THERMODYNAMIC ANALYSIS OF SUPERCRITICAL RANKINE...

54

CHAPTER 4

THERMODYNAMIC ANALYSIS OFSUPERCRITICAL RANKINE CYCLE

The computer program which was developed by the present investigation

as presented in Chapter 3 has been used to find different steam

properties at different operating conditions of pressure and temperature

and thermodynamic analysis of the cycle has been presented in this

chapter. In section 1.2, the basic cycle of operation of steam power plant

based on the Rankine cycle has been presented. To carryout

thermodynamic analysis of this cycle the assumptions and range of

variable parameters are given below.

4.1 ASSUMPTIONS MADE IN THE ANALYSIS

i. Capacity of the power plant = 1000 MW

ii. The isentropic efficiency of the steam turbine is 90%.

iii. The pump efficiency is assumed to be 85%.

iv. Cooling water temperature inlet to the condenser Twi=250C

v. Terminal Temperature Difference (TTD) = 50C

vi. Heat and pressure losses in the transport pipe in between the

different units of the cycle are negligible.

55

4.2 RANGE OF VARIABLE PARAMETERS

The important variables which affect significantly the performance of the

Rankine cycle (energy and exergy efficiency) have been identified and

listed below. As the literature survey revealed that significant amount of

research work has been reported as thermal power plants operating on

Rankine cycle in subcritical range of operating parameters. Hence, the

present investigation has selected the following range of operating

parameters to contribute to the analysis of Rankine cycle in

supercritical/ultra supercritical/advanced ultra supercritical ranges.

i. Steam turbine inlet temperature = 5000C to 8000C

ii. Steam turbine inlet pressure =170bar to 425bar

iii. Optimum reheat pressure ratio

iv. Condenser pressure Pc= 0.03 bar - 0.1bar

v. Temperature of flue gas at the entry of boiler = 9000C -14000C

vi. Temperature of flue gas at the exit of boiler = 800C -3000C.

The above assumptions and range of variable parameters given in

sections 4.1 and 4.2 are used for the analysis of mentioned thermodynamic

cycles in the chapter 4, chapter 5, chapter 6 and chapter 7 respectively.

56

4.3 FLOWCHART FOR THE ENERGY AND EXERGY ANALYSIS OFSUPERCRITICAL RANKINE CYCLE

Fig. 4.1 Flow diagram of finding energy and exergy analysis of SupercriticalRankine cycle

57

4.4 ENERGY EFFICIENCY OF SUPERCRITICAL RANKINE CYCLE

It may be recalled that, the energy efficiency of the cycle is defined as the

ratio of network done to the heat supplied in the boiler of the steam

power cycle,

From the figure 1.1, Energy efficiency = Wnet / H.S (4.1)

Where Wnet = Wturbine - Wpump kJ/kg (4.2)

The work done by the turbine per kg of steam supplied,

Wturbine = h1 – h2 kJ/kg (4.3)

Boiler feed pump required work per kg of steam supplied,

Wpump =h4 – h3 kJ/kg

(4.4)

Heat supplied to water/steam in the boiler per kg of steam produced is

H.S = h1– h4 kJ/kg (4.5)

4.5 EXERGY EFFICIENCY OF SUPERCRITICAL RANKINE CYCLE

The method of exergy analysis aims at the quantitative evaluation of the

exergy losses (irreversibilities) associated with a system. Hence, it is

required to calculate the irreversibility in all the components of the power

cycle for the estimation of exergy efficiency.

The irreversibility or exergy loss in each of the components is calculated

for the specified dead state (P0, T0).

58

The anthracite coal whose chemical composition has been taken from

Kotas [5], as given below, is considered for thermodynamic analysis of all

cycles of the present investigation. The heat content of this fuel is 28,940

kJ/kg.

CO2 H2O N2 O2 SO2 Total

nk[kmol/kgfuel] 6.51 1.634 35.32 9.324 0.047 57.735

xk 0.1234 0.0310 0.6679 0.1768 0.0009 1.000

Further, the equations used for the calculation of enthalpy, exergy, mean

isobaric heat capacity and mean molar isobaric exergy capacity of the

anthracite coal have been taken from Kotas [5] and are reproduced

below.

The enthalpy values are calculated using the equations (4.6 and 4.7)

k

hpkkAA cnh ~0 kJ/kg of fuel (4.6)

k

hphkBB cnh ~0 kJ/kg of fuel (4.7)

where A is the flue gas inlet temperature(0C),

B is the flue gas outlet temperature(0C)

0 is the ambient temperature (0C)

The exergy of the flue gas entry and exit of the boiler is

k

pkkAA cnE ~0 kJ (4.8)

59

k

pkkBB cnE ~0 kJ (4.9)

Mean isobaric heat capacity for evaluating enthalpy changes is

T

Tp

hp dTc

TTTThhc

000

0 1 (4.10)

Mean molar isobaric exergy capacity for evaluating changes in

physical exergy is

T

T

T

T

pp

T

p TdTc

TdTcTTTT

c0 0

000

1 (4.11)

4.5.1 ESTIMATION OF IRREVERSIBILITY OR EXERGY LOSS INDIFFERENT COMPONENT OF THE CYCLE

4.5.1.1 Boiler:

The mass flow rate of steam (ms) required to be generated in the boiler to

produce an output of 1000MW power can be obtained from the energy

balance as given below: ms(Wnet) = 1000 MW

ms= 1000x1000 kW/ Wnet kg/s (4.12)

Using this, the mass of the flue gas (mg) required to obtain the

required mass flow rate of steam can be found by the energy balance

equation i.e., Heat gained by the steam = Heat lost by the flue gas

ms(h1 –h4)= mg (hA – hB)

mg = ms(h1 –h4)/(hA – hB) kg/s (4.13)

