Application of Entropy Balance in Evaluating and Quantifying Losses Sample Turbine Cycle Sources Examined – Boiler, Turbine,

FW Heaters, Piping, BFP Methodology Applicable to Analyze &

Evaluate Losses in Any Power Cycle

Performance Calculations Based on First Law of Thermodynamics (FLT) For Given Mass Flows & Heat Input,

Proper Distribution to Satisfy FLT for Conservation of Mass & Energy FLT - Enthalpy or Quantity of Energy SLT – Entropy or Quality of Energy

FLT – “You Cannot Get Something for Nothing” SLT – “You Cannot Even Get

Everything You Pay For” SLT - “Entropy Ain’t What it Used to

Be” FLT to be Satisfied Before Using SLT

SLT Used to Determine Effectiveness of Energy Utilization For Natural Process, Performance

Loss Results in Increase in Entropy Performance Tool Used to Develop

Sample Turbine Cycle in Figure 1 Zero Imbalances in Mass & Energy

1,847,840 W 544.3 P1519.02 H 1000.0 F

2,115,387 W 2414.7 P1460.39 H 1000.0 F 1,727,364 W 1,727,364 W

976 W 1348.11 H 1348.11 H1460.39 H 3,895 W

1460.39 H

33,144 W1317.94 H 1436.01 H 69.4 P

251.8 P 3,070 W 31.3 P 12.2 P5,114 W 1348.11 H 3.9 P

1317.94 H 604.8 P129.9 P

70,381 W1348.11 H

10,174 W1317.94 H 90,123 W

1080.55 H1,847,840 W

1317.94 H

ELEP = 974.72 HUEEP = 990.48 H 5,000 W

Cond. Press. = 1.00 in.HgA 1343.23 H

70,381 W1348.11 H 1,406,539 W

78.5 F298,308 W Δh = 0.00 47.08 h

214,243 W 84,065 W 332.17 h 81,650 W 79,088 W 74,964 W 90,123 W1317.94 H 1421.26 H 1286.45 H 1217.77 H 1149.73 H 1080.55 H 4,160 W

1343.23 H586.6 P 236.7 P 65.3 P 29.4 P 11.4 P 3.7 P0.0 F TD 0.0 F TD 5.0 F TD 5.0 F TD 5.0 F TD 5.0 F TD

2,115,387 W 1,736,524 W 1,736,524 W 1,406,539 W 1,406,539 W483.8 F 396.2 F 122.1 P 293.2 F 244.1 F 194.6 F 145.8 F 144.9 F 78.5 F469.24 h 374.47 h 342.6 F 263.01 h 213.00 h 163.05 h 114.23 h 113.37 h 47.08 h

483.8 F 396.2 F 313.94 h 298.2 F 249.1 F 199.6 F 149.9 F10.0 F DC 10.0 F DC 10.0 F DC 10.0 F DC 10.0 F DC

214,243 W 298,308 W 81,650 W 160,738 W 235,701 W 329,985 W406.2 F 359.8 F 2,115,387 W 254.1 F 204.6 F 155.8 F 149.9 F382.14 h 332.17 h 3018.4 P 222.86 h 172.71 h 123.77 h 329,985 W 117.89 h

349.8 F 149.9 F326.13 h Δh = 12.19 117.89 h Δh = 0.00

1805 KW ELECT. LOSSES

GENERATOR OUTPUT175,703 KW30 PSIG H2

0.85 PF

WLpExh =1,401,539

853 KW MECH. LOSSES2146 KW ELECT. LOSSES

GENERATOR OUTPUT160,238 KW30 PSIG H2

0.85 PF778 KW MECH. LOSSES

STEAMSEAL

REGULATOR

RHTR

2

3

1

5 6

4

2 5 6

HPT IPT LPT

HTR. 1 HTR. 2

BFP

HTR. 3 HTR. 4 HTR. 5 HTR. 6 HTR. 7

HDP

CP

CONDENSER

IV

Steady-State Conditions All Heaters in Normal Operation Zero Blowdown or Makeup No Radiation or Cycle Isolation Losses TG Performance from Published

Procedures Fixed Throttle Steam Conditions

Reheat Steam Conditions Fixed Reheater Pressure Drop 10% IV Pressure Drop 2% LPT Exhaust Pressure 1.0 in.HgA TD’s, DC’s for Heaters Fixed Extraction Piping Pressure Drops Fixed

