MEM 310 Design Project Assignment

Transcription

1 MEM 310 Design Project Assignment Prepared by Bradley R. Schaffer Drexel University Philadelphia, PA Submitted to: Dr. William J. Danley of MEM Thermodynamic Analysis I on May 28, 2004

2 Abstract With today s soaring energy demands and continually increasing fuel costs, it is detrimental to a company to overlook opportunities that would increase their power plant s efficiency. Companies that have high efficiencies in their plants are given an upper hand in the market. Companies that don t utilize the latest advancements in power generation technology are jeopardizing their economic stability. We ve studied and simulated your system using our proprietary software that utilizes the renowned Danley transfer functions and have concluded that the highest efficiency obtainable is 41.06%. This was the optimal efficiency value that met all of your company s specifications. In addition to testing the system that you specified, we also did further research and analysis on improving this efficiency. These improvement options range from simple additions to your current cycle to scaling up projects to meet future demands greater than 550 megawatts. The end result of these improvements has the potential to raise the overall efficiency of your plant above 50%. 2

3 Table of Contents Abstract 2 System Problem Statement..5 Solution 7 Discussion and Conclusion..9 Recommendations for Future Analysis..12 References..14 Appendix A: Steam Cycle Development..22 Appendix B: Rankin Cycle Flow Diagram...23 Appendix C: Additional Feedwater Heater Flow Diagram..24 Appendix D: Combined Cycle Flow Diagram..25 Appendix E: Thermal Efficiency Increases vs. Year 26 Appendix F: Transfer Function Links and Relations 27 Appendix G: Detailed Hand Calculations.30 Appendix H: Temperature Entropy Diagram

4 Table of Figures Table 1: Design Specifications...15 Table 2: Optimized Design Specifications...16 Table 3: Transfer Function Specifications 17 Table 4: Rankine Cycle Component Mass Flow Rates 18 Table 5: Rankine Cycle State Temperatures & Pressures Table 6: Transfer Function Results...20 Table 7: Tabulated Additional Feedwater Heater Calculations

5 System Problem Statement The objective of this project was to produce a 550 megawatt vapor power plant that meets certain criteria yet maintains a high efficiency. To begin this problem, a complete analysis of the Rankine cycle must be completed. The simplest form of this cycle consists of an isentropic pump, an isobaric boiler, an isentropic turbine, and an isobaric condenser. The cycle analysis starts with the condenser. The condenser is a heat exchanger that acquires exhaust steam from the turbine and then removes heat from the exhaust until it becomes a saturated liquid. This saturated liquid is then sent to the pump. The pump then pressurizes the saturated liquid up to the turbine inlet pressure. After the liquid leaves the pump, it is routed through a boiler which adds heat to the liquid, converting it into a superheated vapor. At the final stage, the superheated vapor is sent through the turbine which internally expands the steam and in return, the output shaft of the turbine rotates. This mechanical energy is then used to turn the input shaft of a generator, thereby producing electricity. This is the simplest form of the Rankine cycle. This cycle will meet the output requirement. However, it doesn t meet the desired efficiency. The first attempt at increasing efficiency was seen in the early 1920 s by implementing regeneration by the use of feedwater heaters (See Appendix A). Feedwater heaters are heat exchanges that use superheated steam bled from the turbine to heat the feedwater before it enters the boiler. This increases the average temperature of heat addition which increases the overall efficiency of the cycle (Cegel, 522). Feedwater heaters come in two types: open and closed. The open feedwater heater mixes the superheated steam directly with the 5

6 feedwater. The advantage of this type is its simplicity and its high efficiency of heat transfer. Conversely, the closed feedwater heater does not mix the two streams. The advantage of this type is the superheated steam and the feedwater can be at two different pressures. The disadvantage, however, is the complexity of closed feedwater heaters creates a comparative cost disadvantage. The second attempt at increasing efficiency was introduced in the late 1920 s by using a reheat cycle (See Appendix A). The reheat cycle sends the exhaust from the high pressure turbine back through the boiler before it enters the low pressure turbine. This allows for greater high-pressure turbine inlet pressures without encountering moisture problems. Higher boiler pressures mean higher feedwater temperatures entering the boiler. This leads to a higher average temperature of heat addition which, in turn, produces a higher efficiency (Cengel, 523). The given specifications for the cycle dictate a maximum temperature of 600 o C, a maximum reheat temperature of 460 o C, a maximum feedwater heater exit temperature of 210 o C, and a maximum pressure of 20 Mpa. The problem also states a minimum condenser temperature of 55 o C (See Table 1). Using these values and accounting for the turbine and pump inefficiencies, the absolute overall maximum efficiency can be calculated. However, the major problem lies in the quality of the low pressure turbine exhaust. It is specified to be a minimum of 98.5%. Using the given specifications yields a quality less than this. Variables must be adjusted to raise this quality yet maintain a high efficiency. 6