Exergy or Availability at state point 1

60

E1 = ms (h1-To s1) kW (4.14)

Exergy or Availability at state point 4

E4 = ms (h4-To s4) kW (4.15)

Irreversibility in the boiler is

Iboiler =(EA-EB)– (E1 – E4)

Substituting the E1, E4 from equation 4.14 and equation 4.15

Iboiler = mg(EA-EB) – ms((h1 – h4) – T0(s1 – s4)) kW (4.16)

4.5.1.2 Steam Turbine:The irreversibility in the steam turbine can be calculated by Gouy-

Stodola equation as given below

Iturbine=T0.ms (s2-s1) kW (4.17)

4.5.1.3 Condenser:Mass flow rate of cooling water circulated to condense ms, kg/s, of steam

is obtained from the energy balance is

mcw Cpw (Twi-Two )= ms (h2-h3)

mcw= ms(h2-h3)/ Cpw (Twi-Two ) (4.18)

Irreversibility in the condenser,

Icondenser= ms(s2-s3)- T0(mcwCpwln(Two/Twi) kW (4.19)

4.5.1.4 Pump:

Irreversibility in the boiler feed pump,

Ipump=ms T0(s4-s3) kW (4.20)

61

4.5.1.5 Exhaust:Irreversibility of the exhaust, Iexhaust = EB (4.21)

4.5.1.6 Total Irreversibility:

Total Irreversibility is

I =(Iboiler + Iturbine + Ipump + Icondenser + Iexhaust) kW (4.22)

4.5.1.7 Exergy Efficiency:

Exergy efficiency is defined as the ratio of exergy output to the exergy

input. Exergy output depends on the degree of Irreversibility of the cycle.

Exergy efficiency = 100*A

A

EIE (4. 23)

4.6 FRACTIONAL EXERGY LOSS

The definition of the fractional exergy loss of the component is the ratio

of irreversibility of the individual component to the total irreversibility of

the cycle. Its value is estimated for all the components of the cycle. It

gives the information regarding the loss of useful energy in all

components for different operating variables. The Fractional exergy loss

formulas of each component are as follows.

Fractional exergy loss in the boiler is,

100* IIboiler (4.24)

Fractional exergy loss in the turbine is,

100* II turbine . (4.25).

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Fractional exergy loss in the condenser is,

100* IIcondenser (4.26)

Fractional exergy loss in the Pump is,

100* II pump (4.27)

Fractional exergy loss in the exhaust is,

100* IIexhaust (4.28)

4.7 PARAMETRIC EFFECT ON THE PERFORMANCE OFSUPERCRITICAL POWER CYCLE

In the sections of 4.1 to 4.6 the fundamental aspects related to

supercritical power cycle regarding its functioning, energy and exergy

analysis was discussed. Based on this, the effect of different variables on

the performance of the cycle is analyzed in detail in the subsequent

sections.

4.7.1 Effect of turbine inlet temperature and pressure on energyefficiency

Figure 4.2 represents the variation of energy efficiency against the

steam turbine inlet temperature at the various turbine inlet

pressures of the steam.

It may observed from the figure that, the energy efficiency increases

with an increase of turbine inlet temperature at a given turbine inlet

pressure. A similar trend in the variation of energy efficiency can be

noted at subcritical pressures of 170 bar, 200 bar and at

63

supercritical pressures of 225 bar, 250 bar etc., turbine inlet

pressures of the steam.

36

38

40

42

44

46

500 550 600 650 700 750 800Turbine inlet temperature (

0C)

En

ergy

Effi

cien

cy(%

)

170 200 225250 275 300325 350 375400 425

Fig. 4.2 Variation of energy efficiency with turbine inlet temperature of steam

At the turbine inlet pressure increases the energy efficiency increases at

a particular turbine inlet temperature. It may be noted from a figure that,

the energy efficiency increases from 37.66% to 45.66% to as the turbine

inlet pressure increases from 170bar to 425bar. Energy efficiency at

turbine inlet pressure of 425bar and at different turbine inlet

Pc=0.05bar

P1,(bar)

64

temperatures of 6000C/6500C/7000C/7500C/8000C are

41.12%/42.17%/43.37%/44.53%/ 45.66%, respectively.

Table 4.1 shows the network done by the turbine, heat supplied and

energy efficiency at different turbine inlet pressures at a given turbine

inlet temperature of 7000C. From the table, it may be inferred that, net

work output from the turbine reduces with increase in turbine inlet

pressure due to significant increase in the pump work and insignificant

variation in the turbine work.

Table 4.1 Energy efficiency at different turbine inlet pressures

P1bar

T1(0C)

Wt(kJ/kg)

Wp(kJ/kg)

Wnet(kJ/kg)

H.S.(kJ/kg)

EnergyEfficiency

(%)225 700 1563.07 26.60 1536.48 3608.455 42.58250 700 1565.65 29.55 1536.10 3594.057 42.74300 700 1567.08 35.46 1531.62 3562.736 42.99350 700 1564.82 41.38 1523.45 3528.138 43.18400 700 1559.91 47.29 1512.62 3491.736 43.32425 700 1556.68 50.24 1506.44 3473.461 43.37

Further, it may be noticed from the Table 4.1 that, the energy input

(Heat Supplied) to the boiler decreases as the turbine inlet pressure

increases. So, as the turbine inlet pressure increases both the Wnet and

heat supplied decreases. But the rate of decrease of heat supplied is

more than the rate of decrease of Wnet. Hence, the energy efficiency

increases as the pressure increases at a given turbine inlet temperature.