Percentages

Boiler Feed Pump Discharge Pressure 125% of Throttle Pressure Boiler Feed Pump efficiency 78% Energy addition in Condensate, Heater

Drain Pumps Neglected

Entropy Increases When There is Performance Loss Entropy for Natural Process as a Whole

Increases Entropy Cannot be Conserved Measure of Irreversibilities in Process Entropy of Saturated Water Zero at 32F

Pressure Drop in FW Heater Piping is Isenthalpic (No Heat Losses) Loss in Pressure Increases Entropy Quality of Energy Suffers - Available at

Reduced Temperature Entropy Flow – Product of Mass Flow

and Specific Entropy (Table 1 in Paper)

(1) (2) (3) (4) (5) = (1) x (4)

Ext. 1 from HPT 214,243 604.80 1317.94 1.557641 333,714Ext. 1 to Htr. 1 214,243 586.66 1317.94 1.560716 334,373Difference 0 18.14 0.00 0.003075 659

Entropy Flow, Btu/hr-°F

Description Pressure, Psia

Enthalpy, Btu/lb

Specific Entropy, Btu/lb-°F

Mass Flow, Lb/hr

In FW Htr. Entropy Losses Occur due to Heat Transfer Inefficiencies On Shell Side, Decrease in Entropy On Tube Side, Increase in Entropy Net Result is Increase in Entropy If No Losses, Overall Entropy Change

Would be Zero

In Turbine, Losses As Steam Expands Flows leaving – Decrease in Entropy

Flow Flows Entering – Increase in Entropy

Flow Last Stage Charged With Exhaust

Losses

3,191,400 S

3,241,311 S 3,197,971 S3,018,484 S 3,018,484 S

1,495 S5,968 S

51,165 S 3,257,420 S69.4 P

5,365 S 31.3 P 12.2 P7,966 S 3.9 P

3,211,985 S 146,107 S122,988 S

143,353 S139,622 S

15,848 S 133,120 S161,105 S

2,878,271 S

333,714 SSELEP = 2,541,537 SSUEEP = 2,582,535 S 9,871 S

Cond. Press. = 1.00 in.HgA

128,624 S123,460 S

127,074 SΔh = 0.00

334,373 S 146,669 S 143,902 S 140,154 S 133,667 S 161,688 S

586.6 P 236.7 P 65.3 P 29.4 P 11.4 P 3.7 P 8,213 S0.0 F TD 0.0 F TD 5.0 F TD 5.0 F TD 5.0 F TD 5.0 F TD

1,396,784 S 1,173,864 S 122.1 P 742,776 S 623,510 S 495,706 S 361,043 S 290,441 S 127,074 S342.6 F

483.8 F 396.2 F 313.94 h 298.2 F 249.1 F 199.6 F 149.9 F10.0 F DC 10.0 F DC 10.0 F DC 10.0 F DC 10.0 F DC

122,865 S 153,804 S 1,044,106 S 30,501 S 48,367 S 52,908 S 70,916 S

1,051,030 S 70,916 SΔh = 12.19 Δh = 0.00

853 KW MECH. LOSSES2146 KW ELECT. LOSSES

GENERATOR OUTPUT160,238 KW30 PSIG H2

0.85 PF778 KW MECH. LOSSES

WLpExh =1,401,539

1805 KW ELECT. LOSSES

GENERATOR OUTPUT175,703 KW30 PSIG H2

0.85 PF

STEAMSEAL

REGULATOR

RHTR

2

3

1

5 6

4

2 5 6

HPT IPTLPT

HTR. 1 HTR. 2

BFP

HTR. 3 HTR. 4 HTR. 5 HTR. 6 HTR. 7

HDP

CP

CONDENSER

IV

Equivalent Loss in Output: ΔKw = (ΔS x TA)/3412.14163 where: ΔS = Entropy Flow, Btu/hr-°F TA = Absolute Sink Temp. = (79.04 + 459.69) = 538.73 °F Table 2 in Paper Shows Losses