7 Solution Once the transfer functions were properly connected, any changes made to the variables instantly showed changes in both efficiency and the quality of the low pressure turbine exhaust (See Appendix F). Knowing that the minimum quality was 98.5%, variables could be changed one at a time until the desired quality was obtained. The first variable that was experimented with was the maximum temperature. When the maximum temperature was decreased, the efficiency dropped substantially but no effect on quality was seen. The next variable that was modified was the condenser temperature. The condenser temperature had to be increased to 94 o C in order to obtain acceptable quality levels. This reduced efficiency by 5.01%. After the condenser temperature was tested, changes in maximum pressure were explored. This produced the same results that were seen when the maximum temperature was decreased. Efficiency was decreased but no effect on quality was seen. The maximum reheat temperature was the next variable that was modified. As this temperature increased so did the quality of the steam. The final variable that was manipulated was the temperature of the open feed water heater exit. When temperature was decreased, quality increased sharply yet efficiency only fell slightly. After experimenting with modifying individual variables, combinations of variables were manipulated. The only combination that had the desired outcome of higher quality was the minimum temperature and the open feedwater heater exit temperature. The best combination that met all specifications was a lowered open feedwater heater temperature of 165 o C and an increased condenser temperature of 60.5 o C (See Table 2). 7

8 The combination of lowered feedwater heater temperature and increased condenser temperature produced a quality of 98.53%, and an efficiency of 41.06%. This efficiency could have been increased further if the open feedwater heater temperature had been lowered below 165 o C and the condenser temperature kept at 55 o C. However, this wasn t possible because the transfer function specified a minimum mid-temperature of 165 o C (See Table 3). Therefore, the condenser temperature had to be increased to account for the final increase in quality. 8

9 Discussion and Conclusion Disregarding low pressure turbine exhaust quality, the overall maximum efficiency of the cycle was 42.97%. When the quality requirements are taken into account, the efficiency only dropped by 1.91%. This was the lowest possible drop in efficiency and was accomplished through temperature adjustments in the feedwater heater and the condenser. Upon analysis of the variables and their impact on the cycle, the choice to modify the temperatures of the feedwater heater and the condenser becomes clear. The following analysis demonstrates how each variable impacts the cycle: The problem with the cycle using the variables as given was that it didn t meet the minimum steam quality upon exiting the low pressure turbine. The factor that affects this quality was the entropy at state 8 (See Appendix B). For a given condenser pressure, the quality increases proportionally to the increase in entropy. The first variable that was modified was the maximum temperature of the cycle. Decreasing this value likewise causes a decrease in efficiency but does not affect quality. The decrease in efficiency was due to the lowering of the average temperature at which heat was transferred to the steam in the boiler. However, the maximum temperature has no effect on the quality of the steam because it doesn t affect the entropy of the steam entering the low pressure turbine. The reheat cycle heats the steam that enters the low pressure turbine to a specified temperature. This negates all changes in temperatures in previous components. The second variable that was modified was the condenser temperature. This had a substantial effect on efficiency and also had an effect on quality. The efficiency 9

10 decreased because the average low temperature increased. However, the quality increased due to the fact that as the condenser temperature rises, the decrease in s fg is greater than the increase in s f. This produces an overall increase in the denominator that is greater than the decrease in the numerator of the quality equation, thereby producing a higher quality. The third variable that was modified was the reheat temperature. As this temperature decreased, both the efficiency and the quality also decreased. The reheat cycle allows higher boiler pressures without causing moisture problems in the low pressure turbine. The reheat cycle reheats the high pressure turbine exhaust before it enters the low pressure turbine. This increase in temperature increased the entropy of the superheated steam. The efficiency also increases due to the fact that as the maximum pressure increases, the temperature of liquid entering the boiler increases which means a higher average temperature of heat addition. The final variable that was modified was the open feedwater heater exit temperature. As this temperature decreased, efficiency also dropped, but quality went up. The efficiency declined due to the fact that as this temperature decreases, the feedwater entering the boiler decreases as well which produces a lower average temperature of heat addition in the boiler. However, the quality of the steam rises because as the temperature of the feedwater heater decreases, the pressure of the steam entering the reheat cycle decreases. When steam is heated to a specified temperature, the entropy of the superheated vapor after the reheat process is inversely proportional to its pressure. In conclusion, there are only three variables that affect the quality of the low pressure turbine exhaust. The first variable-- reheat temperature-- affects quality and 10