In order to appreciate, the effect of the turbine inlet pressure on the

performance of the plant, the same data has been represented in Fig. 4.3

has been drawn with turbine inlet pressure on the abscissa and

efficiency on the ordinate. It may clearly be noted from this figure that

65

the energy efficiency increases with an increase of turbine inlet pressure

at different temperatures. The energy efficiency at turbine inlet

temperature of 8000C are 44.62% at 200bar, 44.97% at 250 bar, 45.22%

at 300 bar, 45.43% at 350 bar, 45.59% at 400 bar and 45.66% at 425

bar, respectively.

35

38

41

44

47

170

225

275

325

375

425

Turbine inlet pressure (bar)

En

ergy

Eff

icie

ncy

(%)

500550600650700750800

Fig. 4.3 Variation of energy efficiency with turbine inlet pressure of steam

Table 4.2 shows the work done by the turbine, heat supplied and energy

efficiency of different turbine inlet temperature at a given turbine inlet

pressure of 350 bar.

Table 4.2 Energy efficiency at different turbine inlet temperatures

P1bar

T1(0C)

Wt(kJ/kg)

Wp(kJ/kg)

Wnet(kJ/kg)

H.S.(kJ/kg)

EnergyEfficiency

(%)350 500 1152.79 41.38 1111.42 2904.914 38.26350 550 1273.90 41.38 1232.52 3113.997 39.58350 600 1377.18 41.38 1335.80 3274.021 40.80350 650 1472.70 41.38 1431.33 3407.117 42.01350 700 1564.82 41.38 1523.45 3528.138 43.18350 750 1655.67 41.38 1614.29 3642.351 44.32350 800 1746.26 41.38 1704.89 3752.785 45.43

Pc=0.05bar T1, (0C)

66

From the Table 4.2, it can be observed that, the turbine power output

(Wt) increases, as the turbine inlet temperature increases, however power

input to the pump (Wp) remains same. So, as a result of this, the net

work output from the turbine (Wt - Wp) increases as the turbine inlet

temperature increases. Further, it is important to note from the Table 4.2

that, the energy input to the boiler increases as the turbine inlet

temperature increases.

On careful observation of Table 4.2, it may also be noted that the energy

efficiency of the cycle increases significantly with turbine inlet

temperature due to faster rate of increase of turbine work compared to

heat supplied.

4.7.2 Effect of turbine inlet temperature and pressure on exergyefficiency

In order to arrive at the effect of variation in turbine inlet temperature on

exergy efficiency at a given turbine inlet pressure for 1000MW capacity

power plant the mass flow rates of the flue gases and steam have been

varied. At each turbine inlet temperature in range of 5000C-8000C the

values of exergy of the flue gas at the boiler entry (EA), exergy of the flue

gas at boiler exit (EB) and irreversibilities in all the components are

estimated. Thereby, the exergy efficiency at different turbine inlet

temperatures in between 5000C-8000C was calculated and variation in

exergy efficiency is presented in figure 4.4 and 4.5 respectively.

67

44

48

52

56

60

64

68

500 550 600 650 700 750 800Turbine inlet temperature (

0C)

Exe

rgy

Effi

cien

cy(%

)

170 200 225250 275 300325 350 375400 425

Fig. 4.4 Variation of exergy efficiency with turbine inlet temperature

Figure 4.4 depicts the variation of exergy efficiency with the turbine

steam inlet temperature at different turbine inlet pressures. It is

observed from the figure that the exergy efficiency increases with an

increase of temperature at a given pressure. It is found that, the exergy

efficiency at turbine inlet pressure of 425 bar and at turbine inlet

temperatures of 6000C/6500C/ 7000C /7500C /8000C are 55.3%

/58.44% /61.18% /63.66% and 65.95%, respectively.

To analyse the reason for the variation of exergy efficiency with turbine

inlet pressure at constant turbine inlet temperature the data required

has been presented in the Table 4.3.

Pc=0.05bar,TFGi =10000C,TFGo =1000C

P1,(bar)


P1,(bar)

68

Table 4.3 Exergy efficiency at different turbine inlet pressuresP1bar

T1(0C)

IboilerkW

IturbinekW

IcondenserkW

IpumpkW

IexhaustkW

IsumkW

ExergyEfficiency

(%)200 700 276887.19 109859.95 29413.55 1385.00 13075.68 430621.38 57.10225 700 268687.56 110066.75 29109.08 1223.40 13075.68 424116.91 57.75250 700 260590.73 110275.20 28857.23 2362.86 13075.68 415161.69 58.64300 700 250141.47 110699.03 28471.09 2046.92 13075.68 404434.19 59.71350 700 241452.86 111132.20 28199.74 3036.09 13075.68 396896.56 60.46400 700 234953.27 111576.18 28010.94 4036.12 13075.68 391652.19 60.98425 700 232996.12 111802.33 27940.82 3888.26 13075.68 389703.22 61.18

We know that, the exergy of the flue gas at the entry of the boiler (EA)

does not vary with turbine inlet pressure and turbine inlet temperature

of the steam. Further, on careful observation it may be noted that the

amount of irreversibility in the boiler and condenser reduces with

increase in turbine inlet pressure and the amount of irreversibility in

turbine and pump increases with increase of turbine inlet pressure. It is

also important to note that, the amount of irreversibility at exhaust does

not vary with turbine inlet pressure. As a consequence of these things;

the total irreversibility of all the components of the cycle put together is

decreasing with increase in the turbine inlet pressure. This results in the

increase of exergy efficiency with turbine inlet pressure at a constant

turbine inlet temperature.

