P • A • R • T1 POWER GENERATION Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) 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 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) 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 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 Determining Best-Relative-Value of Industrial Gas Turbines Using a Life- Cycle 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 Partial- Load 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 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 Condensing Steam-Turbine Power- Output Analysis 1.69 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 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 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 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) 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 1.4 POWER GENERATION Deaerator H-p turbine H-p steam Fuel I-p turbine L-p turbine I-p steam Generator Gas turbine Air H-p superheater Blowdown Blowdown H-p evaporator I-p suprerheater 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 x 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 155- MW natural-gas-fired gas turbine (GT) featuring a dry low NO x 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 /in 2 (gage)/1000 Њ F (9991-kPa/538 Њ C). Unit ratings are for operation at International Standard Organization (ISO) conditions. Evaluate the var- ious technologies considered for summer peaking conditions with a dry bulb (DB) temperature of 95 Њ F and 60 percent RH (relative humidity) (35 Њ 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 sys- tem includes a surface condenser and two 50 percent-capacity pumps. Water- treatment, consumption, and disposal-related O&M (operating & maintenance) Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. 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 HRSG Case 7 2 Supp.- fired HRSG GT output, MW 5.8 20.2 20.2 21.8 15.5 0 0 ST output, MW 0.9 2.4 Ϫ 2.1 Ϫ 13 3.7 8 35 Plant aux. load, MW 0.05 4.5 0.7 400 0.2 0.4 1 Net plant output, MW 6.65 18.1 17.4 8.4 19 7.6 34 Net heat rate, Btu/kWh 3 15 55 70 270 435 90 320 Incremental costs Change in total water cost, $/h 15 35 35 115 85 35 155 Change in wastewater cost, $/h 1 17 17 2 1 1 30 Change in capital cost / net output, $ / kW 180 165 230 75 15 70 450 1 Partial supplementary firing. 2 Full supplementary firing. 3 Based on lower heating value of fuel. 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- nificant capital outlays and affect other performance parameters. Further, the options Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. 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, 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 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 con- ditions of 95 Њ F (35 Њ C) DB and 60 percent RH, an 85 percent effective evaporative cooler can alter the inlet-air temperature and moisture content to 85 Њ F (29 Њ 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 in- creased by 5.8 MW GT output ϩ 0.9 MW ST output—plant auxiliary load of 0.9 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 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 evaporative- cooler 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 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 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, Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. MODERN POWER-PLANT CYCLES AND EQUIPMENT 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 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 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 Њ F (35 Њ C) to 60 Њ F (15.6 Њ C) DB—a level that is generally ac- cepted 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 ϩ 2.4 MW for ST Ϫ 4.5 MW plant auxiliary load ϭ 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)-H 2 O 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 cir- culating water flow by 12,500 gal/min (47.3 m 3 /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 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. 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 370 Њ F (188 Њ C) hot water. Cost-effective supply of this steam or hot water requires a redesign of the ref- erence plant. Steam is extracted from the low-pressure (l-p) steam turbine at 20.3 lb/in 2 (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 re- duces 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 oper- ation. 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 fluorocar- bons 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 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 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. MODERN POWER-PLANT CYCLES AND EQUIPMENT MODERN POWER-PLANT CYCLES AND EQUIPMENT 1.9 Water-injection power sugmentation Steam-injection power sugmentation Attemperating stationWater injection skid HRSG Gas turbine/ generator High-pressure superheater Demin. storage FIGURE 3 Water or steam injection can be used for both power augmentation and NO x 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 installed-cost considerations alone, extracting steam from the HRSG is favored for peaking service and may be accomplished without altering the reheat steam turbine. But if a plant operates in the steam-injection mode for extended periods, extracting steam from the turbine or increasing the h-p turbine exhaust pressure becomes more cost-effective. 