Exergy and exergoeconomic analyses of a novel integration of a 1000 MW pressurized water reactor power plant and a gas turbine cycle through a superheater

Annals of Nuclear Energy 115 (2018) 161–172

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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene

Exergy and exergoeconomic analyses of a novel integration of a 1000 MW pressurized water reactor power plant and a gas turbine cycle through a superheater S.M. Seyyedi a,⇑, M. Hashemi-Tilehnoee b, M.A. Rosen c a b c

Department of Mechanical Engineering, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran Department of Nuclear Engineering, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran Faculty of Engineering and Applied Science, University of Ontario Institute of Technology (UOIT), 2000 Simcoe Street North, Oshawa, ON L1H 7K4, Canada

a r t i c l e

i n f o

Article history: Received 8 October 2017 Received in revised form 14 January 2018 Accepted 20 January 2018

Keywords: Exergy Exergoeconomic Gas turbine Pressurized water reactor Combined cycle Cost rate

a b s t r a c t Combined cycles are used for various reasons, including to increase the efficiency of power generation system. In this study, a gas turbine cycle is combined with a pressurized water reactor (PWR) power plant to increase the total plant efficiency. In this novel cycle, saturated steam produced in the steam generators of the nuclear power plant is superheated by the hot combustion gases exiting the gas turbine. An exergoeconomic analysis is carried out and the effects of compressor pressure ratio and gas turbine inlet temperature are investigated on the net power output, the first and second law efficiencies, the total cost rate and the specific cost of the produced work. The results show that there is an optimum pressure ratio for each gas turbine inlet temperature. The combined cycle total cost rate and the specific cost of the produced work for a gas turbine inlet temperature of 1500 K and a compressor pressure ratio of 13 are determined to be 41,882 $/h and 31.63 $/MWh, respectively. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction To move toward energy sustainability and to address limitations for many conventional energy resources, increased efficiency is usually desirable for power generation systems. Combined cycles can help achieve such aims, as they can help increase the net electrical power output, decrease the fuel consumption and increase the efficiency. The most common combined cycles include Rankine and Brayton cycles (i.e., an integration of a steam turbine cycle and a gas turbine cycle). For the combined cycle considered here, the exhaust gas from the Brayton gas cycle passes through a heat recovery steam generator (HRSG) to produce steam. A Rankine steam cycle uses the produced steam as working fluid. Exergy is an important concept related to the second law of thermodynamics and is defined as the maximum useful work that it can be obtained from a flow of matter or energy in a reference environment. Exergy analysis characterizes the thermodynamic performance of an energy system and determines the efficiency of system components by quantifying their entropy generation (Kwak et al., 2003). The combination of exergy analysis with economics is the branch in engineering known as exergoeconomic or ⇑ Corresponding author. E-mail address: [email protected] (S.M. Seyyedi). https://doi.org/10.1016/j.anucene.2018.01.028 0306-4549/Ó 2018 Elsevier Ltd. All rights reserved.

thermoeconomic analysis. This technique helps the designer to provide information that is not available through economic evaluation and conventional energy analysis (Sahoo, 2008). Many researchers have analyzed combined cycles. Erlach et al. (1999) proposed a structural theory of thermoeconomics and applied it to a 305 MW combined cycle power plant. Kwak et al. (2003) thermo-economically analyzed a 500-MW combined cycle plant. Two criteria for allocations of residue costs of combined cycles have been proposed by Torres et al. (2008) and Seyyedi et al. (2010a). Critical reviews of exergy and exergoeconomic analyses have been reported by Vieira et al. (2004, 2005, 2006), Torres et al. (2008), Sahoo (2008), Zhang et al. (2006), Lazzaretto and Tsatsaronis (2006). However, exergoeconomic analysis and optimization have been utilized in limited ways on nuclear power plants. Using the second law of thermodynamics, the irreversibility of nuclear reactors has been calculated by Gyftopoulos and Beretta (1991). The irreversibility of a fast breeder reactor (FBR) nuclear power plant has also been investigated by Seigel (1970). Dunber et al. (1995) analyzed the exergy of a boiling water reactor (BWR) nuclear power generation plant. A typical pressurized water reactor (PWR) nuclear power plant has been exegetically analyzed by Sayyadi et al. (2007). Sayyadi and Sabzaligoll (2009) thermoeconomically analyzed a typical 1000 MW pressurized water reactor nuclear

