MEM 310 Design Project Assignment

Prepared by

Bradley R. Schaffer Drexel University

Philadelphia, PA 19104

Submitted to: Dr. William J. Danley of MEM 310 - Thermodynamic Analysis I

on May 28, 2004

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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%.

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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�..��������������..33

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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������...��...��..19

Table 6: Transfer Function Results��������������������...20

Table 7: Tabulated Additional Feedwater Heater Calculations���.������...21

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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

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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 oC, a

maximum reheat temperature of 460 oC, a maximum feedwater heater exit temperature of

210 oC, and a maximum pressure of 20 Mpa. The problem also states a minimum

condenser temperature of 55 oC (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.

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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 oC 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 oC and an increased condenser temperature of 60.5oC

(See Table 2).

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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 oC and the condenser temperature kept at 55 oC. However, this

wasn�t possible because the transfer function specified a minimum mid-temperature of

165 oC (See Table 3). Therefore, the condenser temperature had to be increased to

account for the final increase in quality.

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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

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decreased because the average low temperature increased. However, the quality

increased due to the fact that as the condenser temperature rises, the decrease in sfg is

greater than the increase in sf. 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

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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.

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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 oC. 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

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).

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References

1. Cengel, Yunus A., and Michael A. Boles. Thermodynamics: An Engineering

Approach. New York: Jack P. Holman, 2002.

2. Kutz, Myer. Mechanical Engineers' Handbook (2nd Edition). New York: 1998

3. �Combined Cycle Plant Ratings,� [Internet]. Siemens. (2004 [cited 20 May 2004]);

available from <http://www.powergeneration.siemens.com>

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Table 1 Design Specifications

Design Specifications Maximum feedwater heater temperature 210 oC

Maximum pressure entering the High pressure turbine 20 MPa Minimum condenser temperature 55 oC

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 oC

Maximum steam temperature exiting reheater 460 oC

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Table 2 Optimized Design Specifications

Optimized Specifications Maximum feedwater heater temperature 165 oC

Maximum pressure entering the High pressure turbine 20 MPa Minimum condenser temperature 60.5 oC

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 oC

Maximum steam temperature exiting reheater 460 oC

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Table 3 Transfer Function Specifications

Transfer Function Specifications Low 0-100 oC Mid 165-260 oC

Reheat 440-500 oC High 575-625 oC

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Table 4 Rankine Cycle Component Mass Flow Rates

Mass Flow Rate (Kg/hr) Condenser 1,194,480

Low Pressure Pump 1,194,480Open Feedwater Heater

Steam Inlet 254,880

Open Feedwater Heater Feedwater Inlet 1,194,480

High Pressure Pump 1,449,000Boiler 1,449,000

High Pressure Turbine 1,449,000Boiler (Reheat) 1,194,480

Low Pressure Turbine 1,194,480

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Table 5 Rankine Cycle State Temperatures & Pressures

State Pressure & Temperature State Pressure (Mpa) Temperature (oC)

1 .02041 60.5 2 .70029 60.92 3 .70029 165 4 20 177.8 5 20 600 6 .70029 165 7 .70029 460 8 .02041 60.5

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Table 6 Transfer Function Results

State qin Pump win Turbine wout 4 to 5 2816.45 KJ/Kg HP 24.03 KJ/Kg HP 762.56 KJ/Kg6 to 7 620.64 KJ/Kg LP 0.7922 KJ/Kg LP 762.53 KJ/Kg

qin 3327.963qout 1961.626nth 0.410563wnet 1366.337y 0.175819x8 0.9853

State P (kPa) T (C) hf hfg sf sfg vf x hs ha sa 1 20.4068 60.5 253.22 0.837423 0.001018 0 253.22 0.8374232 700.29 253.91 254.0122 0.8374233 700.29 165 0.001108 0 697.28 4 20000 718.6669 721.3096 5 20000 600 3537.755 6.5047876 700.29 2680.95 2775.199 6.5047877 700.29 460 3395.836 7.7979618 20.4068 60.5 253.22 2357.272 0.837423 7.064151 0.985 2575.914 2633.309 7.797961

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Table 7 Tabulated Additional Feedwater Heater Calculations

State P (kPa) T (C) hf hfg sf sfg vf x hs ha sa 1 19.94 60 251.13 0.8312 0.001017 0 251.13 0.83122 158.744 251.2712 251.2886 3 158.744 113 474.01 0.001054 0 474.01 4 20000 494.9286 497.5143 5 20000 697.34 6 700.5 165 0.001108 0 697.34 7 20000 718.7238 719.1603 8 20000 699.2592 9 20000 600 3537.6 6.5048

