Handbook of Mechanical Engineering Calculations

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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 ...

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Handbook of Mechanical Engineering Calculations
Source: HANDBOOK OF MECHANICAL ENGINEERING CALCULATIONS • • • P A R T 1 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.
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 SECTION 1 MODERN POWER-PLANT CYCLES AND EQUIPMENT CYCLE ANALYSES 1.4 Steam-Turbine Regenerative-Cycle Performance 1.71 Choosing Best Options for Boosting Combined-Cycle Plant Output 1.4 Reheat-Regenerative Steam-Turbine Heat Rates 1.74 Selecting Gas-Turbine Heat-Recovery Boilers 1.10 Steam Turbine-Gas Turbine Cycle Analysis 1.76 Gas-Turbine Cycle Efﬁciency Analysis and Output Determination 1.13 Gas Turbine Combustion Chamber Inlet Air Temperature 1.81 Determining Best-Relative-Value of Industrial Gas Turbines Using a Life- Regenerative-Cycle Gas-Turbine Cycle Cost Model 1.18 Analysis 1.83 Tube Bundle Vibration and Noise Extraction Turbine kW Output 1.86 Determination in HRSGs 1.22 STEAM PROPERTIES AND PROCESSES Determining Oxygen and Fuel Input in 1.87 Gas-Turbine Plants 1.25 Steam Mollier Diagram and Steam Heat-Recovery Steam Generator Table Use 1.87 (HRSG) Simulation 1.28 Interpolation of Steam Table Values Predicting Heat-Recovery Steam 1.90 Generator (HRSG) Temperature Constant-Pressure Steam Process Proﬁles 1.33 1.93 Steam Turbogenerator Efﬁciency and Constant-Volume Steam Process Steam Rate 1.36 1.95 Turbogenerator Reheat-Regenerative Constant-Temperature Steam Process Cycle Alternatives Analysis 1.37 1.97 Turbine Exhaust Steam Enthalpy and Constant-Entropy Steam Process Moisture Content 1.42 1.99 Steam Turbine No-Load and Partial- Irreversible Adiabatic Expansion of Load Steam Flow 1.43 Steam 1.101 Power Plant Performance Based on Irreversible Adiabatic Steam Test Data 1.45 Compression 1.103 Determining Turbogenerator Steam Throttling Processes for Steam and Rate at Various Loads 1.47 Water 1.105 Analysis of Reheating-Regenerative Reversible Heating Process for Steam Turbine Cycle 1.48 1.107 Steam Rate for Reheat-Regenerative Determining Steam Enthalpy and Cycle 1.49 Quality Using the Steam Tables Binary Cycle Plant Efﬁciency Analysis 1.109 1.51 Maximizing Cogeneration Electric- CONVENTIONAL STEAM CYCLES 1.53 Power and Process-Steam Output 1.110 Finding Cogeneration System Efﬁciency vs a Conventional Steam ECONOMIC ANALYSES OF Cycle 1.53 ALTERNATIVE ENERGY SOURCES 1.112 Bleed-Steam Regenerative Cycle Layout and T-S Plot 1.55 Choice of Most Economic Energy Source Using the Total-Annual-Cost Bleed Regenerative Steam Cycle Method 1.112 Analysis 1.59 Seven Comparison Methods for Reheat-Steam Cycle Performance Energy Source Choice 1.115 1.62 Selection of Prime Mover Based on Mechanical-Drive Steam-Turbine Annual Cost Analyses 1.120 Power-Output Analysis 1.67 Determining If a Prime Mover Should Condensing Steam-Turbine Power- Be Overhauled 1.122 Output Analysis 1.69 1.3 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 1.4 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 155- MW 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 var- ious 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 sys- tem includes a surface condenser and two 50 percent-capacity pumps. Water- treatment, consumption, and disposal-related O&M (operating & maintenance) H-p I-p turbine L-p turbine turbine Cooling tower Generator H-p steam L-p steam Cold reheat steam Makeup water Hot reheat Condensate I-p steam Feedwater pumps pumps Deaerator Reheater Fuel suprerheater suprerheater economizer economizer economizer evaporator evaporator evaporator Generator H-p H-p L-p L-p I-p I-p I-p I-p 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). 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 1.5 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 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 TABLE 1 Performance Summary for Enhanced-Output Options Case 61 Case 72 Case 1 Case 2 Case 3 Case 4 Case 5 Supp.