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Nomenclature c cf cQ cW C CRF e E_ E_ D E_ Loss;T F h LHV _ m p P PEC PB PR Q_ R s T TIT _ net W _ net;GT W _ net;ST W Z_ T

gI

cost per unit exergy ($/kJ) fuel cost per unit energy ($/MJ) nuclear fuel cost per unit thermal exergy of reactor ($/ kJ) specific cost of produced work ($/MWh) exergoeconomic cost rate ($/h) capital recovery factor specific exergy (kJ/kg) exergy flow rate (kW) exergy destruction rate (kW) total exergy loss rate (kW) fuel exergy rate of a component (kW) specific enthalpy (kJ/kg) lower heating value of fuel (kJ/kg) mass flow rate (kg/s) pressure (kPa) product exergy rate of a component (kW) purchase equipment cost ($) Inlet pressure of steam turbine (MPa) pressure ratio thermal exergy rate generated by reactor (MW) specific entropy (kJ/kg .K) temperature (°C or K) gas turbine inlet temperature (K) net power output of combined cycle (MW) net power output of gas turbine cycle (MW) net power output of steam turbine cycle (MW) investment cost rate ($/h) first law efficiency

power plant and then proposed some optimization approaches for the plant. An intelligent optimization algorithm has been used for multi-objective thermoeconomic optimization of a PWR power plant which has been integrated with a multi-stage desalination facility (Khoshgoftar Manesh and Amidpour, 2009). A similar thermoeconomic optimization was applied to a desalination system coupled with a typical 1000 MW PWR nuclear power plant (Ansari et al., 2010). Chending et al. (2014) proposed and analyzed an ammonia water power/refrigeration co-generation system incorporating a high-temperature gas cooled reactor and a gas turbine cycle energetically and exegetically. Alsairafi (2012) analyzed the energy and exergy characteristics of a hybrid combined cycle nuclear power plant. Khalid et al. (2016) proposed two systems including CANDU 6 and sodium-cooled fast reactors for power production, integrated with reverse osmosis for desalination. On the basis of overall plant exergy efficiency, the sodium-cooled fast reactor based system is found to be more efficient. Stanek et al. (2016) analyzed the multiple design criteria of various power technologies, taking into account thermo-ecological cost, direct and cumulative emissions, and economic evaluation. The environmental and ecological comparison of the nuclear power plant with the existing conventional coal and gas plants requires the evaluation of the overall life cycle of electricity generation. Using exergy analysis, the nuclear power plants are competitive technologies for coal or gas installation and should be taken into account in energy planning and policy development for energy generation. Energy and exergy analyses of a VVER type nuclear power plant have been carried out by (Terzi et al., 2016). The thermodynamic efficiency of this reactor is found as 30%. The leading irreversibilities are encountered in the pressure vessel and the steam generator, which represent 49% and 13% of the total irreversibilities, respectively. Edwards et al. (2016) proposed various thermal energy storage

Greek letters isentropic efficiency w exergy efficiency of cycle 2 effectiveness of superheater e exergy efficiency s annual number of operation hours (h)

g

Subscripts 0 reference environment (reference state) AC air compressor CC combustion chamber cond condenser f fuel GT gas turbine In inlet Out outlet P1 condensate pump P2 boiler feed water pump SG steam generator SH superheater ST steam turbine T total Superscript OM operation and maintenance

methods for small modular nuclear reactors, in part based on exergy and energy density analyses of the thermal energy storage integration with nuclear power plants. Thermal energy storage options such as synthetic heat transfer fluids perform well for light-water-cooled nuclear power plants, whereas liquid storage salt exhibits better performance with advanced nuclear power plants. An assessment of the economy of combined nuclear–gas power plants was performed by Florido et al. (2000). Combining an AP600 nuclear power plant steam cycle with gas turbines has been performed by Darwish et al. (2010). The power cost of the modified AP600 was predicted to be $49.83/MWh where they considered simple gas turbines with fixed power output. Wibisono and Shwageraus (2016), have investigated the thermodynamic performance of a hybrid system (PWR with superheater) for the large reactor and small modular reactor (SMR) application. They considered two schemes for coupling, using exhaust gas from the gas turbines (CCGT concept) and using the conventional gas burner, the nuclear power plant with gas turbine cycle. However, they concluded that CCGT is the best option. In most of these works, saturated steam is produced in the steam generator and then used in the steam turbine for producing electrical power. In the present work, the gas turbine cycle is combined with a PWR nuclear power plant. The saturated steam is superheated by output gases from a gas turbine cycle in a superheater and used in the steam turbine. The main objective of this article is to carry out exergoeconomic analyses for the novel combined cycle to improve understanding of its economic behavior by investigating the effects of air compressor pressure ratio (PR) and gas turbine inlet temperature (TIT) on the system total cost rate and the specific cost of the produced work.

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of the proposed combined cycle. The nuclear power plant includes two main cycles. The first cycle is radioactive coolant cycle (primary loop) and the second is a steam cycle (secondary loop). In the primary loop, thermal energy is released through the fission reaction of nuclear fuel in the reactor core. The coolant (light water) removes the heat generated by fission from the fuel rods. Then, the heat is transferred through the steam generators from the first loop to the second loop. Further details of the nuclear cycle can be found in Sayyadi and Sabzaligoll (2009). Saturated steam is produced in the steam generator and can be superheated by output gases from gas turbine cycle in a superheater. Then the superheated steam is directed to the steam turbine. Mass, energy and exergy balances for each component of the power plant are developed. Appendix A gives these equations for each component of the power plant. The first law efficiency

The main novelty of the research reported herein is twofold. First, the nature of the integrated energy system proposed is unique, and, to the best of the authors’ knowledge, not yet considered. Second, exhaustive investigations of the system are carried out using both exergy and exergoeconomic analyses. Such analyses have not been reported on the system considered, even though the yield many insights on the technoeconomic performance, and thus provide useful information for researchers and designers.