10 700.5 2674.5 2769.441 6.504811 700.5 460 3396.5 7.803412 158.744 251.8 2976.12 3005.547 7.803413 19.94 60 251.13 2358.5 0.8312 7.0784 0.985 2583.2 2574.3 7.8034

y 0.087954z 0.073751

Qin 3410.247Qout 1947.5 nth 0.428927x 0.984997

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Appendix A Steam Cycle Development

(Kutz, Fig 58.1, pg. 1766)

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Appendix B Rankine Cycle Flow Diagram

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Appendix C Additional Feedwater Heater Flow Diagram

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Appendix D Combined Cycle Flow Diagram

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Appendix E

Thermal Efficiency Increases vs. Year

(Kutz, Fig 58.2, pg. 1767)

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Appendix F Transfer Function Relations

Low T to vf

Low T to P

Low T to sfg

Low T to sf

Low T to hf

Low T to hfg

T1

hfg1

hf1

sf1

sfg1

vf1

P1 P8

ha1 hf8

T8

28

Mid T to v f

Mid T to P

Mid P & sgto hg

Mid T to hf

T3

P7

hf3

P6

vf3

P3

P2

hg6

Mid P & Tto sg

29

High T & Pto sg

ReheatT & Pto hg

High T & Pto hg

T7 & P7

sg7

h5

hg7

ReheatT & Pto sg

sg8

T5 & P5

sg5 sg6

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Appendix G Detailed Hand Calculations

State 1: T1 = 60.5 oC h1 = 253.23 kJ/kg v1 = 0.001018 m3/kg P1 = 20.406 kPa s1=0.8376 kJ/kg K State 2: T2 = 60.92oC P2 = 0.7005 MPa h2 = h1 + v1 (P2 � P1) = 254.01 kJ/kg

s2=s1

State 3: P2 = P3 and is saturated liquid h3 = 697.28 kJ/kg v3 = 0.001108 m3/kg s3=1.9925 kJ/kg K T3 = 165 oC State 4: P4 = 20.0 MPa h4 = h3 + v3 (P4 � P3) = 718.65 kJ/kg s4=s3 T4= 177.8 oC

State 5: P4 = P5 T5 = 600oC h5 = 3537.6 kJ/kg s5 = 6.5048 kJ/kg K State 6: P2 = P3 = P6 = P7 = 0.7005 MPa s5 = s6 h6 = 2680.95 kJ/kg T6= 165oC State 7: T7 = 460 oC h7 = 3395.7 kJ/kg s7 = s8 = 7.8167 kJ/kg K

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State 8: P1 = P8 = 20.406 kPa hf = 253.23 kJ/kg hfg = 2357.4 kJ/kg sf = 0.8375 kJ/kg K sfg = 7.0661 kJ/kg K

8 f

fg

s - sx 0.985 98.5%s

= = =

h8 = hf + x hfg = 253.23 + 0.985 * 2357.4 h8 = 2575.9 kJ/kg T8=60.5 oC Adiabatic Efficiency Corrections for Pumps and Turbines

oai

osi

h-hh-h==

a

sP w

wη For Pumps/Compressors

osi

oai

h-hh-h==

s

aT w

wη For Turbines

i = inlet; o = outlet; s = isentropic; a = actual Low pressure pump nP = 87 % = 0.87 .87 = (h1 � h2s)/(h1 � h2a) h2a = 254.01 kJ/kg High pressure pump nP = 89 % = 0.89 .89 = (h3 � h4s)/(h3 � h4a) h4a =721.31 kJ/kg

32

High pressure turbine nT = 89 % = 0.89 .89 = (h5 � h6a)/(h5 � h6s) h6a = 2775.22 kJ/kg Low pressure turbine nP = 93 % = 0.93 .93 = (h7 � h8a)/(h7 � h8s) h8a = 2633.31 kJ/kg h3 = (1-y) h2a + y h6a y = 0.1759 qin = (h5 � h4a) + (1-y) (h7 � h6a) = 3328.0 kJ/kg qout = (1�y) (h8a � h1) = 1961.5 kJ/kg

outTh

in

q1 0.4106q

η = − = or 41.06%

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Appendix H Temperature � Entropy Diagram

Rankine Cycle

s (kJ/kg K)

T (K

)