- Supp.- Measured change from Evap. Mech. Absorp. Steam Water ﬁred ﬁred base case cooler chiller chiller injection injection HRSG HRSG GT output, MW 5.8 20.2 20.2 21.8 15.5 0 0 ST output, MW 0.9 2.4 2.1 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 / kWh3 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. 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 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 in- creased 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 sys- tem, 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 evap- orative 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. 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 1.7 MODERN POWER-PLANT CYCLES AND EQUIPMENT Ambient air (95F, 60% RH) Circulating water pump Chilled- water coils Chilled air Chilled (60F, 100% RH) water HRSG Gas turbine/ generator Cooling tower Electric- Cooling driven water centrifugal chiller Chilled-water loop 25-psia Cooling tower steam from 2-stage HRSG lithium bromide Condensate 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 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 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 cir- culating 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 inlet- air conditions as the mechanical chiller (60 F DB, 100 percent RH) (15.6 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 / 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 ref- erence 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 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 / in2 (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 / in2 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 1.9 MODERN POWER-PLANT CYCLES AND EQUIPMENT Demin. Water-injection storage Steam-injection power sugmentation power sugmentation Attemperating Water station injection skid HRSG Gas turbine/ High-pressure generator 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 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 NOx control during distillate-fuel ﬁring. Thus, no additional capital cost is incurred. When water injection is used for power augmentation or NOx 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 O2 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 NOx 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 NOx 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 F (510 C) and which will generate steam at 205 lb / in2 (gage) (1413.5 kPa). Feedwater enters the boiler at 227 F (108.3 C). Determine if supplementary ﬁring of the exhaust is required to generate the needed steam. Use an approach temperature of 20 F (36 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 1.11 MODERN POWER-PLANT CYCLES AND EQUIPMENT Calculation Procedure: 1. Determine the critical gas inlet-temperature Turbine exhaust gas (TEG) typically leaves a gas turbine at 900–1000 F (482–538 C) and has about 13 to 16 percent free oxygen. If steam is injected into the gas turbine for NOx control, the oxygen content will decrease by 2 to 5 percent by volume. To evaluate whether supplementary ﬁring of the exhaust is required to generate needed steam, a knowledge of the temperature proﬁles in the boiler is needed. Prepare a gas / steam proﬁle for this heat-recovery boiler as shown in Fig. 4. TEG enters on the left at 950 F (510 C). Steam generated in the boiler at 205 lb / in2 (gage) (1413.5 kPa) has a temperature of 390 F (198.9 C), from steam tables. For steam to be generated in the boiler, two conditions must be met: (1) The ‘‘pinch point’’ temperature must be greater than the saturated steam temperature of 390 F (198.9 C), and (2) the temperature of the saturated steam leaving the boiler econ- omizer must be greater than that of the feedwater. The pinch point occurs some- where along the TEG temperature line, Fig. 4, which starts at the inlet temperature of 950 F (510 C) and ends at the boiler gas outlet temperature, which is to be determined by calculation. A pinch-point temperature will be assumed during the calculation and its suitability determined. To determine the