The data of total exergy loss (total irreversibility) at a turbine inlet

temperature of 7000C and at different turbine inlet pressures is

presented in Table 4.3 and the values of total exergy loss at different

values of turbine inlet temperature and pressure are plotted in Fig. 4.5

69

340

380

420

460

500

540

500 550 600 650 700 750 800

Turbine inlet temperature (0C)

Tota

l E

xerg

y Lo

ss(M

W)

170 200225 250275 300325 350375 400425

Fig. 4.5 Variation of total exergy loss with turbine inlet temperature

A similar variation in exergy efficiency can be observed at pressures

varying from 170 to 425 bar. This can be observed from the figure 4.6

also. From this figure 4.5, it can be noted that the exergy efficiency at

turbine inlet temperature of 8000C, turbine inlet pressures at 200

bar,225 bar, 250 bar, 300 bar, 350 bar, 400 bar and 425 bar are

61.63%, 62.33%, 63.14%, 64.25%, 65.07%, 65.69% and

65.95%,respectively.

TFGi =10000C,TFGo =1000CP1=350 bar,Pc=0.05bar

P1,(bar)

70

44

48

52

56

60

64

68

170 200 225 250 275 300 325 350 375 400 425

Turbine inlet pressure ( bar)

Exe

rgy

Effi

cien

cy(%

) 500550600650700750800

Fig. 4.6 Variation of exergy efficiency with turbine inlet pressures

To analyze the reason for the variation of exergy efficiency with turbine

inlet temperature at constant turbine inlet pressure the data required

has been presented in the Table 4.4.

Table 4.4 Exergy efficiency at different turbine inlet temperaturesP1bar

T1(0C)

IboilerkW

IturbinekW

IcondenserkW

IpumpkW

IexhaustkW

IsumkW

ExergyEfficiency

(%)350 500 365197.97 112221.59 32902.32 4161.65 13075.68 527559.19 47.82350 550 324753.59 111825.82 31362.35 3752.72 13075.68 484770.16 51.71350 600 293187.34 111545.01 30162.60 3462.58 13075.68 451433.22 55.03350 650 266000.78 111321.33 29130.58 3231.49 13075.68 422759.88 57.89350 700 241452.86 111132.20 28199.74 3036.09 13075.68 396896.56 60.46350 750 218748.38 110966.84 27339.58 2865.22 13075.68 372995.72 62.84350 800 197505.66 110819.40 26535.36 2712.97 13075.68 350649.06 65.07

On careful observation it may be noted that, the amount of irreversibility

in the boiler, turbine, condenser and pump reduces with increase in

turbine inlet temperature with a given turbine inlet pressure. It is also

important to note that the amount of irreversibility at exhaust does not

vary with turbine inlet pressure. Further it is significant, to point out,

T1, (0C)


71

that the major stake of total irreversibility of the boiler is due to the

irreversibility in the boiler alone. As a consequence of these things; the

total irreversibility of all the components of the cycle put together is

decreasing with increase in the turbine inlet temperature. This results in

the increase in the exergy efficiency with turbine inlet temperature at a

constant turbine inlet pressure.

The values of the total exergy loss at different turbine inlet temperature

at a given turbine inlet pressure of 350 bar are presented in table 4.4.

However, the values of total exergy loss at different values of turbine inlet

pressures and turbine inlet temperatures are plotted in Fig.4.7.

330

370

410

450

490

530

170 200 225 250 275 300 325 350 375 400 425

Turbine inlet pressure ( bar)

Tota

l Exe

rgy

Loss

(MW

)

500550600650700750800

Fig. 4.7 Variation of total exergy loss with turbine inlet pressure at differentturbine inlet temperatures

TFGi =10000C,TFGo =1000C,T1=7000C,Pc=0.05bar

T1, (0C)

72

4.7.3 Effect of turbine inlet temperature and pressure on fractionalexergy loss (FEL)

FEL in a particular component of the cycle reflects the amount of

irreversibility in the particular component.

Figure 4.8 shows that the effect of turbine inlet temperature on fractional

exergy loss of different components of a SCRC.

0

10

20

30

40

50

60

70

500 550 600 650 700 750 800

Turbine inlet temperature (0C)

Frac

tion

al E

xerg

y Lo

ss (%

)

BoilerTurbineCondenserPumpExhaust

Fig. 4.8 Variation of fractional exergy loss of different components with turbineinlet temperature

It may be noted from the figure that, the FEL of the boiler decreases from

68.89% to 55.99%, FEL of the turbine increases from 21.27% to 31.6%

and further FEL of the condenser increases marginally from 6.24% to

7.19% with an increase of turbine inlet temperature from 5000C to

8000C. FEL of the pump is about 1% and FEL of the exhaust increases

TFGi =10000C,TFGo =1000C,P1=350 bar,Pc=0.05bar

73

marginally from 2.71% to 3.73% with increase of turbine inlet

temperature from 5000C to 8000C. In view of large magnitude of FEL in

boiler, an extensive investigation is required to study the ways of

minimizing the FEL in boiler. However, the present investigation has not

focused on this point.

Figure 4.9 represents the variation of fractional exergy loss of different

components of the cycle with turbine inlet pressure.

0

10

20

30

40

50

60

70

170 200 225 250 275 300 325 350 375 400 425

Turbine inlet pressure (bar)

Frac

tion

al E

xerg

y Lo

ss(%

)


Fig. 4.9 Variation of fractional exergy loss of different components with turbineinlet pressure

It may be noted from this figure that, FEL of the boiler decreases with

increase of pressure at a given inlet temperature. It is found that, FEL of

boiler at 200 bar is 64%, 250 bar is 62.46%, 300 bar is 61.21%, 350 bar

TFGi =10000C,TFGo =1000C,T1=7000C,Pc=0.05bar

74

is 60.51%, 400 bar is 59.66% and 425 bar is 59.12% at respectively,

where as in the turbine, the FEL increases with an increase of pressure.

