Handbook of Mechanical Engineering calculation Second Edition by Tyler G. Hicks.pdf PDF

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Source: HANDBOOK OF MECHANICAL ENGINEERING CALCULATIONS P • A • R • T 1 POWER GENERATION Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. POWER GENERATION Copyright © 2006 The McGraw-Hill Companies. All rights reserved....

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Source: HANDBOOK OF MECHANICAL ENGINEERING CALCULATIONS

P

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A

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POWER GENERATION

Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.

POWER GENERATION

Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.

Source: HANDBOOK OF MECHANICAL ENGINEERING CALCULATIONS

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 LifeCycle Cost Model 1.18 Tube Bundle Vibration and Noise Determination in HRSGs 1.22 Determining Oxygen and Fuel Input in Gas-Turbine Plants 1.25 Heat-Recovery Steam Generator (HRSG) Simulation 1.28 Predicting Heat-Recovery Steam Generator (HRSG) Temperature Profiles 1.33 Steam Turbogenerator Efficiency and Steam Rate 1.36 Turbogenerator Reheat-Regenerative Cycle Alternatives Analysis 1.37 Turbine Exhaust Steam Enthalpy and Moisture Content 1.42 Steam Turbine No-Load and PartialLoad Steam Flow 1.43 Power Plant Performance Based on 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

Steam-Turbine Regenerative-Cycle Performance 1.71 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 1.87

Steam Mollier Diagram and Steam Table Use 1.87 Interpolation of Steam Table Values 1.90

Constant-Pressure Steam Process 1.93

Constant-Volume Steam Process 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

1.51

Maximizing Cogeneration ElectricPower and Process-Steam Output

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

1.110

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 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

1.62

Mechanical-Drive Steam-Turbine Power-Output Analysis 1.67 Condensing Steam-Turbine PowerOutput Analysis 1.69 1.3

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MODERN POWER-PLANT CYCLES AND EQUIPMENT 1.4

POWER GENERATION

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 155MW natural-gas-fired gas turbine (GT) featuring a dry low NOx combustor (Fig. 1). The plant has a heat-recovery steam generator (HRSG) which is a triple-pressure design with an integral deaerator. A reheat condensing steam turbine (ST) is used and it is coupled to a cooling-tower / surface-condenser heat sink turbine inlet. Steam conditions are 1450-lb / in2 (gage) / 1000
F (9991-kPa / 538
C). Unit ratings are for operation at International Standard Organization (ISO) conditions. Evaluate the various technologies considered for summer peaking conditions with a dry bulb (DB) temperature of 95
F and 60 percent RH (relative humidity) (35
C and 60 percent RH). The plant heat sink is a four-cell, counterflow, mechanical-draft cooling tower optimized to achieve a steam-turbine exhaust pressure of 3.75 inHg absolute (9.5 cmHg) for all alternatives considered in this evaluation. Base circulating-water system includes a surface condenser and two 50 percent-capacity pumps. Watertreatment, consumption, and disposal-related O&M (operating & maintenance)

H-p turbine

I-p turbine

L-p turbine Cooling tower Generator

H-p steam L-p steam

Cold reheat steam Hot reheat

Makeup water

I-p steam

Feedwater pumps

Condensate pumps Deaerator

Reheater

H-p evaporator I-p suprerheater H-p economizer I-p suprerheater I-p evaporator I-p economizer L-p evaporator L-p economizer

Fuel

Generator

Gas turbine H-p superheater Air

Blowdown

Blowdown I-p pump

I-p pump

FIGURE 1 155-MW natural-gas-fired gas turbine featuring a dry low NOx combustor (Power).

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MODERN POWER-PLANT CYCLES AND EQUIPMENT 1.5

MODERN POWER-PLANT CYCLES AND EQUIPMENT

costs for the zero-discharge facility are assumed to be $3 / 1000 gal ($3 / 3.8 m3) of raw water, $6 / 1000 gal ($6 / 3.8 m3) of treated demineralized water, and $5 / 1000 gal ($5 / 3.8 m3) 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 temperature 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-temperatureoutput 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 significant capital outlays and affect other performance parameters. Further, the options

TABLE 1 Performance Summary for Enhanced-Output Options

Measured change from base case GT output, MW ST output, MW Plant aux. load, MW Net plant output, MW Net heat rate, Btu / kWh3 Incremental costs Change in total water cost, $ / h Change in wastewater cost, $ / h Change in capital cost / net output, $ / kW

Case 61 Case 72 Case 1 Case 2 Case 3 Case 4 Case 5 Supp.- Supp.Evap. Mech. Absorp. Steam fired fired Water cooler chiller chiller injection injection HRSG HRSG 5.8 0.9 0.05 6.65 15

20.2 2.4 4.5 18.1 55

15

20.2 ⫺2.1

21.8 ⫺13

15.5 3.7 0.2 19 435

0 8 0.4 7.6 90

0 35 1 34 320

0.7 17.4 70

400 8.4 270

35

35

115

85

35

155

1

17

17

2

1

1

30

180

165

230

75

15

70

450

1

Partial supplementary firing. Full supplementary firing. 3 Based on lower heating value of fuel. 2

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MODERN POWER-PLANT CYCLES AND EQUIPMENT 1.6