critical gas inlet-temperature, T1, get from the steam tables the properties of the steam generated by this boiler: ts 390 F (198.9 C); hl, heat of saturated liquid 364 Btu / lb (846.7 kJ / kg); hs, total heat of saturated vapor 1199.6 Btu / lb (2790.3 kJ / kg; hw, heat of saturated liquid of feedwater leaving the economizer at 370 F (187.8 C) 342 Btu / lb (795.5 kJ / kg); and hƒ, heat of satu- rated liquid of the feedwater at 227 F (108.3 C) 196.3 Btu / lb (456.6 kJ / kg). Top Numbers: Example 1 T1 Bottom Numbers: Example 2 950 1,550 T2 Pinch point 415 T3 440 317 296 Tl 390 390 Tw Tt 370 227 325 Approach point 227 950˚F (510˚C) 1550˚F (843˚C) 390˚F (199˚C) 390˚F (199˚C) 415˚F (213˚C) 440˚F (227˚C) 370˚F (188˚C) 325˚F (163˚C) 317˚F (158˚C) 296˚F (147˚C) 227˚F (108˚C) 227˚F (108˚C) FIGURE 4 Gas / steam proﬁle and data (Chemical Engineering). 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 1.12 POWER GENERATION Writing an energy balance across the evaporator neglecting heat and blowdown losses, we get: (T1 T2) / (T1 T3) ( hs hw ) / (hs hƒ) X, where T1 gas temperature in boiler, F ( C); T2 pinch-point gas temperature, F ( C); T3 outlet gas temperature for TEG, F ( C); enthalpy, h, values as listed above; X ratio of temperature or enthalpy differences. Substituting, X (1199.6 342) / (1199.9 196.3) 0.855, using enthalpy values as given above. The critical gas inlet-temperature, T1c (ts Xtƒ) / (1 X ), where ts tem- perature of saturated steam, F ( C); tƒ temperature of feedwater, F ( C); other symbols as before. Using the values determined above, T1c [390 (0.855)(227)] / (1 0.855) 1351 F (732.8 C). 2. Determine the system pinch point and gas / steam proﬁle Up to a gas inlet temperature of approximately 1351 F (732.8 C), the pinch point can be arbitrarily selected. Beyond this, the feedwater inlet temperature limits the temperature proﬁle. Let’s then select a pinch point of 25 F (13.9 C), Fig. 4. Then, T2, the gas-turbine gas temperature at the pinch point, F ( C) tƒ pinch-point temperature difference, or 390 F 25 F 415 F (212.8 C). Setting up an energy balance across the evaporator, assuming a heat loss of 2 percent and a blowdown of 3 percent, leads to: Qevap We (1 heat loss)(TEG heat capacity, Btu / F) (T1 T2), where We TEG ﬂow, lb / h; heat capacity of TEG 0.27 Btu / F; T1 TEG inlet temperature, F ( C). Substituting, Qevap 150,000(0.98)(0.27)(950 415) 21.23 106 Btu / h (6.22 MW). The rate of steam generation, Ws Qevap / [(hs hw ) blowdown percent (hl hw )], where the symbols are as given earlier. Substituting, Ws 21.23 106 / [(1199.6 342) 0.03 (364 342)] 24,736 lb / h (11,230 kg / h). Determine the boiler economizer duty from Qecon (1 blowdown)(Ws ) (hw hƒ), where symbols are as before. Substituting, Qecon 1.03(24,736)(342 196.3) 3.71 106 Btu / h (1.09 MW). The gas exit-temperature, T3 T2 Qecon / TEG gas ﬂow, lb / h)(1 heat loss)(heat capacity, Btu / lb F). Since all values are known, T3 415 3.71 106 / (150,000 0.98 0.27) 317 F (158 C). Figure 4 shows the temperature proﬁle for this installation. Related Calculations. Use this procedure for heat-recovery boilers ﬁred by gas-turbine exhaust in any industry or utility application. Such boilers may be un- ﬁred, supplementary ﬁred, or exhaust ﬁred, depending on steam requirements. Typically, the gas pressure drop across the boiler system ranges from 6 to 12 in (15.2 to 30.5 cm) of water. There is an important tradeoff: a lower pressure drop means the gas-turbine power output will be higher, while the boiler surface and the capital cost will be higher, and vice versa. Generally, a lower gas pressure drop offers a quick payback time. If Pe is the additional gas pressure in the system, the power, kW, consumed in overcoming this loss can be shown approximately from P 5 10 8 (We Pe T / E, where E efﬁciency of compression). To show the application of this equation and the related payback period, assume We 150,000 lb / g (68,100 kg / h), T 1000 R (average gas temperature in the boiler, Pe 4 in water (10.2 cm), and E 0.7. Then P 5 10 8 (150,000 4 1000 / 0.7) 42 kW. If the gas turbine output is 4000 kW, nearly 1 percent of the power is lost due to the 4-in (10.2-cm) pressure drop. If electricity costs 7 cent / kWh, and the gas turbine runs 8000 h / yr, the annual loss will be 8000 0.07 42 $23,520. If the incremental cost of a boiler having a 4-in (10.2-cm) lower pressure drop is, say $22,000, the payback period is about one year. 