FEL in the condenser increases marginally from 6.74% to 7.17%, FEL of

the exhaust increases very marginally from 2.95% to 3.36% with an

increase of turbine inlet pressure from 170 bar to 425 bar. FEL of the

pump is very less and it is insignificant.

4.7.4 Effect of Condenser pressure on the performance

Fig.4.10 shows the variation of energy efficiency with different condenser

pressure at different turbine inlet temperature of steam.

38

40

42

44

46

48

0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1Condenser Pressure(bar)

En

ergy

effi

cien

cy(%

) 500550600650700750800

Fig. 4.10 Variation of energy efficiency of SCRC with condenser pressure atdifferent turbine inlet temperatures

It is interesting to note from Fig 4.10 that, the energy efficiency decreases

with increase of condenser pressure at a turbine inlet temperature. It

P1=350barT1,(0C)

75

may be noted that the maximum energy efficiency occurred at a

condenser pressure of 0.03bar at all turbine inlet temperatures. At a

turbine inlet pressure of 350bar, the values of energy efficiency at 5000C,

6000C, 7000C and 8000C are 40.90%, 42.47%, 44.08% and 45.72%,

respectively.

Fig.4.11 shows the variation of energy efficiency with condenser pressure

at different turbine inlet pressures at turbine inlet temperature of 7000C.

38

40

42

44

46

48


En

ergy

effi

cien

cy(%

)

225 250 300350 400 425

Fig. 4.11 Variation of energy efficiency of SCRC on condenser pressure ofdifferent turbine inlet pressure

It may be noted that the energy efficiency decreases with increase of

condenser pressure at a turbine inlet pressure. It may be interesting to

note that the maximum energy efficiency occurred at a condenser

pressure of 0.03bar at all turbine inlet pressures. At a turbine inlet

T1=7000C

P1,(bar)

76

temperature of 7000C, the values of energy efficiency at 225bar, 250bar,

300bar, 350bar, 400bar and 425 bar are 43.00%, 43.32%, 43.69%,

44.08%, 44.39% and 44.70% respectively.

To analyze the possible reason for this variation of energy efficiency of

supercritical cycle without reheat with condenser pressure at a turbine

inlet temperature and turbine inlet pressure different values of turbine

work, pump work, network done by the turbine, heat supplied and

energy efficiency have been presented in Table 4.5.

Table 4.5 Energy efficiency at different condenser pressures

As the condenser pressure increases from 0.03bar to 0.1bar, work done

by the turbine, pump work decreases, hence the net work output

decreases. The heat supplied to the boiler does not vary with increase of

condenser pressure. Hence, energy efficiency decreases with increase of

condenser pressure.

The data pertaining to variation of energy efficiency with condenser

pressure at a turbine inlet temperature of 7000C has been presented in

the table 4.5. However, a similar variation in the energy efficiency at

Pc

(bar)Wt

(kJ/kg)Wp(kJ/kg)

Wnet(kJ/kg)

H.S.(kJ/kg)

Energyefficiency(%)

0.03 1596.49 41.29 1555.20 3528.13 44.080.04 1577.66 40.11 1537.55 3528.13 43.580.05 1564.82 41.38 1523.45 3528.13 43.180.06 1550.13 38.33 1511.80 3528.13 42.850.07 1538.73 37.16 1501.57 3528.13 42.560.08 1529.20 36.45 1492.75 3528.13 42.310.09 1520.29 35.66 1484.63 3528.13 42.080.1 1513.27 35.34 1477.93 3528.13 41.89

77

different turbine inlet temperature values ranges 5000C-8000C has been

presented in Fig. 4.12.

56

57

58

59

60

61

62

63

64

65


Exe

rgy

effic

ien

cy(%

)

500 550 600650 700 750800

Fig. 4.12 Variation of exergy efficiency of SCRC on condenser pressure ofdifferent turbine inlet temperature

It may be noted from this figure that, the exergy efficiency decreases with

increase of condenser pressure at a turbine inlet temperature and the

similar variation in exergy efficiency is noticed at different turbine inlet

temperature. It may also be noted that the maximum exergy efficiency

occurred at a condenser pressure of 0.03 bar at all turbine inlet

temperatures. At a turbine inlet pressure of 350 bar, the values of exergy

efficiency at 5000C, 6000C, 7000C and 8000C are 59.68%, 60.42%,

61.37% and 62.59% respectively. The Fig.4.12 reveals the variation in

the exergy efficiency with condenser pressure at a turbine inlet pressure

TFGi =10000C,TFGo =1000CP1=350bar

T1,(0C)

78

of 350 bar and at different turbine inlet temperatures varying from

5000C-8000C. In order to observe a similar variation at different turbine

inlet pressures, Fig. 4.13 has been plotted at turbine inlet temperature of

7000C and at various turbine inlet pressures varying from 225bar –

425bar.

56

57

58

59

60

61

62

63

64

65


Exe

rgy

effic

ien

cy(%

)

225 250300 350400 425

Fig. 4.13 Variation of exergy efficiency of SCRC with condenser pressure atdifferent turbine inlet pressure

It may be noted that, the exergy efficiency decreases with increase of

condenser pressure at a turbine inlet pressure. It may be interesting to

note that the maximum exergy efficiency occurred at a condenser

pressure of 0.03 bar at all turbine inlet pressures. At a turbine inlet

temperature of 7000C, the values of energy efficiency at 225bar, 250bar,

TFGi =10000C,TFGo =1000CT1=7000C,R=0.25

P1,(bar)

79

300bar, 350bar, 400bar and 425bar are 63.67%, 63.91%, 64.14%,


The possible reason for the decreasing trend in exergy efficiency of this

cycle with condenser pressure, Table 4.6 has been presented in the next

page.