11 efficiency in an adverse way. The only two variables that will increase quality are condenser temperature and open feedwater heater temperature. Although modifying these two variables lowered efficiency, they were modified in such a way that limited this decrease. This system s efficiency was only reduced by 1.91%. This decrease in efficiency can be recouped along with a gain in overall efficiency through the use of additional components in the cycle, namely multiple feedwater heaters. 11

12 Recommendations for Future Analysis One addition that could be added to the original cycle is an additional feedwater heater (See Appendix C). This type of addition could be done during a routine maintenance shut-down to minimize downtime. The addition of just a single feedwater heater could boost efficiency as high as 42.89% (See Table 4). This is gain of 1.83% over the original cycle. The cycle that was chosen for this additional analysis was based on the original system with the addition of a closed feedwater heater. The open feedwater heater was designed to heat the feedwater to a mid temperature between the condenser and the closed feedwater heater. The closed feedwater heater was designed to heat the feedwater to the original systems feedwater heater temperature of 165 o C. The first feedwater heater was chosen to be an open type for its secondary purpose as a feedwater deaerater. This prevents any air that may have leaked into the lines through the condenser from entering the boiler which would otherwise cause internal corrosion. The second feedwater heater was chosen to be a closed type. The advantage of a closed feedwater heater is the ability to have the steam that heats the feedwater at a different temperature than the feedwater itself. This means that the third pump only has to pressurize the saturated liquid produced by the steam, which means a smaller pump will be suitable for this task. This is advantageous for two reasons: the pump can be smaller which will save capital, and it will also require less input work. Using the same values calculated in the first system, the increase in efficiency was 1.83%. This idea of increasing the number of feedwater heaters will continue to increase the efficiency. However, with each additional feedwater heater, the change in efficiency 12

13 continually decreases. A cost-benefit analysis must be done to decide how many feedwater heaters will optimize the cycle. Some of today s larger power generation plants use up to eight feedwater heaters (Cengel, 531). A second improvement to the cycle would be a larger scaling-up operation. If the demand exceeds the wattage that the original cycle was designed to supply, a second generation system may need to be implemented to increase the overall net output of the power plant. A combined cycle, which is a combination of the Rankine cycle and the Brayton cycle is a valuable cycle to consider (See Appendix D). This cycle can produce efficiencies in the 50 percent range (See Appendix E). This is a greater efficiency than either cycle could obtain individually (Siemens). 13

14 References 1. Cengel, Yunus A., and Michael A. Boles. Thermodynamics: An Engineering Approach. New York: Jack P. Holman, Kutz, Myer. Mechanical Engineers' Handbook (2nd Edition). New York: Combined Cycle Plant Ratings, [Internet]. Siemens. (2004 [cited 20 May 2004]); available from < 14

15 Table 1 Design Specifications Design Specifications Maximum feedwater heater temperature 210 o C Maximum pressure entering the High pressure turbine 20 MPa Minimum condenser temperature 55 o C High pressure turbine adiabatic efficiency 89 % Low pressure turbine adiabatic efficiency 93 % Low pressure pump adiabatic efficiency 87 % High pressure pump adiabatic efficiency 89 % Minimum steam quality entering the condenser 98.5 % Maximum steam temperature 600 o C Maximum steam temperature exiting reheater 460 o C 15

16 Table 2 Optimized Design Specifications Optimized Specifications Maximum feedwater heater temperature 165 o C Maximum pressure entering the High pressure turbine 20 MPa Minimum condenser temperature 60.5 o C High pressure turbine adiabatic efficiency 89 % Low pressure turbine adiabatic efficiency 93 % Low pressure pump adiabatic efficiency 87 % High pressure pump adiabatic efficiency 89 % Minimum steam quality entering the condenser 98.5 % Maximum steam temperature 600 o C Maximum steam temperature exiting reheater 460 o C 16