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 1.13 MODERN POWER-PLANT CYCLES AND EQUIPMENT Fuel F, Wf We, T1´ (We Wf),T1´ Burner TEG (Weh1´ LHV Wt) (We Wf)h1 FIGURE 5 Gas / steam proﬁle for ﬁred mode (Chemical Engineering). If steam requirements are not stated for a particular gas inlet condition, and maximum 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 steam ﬂow and gas-pressure drop. For example, Boiler A generates 24,000 lb / h (10,896 kg / h), while Boiler B provides 25,000 lb / h (11,350 kg / h) for the same gas pres- sure-drop but costs $30,000 more. Is Boiler B worth the extra expense? To answer this question, look at the annual differential gain in steam ﬂow. As- suming steam costs $3.50 / 1000 lb (3.50 / 454 kg), the annual differential gain in steam ﬂow 1000 3.5 8000 / 1000 $28,000. Thus, the simple payback is about a year ($30,000 vs $28,000), which is attractive. You must, however, be certain you assess payback time against the actual amount of time the boiler will operate. If the boiler is likely to be used for only half this period, then the payback time is actually two years. The general procedure presented here can be used for any type industry using gas-turbine heat-recovery boilers—chemical, petroleum, power, textile, food, etc. This procedure is the work of V. Ganapathy, Heat-Transfer Specialist, ABCO In- dustries, Inc., and was presented in Chemical Engineering magazine. When supplementary fuel is added to the turbine exhaust gas before it enters the boiler, or between boiler surfaces, to increase steam production, one has to perform an energy balance around the burner, Fig. 5, to evaluate accurately the gas temperature increase that can be obtained. V. Ganapathy, cited above, has a computer program he developed to speed this calculation. GAS-TURBINE CYCLE EFFICIENCY ANALYSIS AND OUTPUT DETERMINATION A gas turbine consisting of a compressor, combustor, and an expander has air entering at 60 F (15.6 C) and 14.0 lb / in2 (abs) (96.5 kPa). Inlet air is compressed 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 1.14 POWER GENERATION to 56 lb / in2 (abs) (385.8 kPa); the isentropic efﬁciency of the compressor is 82 percent. Sufﬁcient fuel is injected to give the mixture of fuel vapor and air a heating value of 200 Btu / lb (466 kJ / kg). Assume complete combustion of the fuel. The expander reduces the ﬂow pressure to 14.9 lb / in2 (abs), with an engine efﬁciency of 85 percent. Assuming that the combustion products have the same thermody- namic properties as air, cp 0.24, and is constant. The isentropic exponent may be taken as 1.4. (a) Find the temperature after compression, after combustion, and at the exhaust. (b) Determine the Btu / lb (kJ / kg) of air supplied, the work delivered by the expander, the net work produced by the gas turbine, and its thermal efﬁ- ciency. Calculation Procedure: 1. Plot the ideal and actual cycles Draw the ideal cycle as 1-2-3-4-1, Figs. 6 and 7. Actual compression takes place along 1-2 . Actual heat added lies along 2 -3 . The ideal expansion process path is 3 -4 . Ideal work cp (ideal temperature difference). Actual work cp (actual temperature difference). 2. Find the temperature after compression Use the relation (T2 / T1) (P2 / P1)(k 1) / k, where T1 entering air temperature, R; T2 temperature after adiabatic compression, R; P1 entering air pressure, in units given above; P2 pressure after compression, in units given above; k isentropic exponent 1.4. With an entering air temperature, T1 of 60 F (15.6 C), 520 R, and using the data given, T2 520[(56 / 14)](1.4 1) / 1.4 or 60 460 772.7 R, or 772.7 520 252.7 F (122.6 C). (a) Here we have isentropic compression in the compressor with an efﬁ- ciency of 85 percent. Using the equation, Efﬁciency, isentropic (cp )(T2 T1) / (cp )(T2 T1), and solve for T2 , the temperature after isentropic compression. Solv- ing, T2 0.82 0.24(772.7 520) / 0.24(T2 520) 828.4 R, or 368 F. This is the temperature after compression. 