCO Industries, Inc

PREDICTING HEAT-RECOVERY STEAM

GENERATOR (HRSG) TEMPERATURE PROFILES

There is a heat loss of 1 percent in the HRSG Find the ASME efficiency for thisHRSG unit

Calculation Procedure:

1. Select the pinch and approach points for the HRSG

Gas turbine heat recovery steam generators (HRSGs) are widely used in ation and combined-cycle plants Unlike conventionally fired steam generatorswhere the rate of steam generation is predetermined and can be achieved, steam-flow determination in an HRSG requires an analysis of the gas / steam temperatureprofiles This requirement is mainly because we are starting at a much lower gas

the exit gas temperature from an HRSG cannot be assumed It is a function of theoperating steam pressure, steam temperature, and pinch and approach points used,Fig 18

Higher values may be used if less steam generation is required In this case, we

2. Compute the steam generation rate

FIGURE 18 Gas / steam temperature profiles.

evaporator, all expressed in Btu / lb) Or, enthalpy absorbed in the evaporator and

kJ / kg)

3. Calculate the energy absorbed by the superheater and the exit gas

temperature

specific heat is taken as 0.273 because the gas temperature in the superheater isdifferent from the inlet gas temperature

4. Compute the energy absorbed by the evaporator

The total energy absorbed by the superheater and evaporator, from the above, is

14.31 MM Btu / h (4.19 MW)

MODERN POWER-PLANT CYCLES AND EQUIPMENT 1.35

TABLE 3 HRSG Exit Gas Temperatures Versus Steam Parameters*

5. Determine the economizer duty and exit-gas temperature

MW)

gas temperature of each of the heat-transmission surfaces

6. Compute the ASME HRSG efficiency

Related Calculations. Note that the exit gas temperature is high Further, out having done this analytical mathematical analysis, the results could not havebeen guessed correctly Minor variations in the efficiency will result if one assumesdifferent pinch and approach points Hence, it is obvious that one cannot assume a

generation

The gas / steam temperature profile is also dependent on the steam pressure andsteam temperature The higher the steam temperature, the lower the steam gener-ation rate and the higher the exit gas temperature Arbitrary assumption of the exitgas temperature or pinch point can lead to temperature cross situations Table 3shows the exit gas temperatures for several different steam parameters From thetable, it can be seen that the higher the steam pressure, the higher the saturationtemperature, and hence, the higher the exit gas temperature Also, the higher thesteam temperature, the higher the exit gas temperature This results from the re-duced steam generation, resulting in a smaller heat sink at the economizer

This procedure is the work of V Ganapathy, Heat Transfer Specialist, ABCOIndustries, who is the author of several works listed in the references for this sec-tion

FIGURE 19 T-S diagrams

for steam turbine.

STEAM TURBOGENERATOR EFFICIENCY AND

STEAM RATE

absolute At best efficiency, the steam rate is 10 lb (25.4 kg) per kWh (a) What is the combined thermal efficiency (CTE) of this unit? (b) What is the combined engine efficiency (CEE)? (c) What is the ideal steam rate?

Calculation Procedure:

1. Determine the combined thermal efficiency

backpres-sure, Btu / lb (kJ / kg) Using the steam tables and Mollier chart and substituting in

2. Find the combined engine efficiency

ideal engine, lb / kWh) / (weight of steam used by actual engine, lb / kWh) Theweights of steam used may also be expressed as Btu / lb (kJ / kg) Thus, for the ideal

Since the steam expands isentropically into the wet region below the dome of

the T-S diagram, Fig 19, we must first determine the quality of the steam at point

2 either from a T-S diagram or Mollier chart or by calculation By calculation using

885.3 Btu / lb (2062.7 kJ / kg)

a plant and is in a range being achieved today

Related Calculations. Use this approach to analyze the efficiency of any bogenerator used in central-station, industrial, marine, and other plants

tur-MODERN POWER-PLANT CYCLES AND EQUIPMENT 1.37

TURBOGENERATOR REHEAT-REGENERATIVE

CYCLE ALTERNATIVES ANALYSIS

A turbogenerator operates on the reheating-regenerative cycle with one stage of

under these conditions, find: (a) Percentage of throttle steam bled for feedwater heating; (b) Heat converted to work per pound (kg) of throttle steam; (3) Heat supplied per pound (kg) of throttle steam; (d ) Ideal thermal efficiency; (e) Other

ways to heat feedwater and increase the turbogenerator output Figure 20 showsthe layout of the cycle being considered, along with a Mollier chart of the steamconditions

2. Determine the percentage of throttle steam bled for feedwater heating

(a) Set up the ratio for the feedwater heater of (heat added in the feedwater

heater) / (heat supplied to the heater)(100) Or, using the enthalpy data from step 1

percent of the throttle steam is bled for feedwater heating

3. Find the heat converted to work per pound (kg) of throttle steam

(b) The heat converted to work is the enthalpy difference between the throttle steam

and the bleed steam at point 2 plus the enthalpy difference between points 3 and

4 times the percentage of throttle flow between these points In equation form, heat

4. Calculate the heat supplied per pound (kg) of throttle steam

MODERN POWER-PLANT CYCLES AND EQUIPMENT 1.39

FIGURE 21 Heat input to the economizer may be increased by the addition of induct burners,

by bypassing hot furnace gases into the gas path ahead of the economizer, or by recirculation

(Power).

5. Compute the ideal thermal efficiency

Today steam turbines are built with more heavily loaded exhaust ends so thatthe additional capacity is not available Further, turbine manufacturers place restric-tions on the removal of feedwater heaters from service However, if the steam output

of the boiler is less than the design capacity of the steam turbine, because of aconversion to coal firing, additional turbogenerator capacity is available and can beregained at a far lower cost than by adding new generator capacity

Compensation for the colder feedwater can be made, and the lost efficiencyregained, by using a supplementary fuel source to heat feedwater This can be done

in one of two ways: (1) increase heat input to the existing boiler economizer, or(2) add a separately fired external economizer

Additional heat input to a boiler’s existing economizer can be supplied by duct burners, Fig 21, from slagging coal combustors, Fig 22, or from the furnaceitself Since the economizer in a coal-fired boiler is of sturdier construction than aheat-recovery steam generator (HRSG) with finned tubing, in-duct burners can beplaced closer to the economizer, Fig 21 Burner firing may be by coal or oil.Slagging coal combustors are under intense development A low-NOx, low-ash

be commercially available

To accommodate any of the changes shown in Fig 21, a space from 12 (3.66m) to 15 ft (4.57 m) is needed between the bottom of the primary superheater andthe top of the economizer This space is required for the installation of the in-duct

FIGURE 22 Slagging combustors can be arranged to inject hot combustion gases into gas

pas-sages ahead of economizer (Power).

Generator L-p

turbine

H-p

FIGURE 23 Gas-turbine exhaust gases can be used in place of high-pressure heaters, using a

compact heat exchanger (Power).