17 Table 3 Transfer Function Specifications Transfer Function Specifications Low Mid Reheat High o C o C o C o C 17

18 Table 4 Rankine Cycle Component Mass Flow Rates Mass Flow Rate (Kg/hr) Condenser 1,194,480 Low Pressure Pump 1,194,480 Open Feedwater Heater Steam Inlet 254,880 Open Feedwater Heater Feedwater Inlet 1,194,480 High Pressure Pump 1,449,000 Boiler 1,449,000 High Pressure Turbine 1,449,000 Boiler (Reheat) 1,194,480 Low Pressure Turbine 1,194,480 18

19 Table 5 Rankine Cycle State Temperatures & Pressures State Pressure & Temperature State Pressure (Mpa) Temperature ( o C)

20 Table 6 Transfer Function Results State P (kpa) T (C) h f h fg s f s fg v f x h s h a s a State q in Pump w in Turbine w out 4 to KJ/Kg HP KJ/Kg HP KJ/Kg 6 to KJ/Kg LP KJ/Kg LP KJ/Kg q in q out nth w net y x

21 Table 7 Tabulated Additional Feedwater Heater Calculations State P (kpa) T (C) h f h fg s f s fg v f x h s h a s a y z Qin Qout nth x

22 Appendix A Steam Cycle Development (Kutz, Fig 58.1, pg. 1766) 22

23 Appendix B Rankine Cycle Flow Diagram 23

24 Appendix C Additional Feedwater Heater Flow Diagram 24

25 Appendix D Combined Cycle Flow Diagram 25

26 Appendix E Thermal Efficiency Increases vs. Year (Kutz, Fig 58.2, pg. 1767) 26

27 Appendix F Transfer Function Relations Low T to h fg h fg1 Low T to h f h f1 h a1 h f8 Low T to s f s f1 T 1 Low T to s fg s fg1 Low T to v f v f1 Low T to P P 1 P 8 T 8 27

28 Mid T to h f h f3 Mid T to v f v f3 T 3 Mid T to P Mid P & T to s g P 3 P2 P 6 P 7 Mid P & s g to h g h g6 28

29 High T & P to h g h 5 T 5 & P 5 High T & P to s g s g5 s g6 Reheat T & P to s g s g7 s g8 T 7 & P 7 Reheat T & P to h g h g7 29

30 Appendix G Detailed Hand Calculations State 1: T 1 = 60.5 o C h 1 = kj/kg v 1 = m 3 /kg P 1 = kpa s 1 = kj/kg K State 2: T 2 = o C P 2 = MPa h 2 = h 1 + v 1 (P 2 P 1 ) = kj/kg s 2 =s 1 State 3: P 2 = P 3 and is saturated liquid h 3 = kj/kg v 3 = m 3 /kg s 3 = kj/kg K T 3 = 165 o C State 4: P 4 = 20.0 MPa h 4 = h 3 + v 3 (P 4 P 3 ) = kj/kg s 4 =s 3 T 4 = o C State 5: P 4 = P 5 T 5 = 600 o C h 5 = kj/kg s 5 = kj/kg K State 6: P 2 = P 3 = P 6 = P 7 = MPa s 5 = s 6 h 6 = kj/kg T 6 = 165 o C State 7: T 7 = 460 o C h 7 = kj/kg s 7 = s 8 = kj/kg K 30

31 State 8: P 1 = P 8 = kpa h f = kj/kg s f = kj/kg K h fg = kj/kg s fg = kj/kg K s - s 8 f x = = = 98.5% sfg h 8 = h f + x h fg = * h 8 = kj/kg T 8 =60.5 o C Adiabatic Efficiency Corrections for Pumps and Turbines w w h h s i os η P = = For Pumps/Compressors a w w i h h i - h - h - h - h a i oa η T = = For Turbines s oa os i = inlet; o = outlet; s = isentropic; a = actual Low pressure pump n P = 87 % = = (h 1 h 2s )/(h 1 h 2a ) h 2a = kj/kg High pressure pump n P = 89 % = = (h 3 h 4s )/(h 3 h 4a ) h 4a = kj/kg 31

32 High pressure turbine n T = 89 % = = (h 5 h 6a )/(h 5 h 6s ) h 6a = kj/kg Low pressure turbine n P = 93 % = = (h 7 h 8a )/(h 7 h 8s ) h 8a = kj/kg h 3 = (1-y) h 2a + y h 6a y = q in = (h 5 h 4a ) + (1-y) (h 7 h 6a ) = kj/kg q out = (1 y) (h 8a h 1 ) = kj/kg q out η Th = 1 = or 41.06% q in 32

33 Appendix H Temperature Entropy Diagram Rankine Cycle T (K) s (kj/kg K) 33