3. Determine the temperature after combustion To ﬁnd the temperature after combustion, use the relation Heating value of fuel Q cp (T3 T2 ), where T3 temperature after combustion, R. Substituting, 200 0.24(T3 828). Solving, T3 1661.3 R; 1201.3 F (649.6 C). 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 . 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 1.15 MODERN POWER-PLANT CYCLES AND EQUIPMENT FIGURE 7 Ideal gas-turbine cycle T-S diagram with the same processes as in Fig. 6; complete- cycle gas turbine shown below the T-S diagram. 4. Find the temperature at the exhaust of the gas turbine Using an approach similar to that above, determine T4 from (T4 / T3 ) [(P4 / P3 )]k 1 / k. Substituting and solving for T4 1661[(14.9 / 56)](1.4 1) / 1.4 1137.9 R, or 677.8 F (358.8 C). Now use the equation for gas-turbine efﬁciency, namely, Turbine efﬁciency cp (T3 T4 )/ cp (T3 T4 ) 0.85, and solve for T4 , the temperature after expan- sion, at the exhaust. Substituting as earlier, T4 1218.2 R, 758.2 F (403.4 C). This is the temperature after expansion, i.e., at the exhaust of the gas turbine. 5. Determine the work of compression, expander work, and thermal efﬁciency (b) The work of compression cp(T2 T1) 0.24(828 520) 74.16 Btu (78.23 J). The work delivered by the expander cp(T2 T1) 0.24 (1661 1218) 106.32 Btu (112.16 J). The net work 106.3 74.2 32.1 Btu (33.86 J). Then, the thermal efﬁciency net work / heat supplied 32.1 / 200 0.1605, 16.6 percent thermal efﬁciency. Related Calculations. With the widespread use today of gas turbines in a va- riety of cycles in industrial and central-station plants, it is important that an engineer be able to analyze this important prime mover. Because gas turbines can be quickly installed and easily hooked to heat-recovery steam generators (HRSG), they are more popular than ever before in history. 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 1.16 POWER GENERATION Further, as aircraft engines become larger—such as those for the Boeing 777 and the Airbus 340—the power output of aeroderivative machines increases at little cost to the power industry. The result is further application of gas turbines for topping, expansion, cogeneration and a variety of other key services throughout the world of power generation and energy conservation. With further reﬁnement in gas-turbine cycles, speciﬁc fuel consumption, Fig. 8, declines. Thus, the complete cycle gas turbine has the lowest speciﬁc fuel con- sumption, with the regenerative cycle a close second in the 6-to-1 compression- ratio range. Two recent developments in gas-turbine plants promise much for the future. The ﬁrst 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 electric generating system available today. Further, its capital costs are signiﬁcantly lower than competing nuclear, fossil-ﬁred steam, and renewable-energy stations. Other advantages 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. 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). 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 1.17 MODERN POWER-PLANT CYCLES AND EQUIPMENT Stack Inlet air Generator Gas turbine H-p I-p L-p L-p I-p H-p HRSG Synchronous Steam turbine clutch Fuel 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). 68.5 ft (20.9 m) (51.9 m) 170.6 ft 29.5 ft 95 ft 152 ft (8.99 m) (46.33 m) (28.95 m) FIGURE 10 Steam turbine, electric generator, and gas turbine ﬁt into one compact building when all three machines are arranged on a single shaft. Net result: Reduced site footprint and civil- engineering work (Power). Having the gas turbine, steam turbine, and generator all on one shaft simpliﬁes plant design and operation, and may lower ﬁrst costs. When used for large reheat cycles, as shown here, separate high-pressure (h-p), intermediate-pressure (i-p), and low-pressure (l-p) turbine elements are all on the same shaft as the gas turbine and generator. Modern high-technology combined-cycle single-shaft units deliver a simple-cycle net efﬁciency of 38.5 percent for a combine-cycle net efﬁciency of 58 percent on a lower heating value (LHV) basis. 