POWER GENERATION

may uniquely impact the operation and / or selection of other components, including boiler feedwater and condensate pumps, valves, steam turbine / generators, condensers, 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 density and mass flow of the air entering the unit. Water sprayed into the inlet-air stream cools the air to a point near the ambient wet-bulb temperature. At reference conditions of 95
F (35
C) DB and 60 percent RH, an 85 percent effective evaporative cooler can alter the inlet-air temperature and moisture content to 85
F (29
C) and 92 percent RH, respectively, using conventional humidity chart calculations, page 16.79. 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 increased by 5.8 MW GT output ⫹ 0.9 MW ST output—plant auxiliary load of 0.9 MW ⫽ 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 system, based on estimates provided by contractors and staff, is $1.2-million. The incremental cost is $1,200,000 / 6650 kW ⫽ $180.45 / kW for this ambient condition. The effectiveness of the same system operating in less-humid conditions—say 95
F DB (35
C) and 40 percent RH—is much greater. In this case, the same evaporative cooler can reduce inlet-air temperature to 75
F DB (23.9
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. Because 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 and system scaling. Overall, the evaporation process can significantly increase a plant’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 first approach, and $20 / h for the second, lower RH mode. Disposal of evaporativecooler blowdown costs $1 / h in the first mode, $2 / h in the second. Evaporative cooling 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 the inlet air. Thus, chillers may be used for further cooling of the inlet air below the wet-bulb temperature. To achieve this goal, industrial-grade mechanical or absorption 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 for extracting heat from the inlet air, and a heat-rejection system. A mechanical chilling system, Case 2, Table 1, is based on a compressor-driven unit. The compressor is the most expensive part of the system and consumes a significant amount of energy. In general, chillers rated above 12-million Btu / h (3.5 MW) (1000 tons of refrigeration) (3500 kW) employ centrifugal compressors. Units smaller than this may use either screw-type or reciprocating compressors. Overall,

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MODERN POWER-PLANT CYCLES AND EQUIPMENT MODERN POWER-PLANT CYCLES AND EQUIPMENT

Circulating water pump

1.7

Ambient air (95F, 60% RH) Chilledwater coils

Chilled water

Chilled air (60F, 100% RH) HRSG

Gas turbine/ generator Electricdriven centrifugal chiller

Cooling tower

Cooling water

Chilled-water loop 25-psia steam from HRSG

Cooling tower

2-stage lithium Condensate bromide adsorption return chiller

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 changes without difficulty. A centrifugal-compressor-based chiller can easily reduce the temperature of the GT inlet air from 95
F (35
C) to 60
F (15.6
C) DB—a level that is generally accepted as a safe lower limit for preventing icing on compressor inlet blades—and achieve 100 percent RH. This increases plant output by 20.2 MW for GT ⫹ 2.4 MW for ST ⫺ 4.5 MW plant auxiliary load ⫽ 18.1 MW, or 8.9 percent. But it degrades the net CC heat rate by 0.8 percent and results in a 1.5-in-(3.8-cm)-H2O inlet-air pressure drop because of heat-exchanger equipment located in the inlet-air stream. Cooling requirements of the chilling system increase the plant’s required circulating water flow by 12,500 gal / min (47.3 m3 / 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 ⫽ $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 inletair conditions as the mechanical chiller (60
F DB, 100 percent RH) (15.6
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 / in2 (gage) (70.9-kPa) saturated steam, or 6830 gal / min (25.9 m3 / min) of 370
F (188
C) hot water. Cost-effective supply of this steam or hot water requires a redesign of the reference plant. Steam is extracted from the low-pressure (l-p) steam turbine at 20.3 lb / in2 (gage) (139.9 kPa) and attemperated until it is saturated. In this case, the absorption chiller increases plant output by 8.7 percent or 17.4 MW but degrades the plant’s heat rate by 1 percent. Although the capacity of the absorption cooling system’s cooling-water loop must be twice that of the mechanical chiller’s, the size of the plant’s overall heat sink is identical—25 percent larger than the base case—because the steam extracted from the l-p turbine reduces the required cooling capacity. Note that this also reduces steam-turbine output by 2 MW compared to the mechanical chiller, but has less effect on overall plant output. Cost estimates summarized in Table 1 show that the absorption chilling system required 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 the chiller 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 operation. When forced to operate below their rated capacity, absorption chillers suffer a loss in efficiency and reportedly require more operator attention than mechanical systems. Refrigerant issues affect the comparison between mechanical and absorption chilling. Mechanical chillers use either halogenated or nonhalogenated fluorocarbons at this time. Halogenated fluorocarbons, preferred by industry because they 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 electrical 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 injection, 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 extraction point. For example, advanced, large-frame GTs require steam pressures of 410 to 435 lb / in2 (gage) (2825 to 2997 kPa). This is typically higher than the economically optimal range of h-p steam turbine exhaust pressures of 285 to 395 lb / in2

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MODERN POWER-PLANT CYCLES AND EQUIPMENT MODERN POWER-PLANT CYCLES AND EQUIPMENT

Demin. storage

Water-injection power sugmentation

Water injection skid

1.9

Steam-injection power sugmentation

Attemperating station

HRSG Gas turbine/ generator

High-pressure superheater

FIGURE 3 Water or steam injection can be used for both power augmentation and NOx control (Power).

(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 ins...