Table 4.6 Exergy efficiency at different condenser pressures

Further, on careful observation from the Table 4.6, the irreversibility in

the boiler, turbine and pump are decreasing with an increase of

condenser pressure from 0.03bar to 0.1bar. Irreversibility of exhaust

does not change and irreversibility of the condenser increases

significantly with an increase of condenser pressure and thereby

increasing the total irreversibility and the value of EA does not vary with

condenser pressure. Hence, exergy efficiency decreases with increase of

condenser pressure.

The data of total exergy loss at a turbine inlet temperature of 7000C and

at a turbine inlet pressure of 350 bar and are presented in the Table 4.6.

However, the values of total exergy loss at different values of turbine inlet

temperatures are presented in Fig.4.14.

Pc

(bar)Iboiler

kWIturbine

kWIcondenser

kWIpump

kWIexhaust

kWIsum

kWExergyEfficiency

(%)0.03 247548.81 114318.27 9540.51 3250.07 13075.68 387733.34 61.370.04 243944.27 112522.45 19935.10 3130.35 13075.68 392607.84 60.890.05 241508.44 111132.20 28199.74 2980.51 13075.68 396896.56 60.460.06 239346.72 109979.57 35286.86 2753.20 13075.68 400442.03 60.110.07 237572.67 109023.23 41160.47 2580.02 13075.68 403412.06 59.810.08 235842.13 108177.49 46554.42 2461.02 13075.68 406110.75 59.540.09 234700.53 107440.02 51282.58 2239.71 13075.68 408738.53 59.280.1 233292.05 106773.67 55617.84 2208.01 13075.68 410967.25 59.06

80

350

370

390

410

430

450


Tota

l exe

rgy

loss

, MW

500550600650700750800

Fig 4.14 Variation of total exergy loss of condenser pressure of thecycle

The variation of fractional exergy loss at a condenser pressure of 0.05

bar was already discussed. Further, it may be observed from the Fig.4.15

that FEL in case of condenser pressure increases with an increase of

condenser pressure with a minimum of exergy loss of 2.22% at 0.03 bar

condenser pressure and a maximum of 12.21% at a condenser pressure

of 0.1 bar. FEL increases with decrease in condenser pressure. However,

FEL of the boiler and turbine decreases with increase in condenser

pressure. In the boiler, at 0.1 bar is 60.39%, 0.05 bar is 64.38% and at

0.03 bar is 67.01% respectively. FEL of the steam turbine is decreases

with decrease in condenser pressure. FEL of the turbine at 0.1 bar is

23.45%, at 0.05 bar is 25.26% and at 0.03 bar is 26.59% respectively.

FEL of the pump is nearly 1% and FEL of the exhaust decreases very

P1=350bar,T1=7000C,TFGi =10000C,TFGo =1000C

T1,(0C)

81

marginally from 3.04% to 2.87% with increase of condenser pressure

from 0.03 bar to 0.01 bar.

0

10

20

30

40

50

60

70


Frac

tion

al E

xerg

y Lo

ss


Fig 4.15 Variation of fractional exergy loss with condenser pressure

4.7.5 Effect of boiler inlet flue gas temperature on exergy efficiencyFor the generation of 1000 MW power from steam power plant at

different turbine inlet pressure and turbine inlet temperatures the values

of exergy efficiency, irreversibilities in all the components at different flue

gas inlet temperatures from 9000C to 14000C have been formed in Table

4.7a and 4.7b and presented in Fig.4.16, 4.17 and 4.18.

Fig 4.16 shows the variation of exergy efficiency on different temperature

of boiler flue gas inlet temperature with different turbine inlet

temperature, at a given turbine inlet pressure and at boiler flue gas

outlet temperature of 1000C.

TFGi =10000C,TFGo =1000CT1=7000C,P1=350bar

82

54

58

62

66

70

900 1000 1100 1200 1300 1400Boiler flue gas inlet Temperature(

0C)

Exe

rgy

effic

ien

cy(%

)500550600650700750800

Fig. 4.16 Variation of exergy efficiency of SCRC on boiler flue gas inlettemperature of different turbine inlet temperature

It may be noted that exergy efficiency increases with increase of boiler

flue gas inlet temperatures at a boiler flue gas exit temperature at all

turbine inlet temperatures at a turbine inlet pressure. It may be noted

that the minimum and maximum exergy efficiency occurred at a boiler

flue gas inlet and outlet temperatures of boiler are 9000C and 14000C. At

turbine inlet pressure of 350 bar and at boiler flue gas exit temperature

of 1000C, it is interesting to note that the maximum exergy efficiency at

5000C, 6000C, 7000C and 8000C are 64.11%, 66.42%, 68.34% and

71.56% respectively at boiler flue gas inlet temperature of 14000C.

Figure 4.17 shows the variation of exergy efficiency on different flue gas

inlet temperature of the boiler at a boiler flue gas outlet temperature at

different turbine inlet pressures at a turbine inlet temperature.

TFGo =1000C,P1=350bar

T1,(0C)

83

56

60

64

68

72


0C)

Exe

rgy

effic

ien

cy(%

)

225 250300 350400 425

Fig. 4.17 Variation of exergy efficiency of SCRC on boiler flue gas inlettemperature of different turbine inlet pressure

A similar trend in variation of exergy efficiency is observed in Fig.4.16. At

turbine inlet temperature of 7000C bar and at boiler flue gas exit

temperature of 1000C, it is interesting to note that the maximum exergy

efficiency at 225 bar, 250 bar, 300bar, 350bar, 400bar and 425bar are

64.71%, 68.60%, 69.67%, 70.42%, 70.94% and 71.14% respectively at

boiler flue gas inlet temperature of 14000C.