(1) (3) (4) (5)Heat

Transferred/Work Done, Btu/hr

Equivalent Kw

% of Shaft

Output% of Total

Heat Added

2,096,666,710 614,472 179.921 84.068 371,569,090 108,896 31.885 14.898

25,779,982 7,555 2.212 1.034 2,494,015,782 730,924 214.019 100.000

296,745,990 8,386 2.456 1.147 313,010,510 5,609 1.642 0.767 555,569,681 22,302 6.530 3.051 --------- 36,297 10.628 4.966 --------- 343,784 100.662 47.034

1,328,689,601 389,400 114.019 53.275 1,165,326,181 341,523 100.000 46.725

(2)

A. SuperheaterB. Reheater

Equiv. Entropy Change, Btu/hr/ºF

5. Turbine LossA. HP Turbine 53,117

1. Boiler Output

Total Heat Added in Boiler, BFP 4,629,428

C. LP Turbine

8. Turbine Power Output 2,163,095 7. Condenser Loss 2,466,333

141,251

6. Theoretical Cycle Loss 2,177,411

B. IP Turbine

3,891,863 689,712

35,523

Description

2. Boiler Feed Pump 47,853

Total Turbine Loss 229,891

(1) (3) (4) (5)Heat

Transferred/Work Done, Btu/hr

Equivalent Kw

% of Shaft

Output% of Total

Heat Added

200,488,736 35,196 10.306 4.815 200,488,736 (33,394) (9.778) (4.569) --------- 1,802 0.528 0.247

102,259,191 19,394 5.679 2.653 102,259,191 (18,272) (5.350) (2.500) --------- 1,122 0.328 0.153 664,105,674 --------- 1,298 0.380 0.178

86,842,156 18,831 5.514 2.576 86,842,156 (17,904) (5.243) (2.450)

--------- 926 0.271 0.127

86,746,678 20,178 5.908 2.761 86,746,678 (19,308) (5.653) (2.642)

--------- 871 0.255 0.119

84,776,686 21,261 6.225 2.909 84,776,686 (20,387) (5.970) (2.789)

--------- 874 0.256 0.120

93,241,518 25,793 7.552 3.529 88,143,676 (23,982) (7.022) (3.281)

--------- 1,812 0.530 0.248 --------- 8,704 2.549 1.191

(2)

3. Feedwater Heaters Heat Transfer LossA. Heater 1

Tube Side

Equiv. Entropy Change, Btu/hr/ºF

Tube Side

222,920 (211,508)

11,412 Shell Side

Overall Heat Transfer Loss in Heater 1B. Heater 2

122,834 (115,729)

7,105 Shell Side

8,219

Shell Side (113,401)

Overall Heat Transfer Loss in Heater 2C. Heater 3 (Deaerator)Overall Heat Transfer Loss in Heater 3D. Heater 4

Tube Side 119,267

Shell Side (122,288) Overall Heat Transfer Loss in Heater 5 5,516

5,866 E. Heater 5

Tube Side 127,804

Overall Heat Transfer Loss in Heater 4

Shell Side (129,126) Overall Heat Transfer Loss in Heater 6 5,536

F. Heater 6Tube Side 134,662

Shell Side (151,892) Overall Heat Transfer Loss in Heater 7 11,474

G. Heater 7Tube Side 163,366

Total Heat Transfer Loss in Heaters 55,128

Description

(1) (3) (4) (5)Heat

Transferred/Work Done, Btu/hr

Equivalent Kw

% of Shaft

Output% of Total

Heat Added

--------- 104 0.030 0.014 --------- 89 0.026 0.012 --------- 75 0.022 0.010 --------- 87 0.025 0.012 --------- 84 0.025 0.012 --------- 86 0.025 0.012 --------- 92 0.027 0.013 --------- 616 0.180 0.084

(2)Equiv. Entropy

Change, Btu/hr/ºF

Total Heaters Ext. Piping Loss 3,903

4. Feedwater Heaters Ext. Piping LossA. Heater 1 Ext. Piping Loss 659

E. Heater 5 Ext. Piping Loss 532

B. Heater 2 Ext. Piping Loss 562 C. Heater 3 Ext. Piping Loss 472

549

Description

F. Heater 6 Ext. Piping Loss 546 G. Heater 7 Ext. Piping Loss 583

D. Heater 4 Ext. Piping Loss

Quantification of Losses Using Entropy Balance Using Economic Data, Equipment

Mods or Upgrades May be Prioritized Detailed Performance Modeling To

Consider Additional Effects - Pressure Drops Within Heaters, Heat Losses From Piping, etc.