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 The amount of excess O 2 in a GT exhaust gas generally permits the efficient firing of gaseous and liquid fuels upstream of the HRSG, thereby increasing the output Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. MODERN POWER-PLANT CYCLES AND EQUIPMENT 1.10 POWER GENERATION from the steam bottoming cycle. For this study, two types of supplementary firing are 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 en- hancement, including 910 lower cycle efficiency, (2) higher NO x and CO emissions, (3) higher costs for the larger plant equipment required. For this plant, each 100-million Btu /h (29.3 MW) of added supplementary firing capacity 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 because all the following equipment is affected: (1) boiler feed pumps, (2) condensate pumps, (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-design condition 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 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 (gage) (1413.5 kPa). Feedwater enters the boiler at 227 Њ F (108.3 Њ C). Determine if supplementary firing of the exhaust is required to generate the needed steam. Use an approach temperature of 20 Њ F (36 Њ C) between the feedwater and the water leav- ing the economizer. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. MODERN POWER-PLANT CYCLES AND EQUIPMENT [...]... the steam tables the properties of the steam generated by this boiler: ts ϭ 390ЊF (198.9ЊC); hl, heat of saturated liquid ϭ 364 Btu / lb (846.7 kJ / kg); hs, total heat of saturated vapor ϭ 1199.6 Btu / lb (2790.3 kJ / kg; hw, heat of saturated liquid of feedwater leaving the economizer at 370ЊF (187.8ЊC) ϭ 342 Btu / lb (795.5 kJ / kg); and hƒ, heat of saturated liquid of the feedwater at 227ЊF (108.3ЊC)... (10,442 kg / h) of steam with an energy absorption of 23 MM Btu / h (24.3 MM J / h), approximately, the amount of steam that can be generated by firing fuel in the HRSG ϭ 23 ϩ 105 ϭ 128 MM Btu / h (135 MM J / h), or 128,000 lb / h (58,112 kg / h) of steam This is close to a firing temperature of 3000 to 3100ЊF (1648 to 1704ЊC) Related Calculations Using the methods given elsewhere in this handbook, one... 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... estimation of various frequencies 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 Mode of vibration End conditions Both ends clamped One end clamped, one end hinged Both hinged 1 2 3 22.37 15.42 9.87 61.67 49.97 39.48 120.9 104.2 88.8 Since the tubes are fixed at both ends, i.e., clamped, select the mode of. .. conditions 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 in the above case, tube bundle vibration is likely, while at high loads acoustic vibration is likely without baffles Hence, a wide range of performance... 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 can be neglected Using a specific heat for the gases of 0.31 Btu / lb ЊF (1297.9 J / kg K), we have, Q ϭ 150,000(0.31)(1575 Ϫ 950) ϭ 29 ϫ 106 Btu / h (8.49 kW) The percent of oxygen by... is subject to the Terms of Use as given at the website MODERN POWER-PLANT CYCLES AND EQUIPMENT 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 equipment, found... kg) ϭ (enthalpy of the saturated steam in the HRSG outlet Ϫ enthalpy of the feedwater entering the evaporator at 373ЊF) ϩ (blowdown percentage)(enthalpy of the saturated liquid of the outlet steam Ϫ enthalpy of the water entering the evaporator, all in Btu / lb) Or, enthalpy absorbed in the evaporator ϭ (1199.3 Ϫ 345) ϩ (0.05)(362.2 Ϫ 345) ϭ 855.2 Btu / lb (1992.6 kJ / kg) The quantity of steam generated... to the normal flow of the fluid It is a self-excited vibration If the frequency of the Von Karman vortices, as they are termed, coincides with the natural frequency of vibration of the tubes, then resonance 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... consists of annual investment cost (Cp ) ϩ annual fuel cost (Cƒ) ϩ annual maintenance cost (Cm ) Equations for these values are: Cp ϭ where l i n A kW 8760 G ϭ ϭ ϭ ϭ ϭ ϭ ϭ l {i / [1 Ϫ (1 Ϫ i )Ϫn ]} (A )(kW)(8760)(G ) initial capital cost of equipment, dollars interest rate number of payment periods availability (expressed as decimal) kilowatts of electricity produced total hours in year efficiency of electric . subject to the Terms of Use as given at the website. Source: HANDBOOK OF MECHANICAL ENGINEERING CALCULATIONS Downloaded from Digital Engineering Library. subject to the Terms of Use as given at the website. Source: HANDBOOK OF MECHANICAL ENGINEERING CALCULATIONS 1.4 POWER GENERATION Deaerator H-p turbine H-p