At given each turbine inlet temperatures/pressure the values of exergy of

the flue gas at the boiler entry (EA), exergy of the flue gas at boiler exit

(EB) and irreversibilities in all the components are estimated and are

shown in Table 4.7a and 4.7b, this may be the possible reason to

increasing the exergy efficiency.

TFGi =10000C,TFGo =1000C,T1=7000C

P1,(bar)

84

Table 4.7a Energy efficiency, enthalpy, exergy, different boiler flue gas inlettemperature

FGi EnergyEfficiency

(%)

ms

(kg/sec]mg

(kg/sec] hA

kJ/kghB

kJ/kgEA

kJEB

kJ

900 43.18 656.40 1.591423 1575629.88 120400.21 856472.94 13075.681000 43.18 656.40 1.403148 1770892.63 120400.21 1003827.38 13075.681100 43.18 656.40 1.253402 1968080.25 120400.21 1156579.63 13075.681200 43.18 656.40 1.132592 2165165.25 120400.21 1313820.25 13075.681300 43.18 651.00 1.043991 2368081.75 120400.21 1475446.88 13075.681400 43.18 656.40 0.909170 2667652.00 120400.21 1640968.00 13075.68

It may be noted from the Table enthalpy and exergy of flue gases at the

exit from the boiler does not vary. Enthalpy and exergy of flue gases at

the entrance of the boiler increases with an increase of boiler flue gas

inlet temperature from 9000C to 14000C at a given steam turbine inlet

temperature of 7000C and a given steam turbine inlet pressure.

Table 4.7b Exergy efficiency different boiler flue gas inlet temperature

FGi Iboiler

kW

Iturbine

kW

Icondenser

kW

Ipump

kW

Iexhaust

kW

ISUM,

kW

ExergyEfficiency(%)

900 192184.9 111132.20 28199.74 4334.51 13075.68 348927.1 59.261000 240171.2 111132.20 28199.74 4334.51 13075.68 396913.3 60.461100 283220.8 111132.20 28199.74 4334.51 13075.68 439962.9 61.961200 323327.8 111132.20 28199.74 4334.51 13075.68 480069.9 63.471300 379198.1 111132.20 28199.74 4334.51 13075.68 535940.1 65.201400 414314.7 111132.20 28199.74 4334.51 13075.68 571056.9 67.34

As the boiler flue gas inlet temperature increases from 9000C to 14000C,

the energy efficiency does not change due to increase of flue gas

temperature, exergy value of the boiler entrance EA, enthalpy of the flue

gas entry hA are increases and exergy value at the boiler exit, EB,

enthalpy of the flue gas exit hB, mass of the steam, enthalpy of the flue

gas exit hB are does not vary and mass of the flue gas decreases of the

given boiler flue gas inlet temperature exit for the given 1000 MW

85

capacity. Further, irreversibility of the boiler increases; irreversibility of

the turbine, condenser, pump and exhaust does not change as the

increase of boiler flue gas inlet temperature and there by total

irreversibility of the boiler increases. Hence, exergy efficiency increases

with an increase of flue gas temperature and are shown in the Table 4.7a

and 4.7b.

On further careful observation, the total exergy loss at boiler flue gas

temperature at different turbine inlet temperature at a turbine inlet

pressure presented in the Table 4.7b. However, the values of total exergy

loss are plotted in Fig.4.18.

300

350

400

450

500

550

600


0C)

Tota

l exe

rgy

loss

(MW

)

500550600650700750800

Fig. 4.18 Variation of total exergy loss of SCRC on boiler flue gas inlettemperature of different turbine inlet temperature

T1,(0C)

P1=350bar,Pc=0.05bar,TFGo =1000C

86

For 1000 MW capacity power plant the effect of varying the inlet flue gas

temperature of the boiler on FEL of all the components has been

presented in Figure 4.19.

0

10

20

30

40

50

60

70

900 1000 1100 1200 1300 1400

Boiler flue gas inlet temperature(0C)

Frac

tion

al E

xerg

y Lo

ss(%

)

Boiler TurbineCondenser PumpExhaust

Fig 4.19 Variation of fractional exergy loss with boiler flue gas inlettemperature

It may be noted from the figure 4.19 that, FEL of the boiler was found

vary 59.45% to 57.82% as flue gas inlet temperature from 9000C to

14000C. However, FEL of the turbine decreases from 29.86% to 16.74%

with an increase of boiler flue gas inlet temperature. FEL of exhaust

rapidly increases from 1.94% to 20.53% with an increase of flue gas inlet

temperature. FEL of the condenser decreases from 7.58% to 4.25% and

FEL of the pump is negligible.

T1=7000C,P1=350barPc=0.05bar,TFGo =1000C

87

4.7.6 Effect of boiler flue gas outlet temperature on exergyefficiency

For 1000 MW power generation from steam power plant at steam turbine

inlet pressure of 350 bar and steam turbine inlet temperature of 7000C

the values of energy efficiency, exergy efficiency, irreversibilities in all the

components, mass flow rates of steam and flue gas at different flue gas

exit temperatures from 800C to 3000C have been formed and presented

in the Table 4.8a and 4.8b.

Figure 4.20 represents the variation of exergy efficiency of boiler flue gas

outlet temperature of different turbine inlet temperature, at a turbine

inlet pressure of 350 bar and at boiler flue gas inlet temperature of

10000C.