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 1.18 POWER GENERATION The second important gas-turbine development worth noting is the dual-fueled turbine located at the intersection of both gas and oil pipelines. Being able to use either fuel gives the gas turbine greater opportunity to increase its economy by switching to the lowest-cost fuel whenever necessary. Further developments along these lines is expected in the future. The data in the last three paragraphs and the two illustrations are from Power magazine. DETERMINING BEST-RELATIVE-VALUE OF INDUSTRIAL GAS TURBINES USING A LIFE-CYCLE COST MODEL An industrial application requires a 21-MW continuous electrical output year-round. Five different gas turbines are under consideration. Determine which of these ﬁve turbines 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 initial cost, $ / 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 capital investment for each turbine will vary, depending on the amount invested and the way in which the loan must be repaid and will be provided by the accounting department of the ﬁrm considering gas-turbine purchase. Equipment Attributes for Typical Candidates* Gas-turbine candidates Parameter A B C D E Initial cost, $ / kW 205 320 275 320 200 Thermal efﬁciency, % 32.5 35.5 34.0 36.5 30.0 Loan period, yr 20 20 20 20 20 Availability 0.96 0.94 0.95 0.94 0.96 Fuel cost, $ / million Btu 4 4 4 4 4 Interes, % 6.5 8.0 7.0 8.5 7.5 Generator efﬁciency, % 98.0 98.5 98.5 98.0 98.5 Maintenance cost, $ / kWh 0.004 0.005 0.005 0.005 0.004 *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: (1) the annual investment cost, Cp ; (2) annual fuel cost, Cƒ; (3) annual maintenance cost, Cm. Summing these three annual costs, all of which are expressed in mils / kWh, gives CT , the life-cycle cost model. The equations for each of the three components are given below, along with the life-cycle working model, CT : 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 1.19 MODERN POWER-PLANT CYCLES AND EQUIPMENT The life-cycle cost model (CT ) consists of annual investment cost (Cp ) annual fuel cost (Cƒ) annual maintenance cost (Cm ). Equations for these values are: l {i / [1 (1 i ) n ]} Cp (A )(kW)(8760)(G ) where l initial capital cost of equipment, dollars i interest rate n number of payment periods A availability (expressed as decimal) kW kilowatts of electricity produced 8760 total hours in year G efﬁciency of electric generator Cƒ E(293) where E thermal efﬁciency of gas turbine 293 conversion of Btu to kWh Cm M / kW where M maintenance cost, dollars per operating (ﬁred) hour. Thus, the life-cycle working model can be expressed as l {i / [1 (1 i ) n ]} CT F / E(293) M / kW (A )(kW)(8760)(G ) where F fuel cost, dollars per million Btu (higher heating value) To evaluate the comparative capital cost of a gas-turbine electrical generating package the above model uses the capital-recovery factor technique. This approach spreads the initial investment and interest costs for the repayment period into an equal annual expense using the time value of money. The approach also allows for the comparison of other periodic expenses, like fuel and maintenance costs. 3. Perform the computation for each of the gas turbines being considered Using the compiled data shown above, compute the values for Cp, Cƒ, and Cm, and sum the results. List for each of the units as shown below. Results from Cost Model Unit Mils / kWh produced A 48.3 B 47.5 C 48.3 D 46.6 E 51.9 4. Analyze the ﬁndings of the life-cycle model Note that the initial investment cost for the turbines being considered ranges be- tween $200 and $320 / kW. On a $ / kW basis, only unit E at the $200 level, would be considered. However, the life-cycle cost model, above, shows the cost per kWh 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.