30

35

40

45

50

55

60

65

70

80 100 150 200 250 300Boiler flue gas outlet Temperature(

0C)

Exe

rgy

effic

ien

cy(%

) 500550600650700750800

TFGi =10000C,P1=350bar

T1,(0C)

88

Fig. 4.20 Variation of exergy efficiency of SCRC on boiler flue gas outlettemperature of different turbine inlet temperature

It may be observed from the figure 4.20 that, the exergy efficiency

decreases with an increase in flue gas inlet temperature and may be

noted that the maximum exergy efficiency occurs at a boiler flue gas

outlet temperature of 800C. The values of exergy efficiency of boiler flue

gas outlet temperature of 800C at turbine inlet temperatures of 5000C,

6000C, 7000C and 8000C are 60.58%, 62.86%, 65.22% and 67.66%

respectively.

Figure 4.21 shows the variation of exergy efficiency of boiler flue gas

outlet temperature of different turbine inlet pressure, at a turbine inlet

temperature of 7000C and at boiler flue gas inlet temperature of 10000C.

35

40

45

50

55

60

65

70

80 100 150 200 250 300Boiler flue gas outlet temperature(

0C)

Exe

rgy

effic

ien

cy(%

)

225

300

400

425

TFGi =10000C,T1=7000C

P1,(bar)

89

Fig. 4.21 Variation of exergy efficiency of SCRC on boiler flue gas outlettemperature of different turbine inlet pressure

It may be noted from the figure 4.21 that, the exergy efficiency decreases

with an increase in flue gas inlet temperature. It may be noted that the

maximum exergy efficiency occurs at a boiler flue gas outlet temperature

of 800C. The values of exergy efficiency of boiler flue gas outlet

temperature of 800C at turbine inlet pressures of 225bar, 250bar,

300bar, 350 bar, 400 bar and 425bar are 61.69%, 62.01%, 62.32%,


At given each turbine inlet temperatures/pressure the values of exergy of

the flue gas at the boiler entry (EA), exergy of the flue gas at boiler exit

(EB) and irreversibilities in all the components are estimated and are

shown in Table 4.8a and 4.8b, this may be the possible reason to

increasing the exergy efficiency with an increase of boiler flue gas outlet

temperature from 800C to 3000C at a given turbine inlet temperature of

7000C and a given steam turbine inlet pressure.

Table 4.8a Energy efficiency, enthalpy, exergy, different boiler flue gas inlettemperature

FGo EnergyEfficiency

(%)

ms

(kg/secmg

(kg/sec) HA

kJHB

kJEA

kJEB

kJ

80 43.18 656.406 1.375947 1770892.63 87771.67 1003827.38 7231.65100 43.18 656.406 1.403148 1770892.63 120400.21 1003827.38 13075.68150 43.18 656.406 1.477369 1770892.63 203318.22 1003827.38 33823.10200 43.18 656.406 1.561598 1770892.63 287869.78 1003827.38 62097.98250 43.18 656.406 1.657758 1770892.63 373893.91 1003827.38 96560.63300 43.18 656.406 1.768100 1770892.63 461076.66 1003827.38 136312.89

90

As the boiler flue gas outlet temperature increases from 800C to 3000C,

the energy efficiency does not change due to increase of boiler flue gas

outlet temperature, exergy value of the boiler entrance EA, enthalpy of the

flue gas entry hA are does not vary and exergy value at the boiler exit, EB,

enthalpy of the flue gas exit hB, are increasing with increase of boiler flue

gas temperature exit for the given 1000 MW capacity.

Table 4.8b Exergy efficiency different boiler flue gas inlet temperature

FGo Iboiler

kW

Iturbine

kW

Icondenser

kW

Ipump

kW

Iexhaust

kW

ISUM,

kW

ExergyEfficiency(%)

80 233066 111132 28199.7 4334.51 7231.65 383964 61.75100 240171 111132 28199.7 4334.51 13075.70 396913 60.46150 271623 111132 28199.7 4334.51 33823.10 449112 55.26200 295145 111132 28199.7 4334.51 62098.00 500910 50.10250 315994 111132 28199.7 4334.51 96560.60 556221 44.59300 334664 111132 28199.7 4334.51 136313.0 614644 38.77

Further, irreversibility of the boiler increases; irreversibility of the

turbine, condenser and pump does not change and irreversibility of

exhaust increases rapidly with an increase of boiler flue gas inlet

temperature, and there by total irreversibility of the boiler increases.

Hence, exergy efficiency increases with an increase of flue gas

temperature and are shown in the Table 4.8a and 4.8b.

On further careful observation, the total exergy loss at boiler flue gas

temperature at different turbine inlet temperature at a turbine inlet

pressure presented in the Table 4.8b. However, the values of total exergy

loss are plotted in Fig.4.22.

91

300

350

400

450

500

550

600

650

700


0C)

Tota

l Exe

rgy

loss

, MW

500 550 600650 700 750800

Fig. 4.22 Variation of exergy efficiency of SCRC on boiler flue gas outlettemperature of different turbine inlet temperature

Figure 4.23 represents variation of fractional exergy loss as function of

flue gas outlet temperature.

It may be noted fractional exergy loss of the boiler was found to be vary

59.45% to 57.82%. FEL of the turbine decreases from 29.86% to 16.74%.

FEL of exhaust has significant effect on the boiler flue gas outlet

temperature, which increases from 1.94% to 20.53% with increase of

boiler flue gas outlet temperature from 800C to 3000C. FEL of the

condenser decreases from 7.58% to 4.25% and FEL of the pump is nearly

1%.

TFGi =10000C,TFGo =1000CP1=350bar

T1,(0C)

92

0

10

20

30

40

50

60

70


0C)

Frac

tion

al E

xerg

y Lo

ss BoilerTurbineCondenserPumpExhaust

Fig 4.23 Variation of fractional exergy loss with flue gas outlet temperature

T1=7000C,P1=350barPc=0.05bar,TFGi =10000C

THERMODYNAMIC ANALYSIS OF SUPERCRITICAL RANKINE...

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