2. Method and materials 2.1. Thermodynamic model The combined cycle includes an open gas turbine cycle coupled with a PWR nuclear power plant. Fig. 1 shows the physical model

7A

7B

CC

CC

2A

3A

2B

3B

9A

9B

8A

8B GT

GT

AC

1

AC

1A

1

1

6

1B Air

4A Air

4B

Stack Superheater 4

5

18

19

12

. QR

24 ST SG

Reactor

21

11

Pump

10

1

21

26

Deaerator

Cond

13 17

16

15

P2

23

P2

22

Fig. 1. Physical structure of the proposed nuclear combined cycle.

25

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and second law efficiency (exergy efficiency) for the combined cycle are defined respectively as:

gI ¼

_ net;GT þ W _ net;ST 2W _ f LHV þ Q_ R 2m

No. of component

ð1Þ

_ net;GT þ W _ net;ST 2W W¼ _ _ 2  mf ef þ Q R  E_ Loss;T

ð2Þ

Note that the total inflow exergy of nuclear fission in the reactor is approximated by the heat released from the reaction, i.e. efiss ffi qfiss ffi cv T fiss (Sayyadi and Sabzaligoll, 2009). 2.2. Exergoeconomic analysis Energy and exergy rate balance equations for each component are summarized in Table 1. For each component, the exergy rate balances include the exergy destruction rates. Table 2 lists the definition the fuel and product for each component (more details are included in Bejan et al. (1996)). The exergy efficiency for each component can be defined as:

ek ¼ Pk =F k ¼ 1  E_ D;k =F k

ð3Þ

The cost rate balance equation of a component of an energy system is written as follows (Bejan et al., 1996): n m X X ðcj E_ j Þk;in þ Z_ k ¼ ðcj E_ j Þk;out j¼1

Table 2 Fuel and product for system components.

ð4Þ

Component

Fuel

1

AC

F AC

2

CC

F CC

3

GT

4

SH

5

Stack

6

Reactor

7

SG

8

Pump

9

P1

10

P2

11

ST

12

Deaerator

13

Condenser

Z_ T ¼

Product

_ AC ¼W ¼ E_ 2 þ E_ 7

F GT ¼ E_ 3  E_ 4 F SH ¼ E_ 4  E_ 5 F Stack ¼ E_ 5

F Reactor ¼ Q_ R F SG ¼ E_ 12  E_ 10 _ Pump F Pump ¼ W _ P1 F P1 ¼ W

_ P2 F P2 ¼ W F ST ¼ E_ 19  E_ 20  E_ 21 F Deaerator ¼ E_ 15 þ E_ 20 F Cond ¼ E_ 21  E_ 14

P AC ¼ E_ 2  E_ 1 P CC ¼ E_ 3

_ GT P GT ¼ W P SH ¼ E_ 19  E_ 18

P Stack ¼ E_ 6 P Reactor ¼ E_ 12  E_ 11 P SG ¼ E_ 18  E_ 17 P Pump ¼ E_ 11  E_ 10 P P1 ¼ E_ 15  E_ 14 P P2 ¼ E_ 17  E_ 16 _ ST P ST ¼ W

P Deaerator ¼ E_ 16 P Cond ¼ E_ 26  E_ 25

m X Z_ k

ð8Þ

k¼1

_ net C_ T ¼ cW W

ð9Þ

In the above equations, cf is the fuel cost per unit energy ðcf ¼ 4 $=GJÞ (Valero et al., 1994; Seyyedi et al., 2010b) and cQ is the nuclear fuel cost per unit thermal exergy of the reactor ðcQ ¼ 0:4 $=GJÞ (Sayyadi and Sabzaligoll, 2009).

j¼1

Here, cj is the unit cost of exergy ($/kJ) for the jth stream to/ from the component, Z_ k ($/s) is the cost rate associated with the capital investment and operating and maintenance expenses for the kth component and E_ j (kW) is the exergy flow rate of the jth stream to/from the component (Sayyadi and Sabzaligoll, 2009). The cost rate balance equations and expressions for the purchase equipment cost for each component are listed in Appendix B. Total cost rate ðC_ T Þ is the objective function. It is the sum of the

fossil fuel cost rate ðC_ F Þ, the nuclear fuel cost rate ðC_ Q Þ and the

investment cost rate ðZ_ T Þ. That is,

C_ T ¼ C_ F þ C_ Q þ Z_ T

ð5Þ

where

_ f cf LHV C_ F ¼ 2  m

ð6Þ

C_ Q ¼ cQ Q_ R

ð7Þ

3. Results and discussion To validate the combined cycle simulation results, a code was developed in MATLAB and applied to the benchmark CGAM cogeneration system (Valero et al., 1994). Then, it was applied to a typical 1000 MW PWR nuclear power plant (Sayyadi and Sabzaligoll, 2009). The results are in good agreement for each case. Some of the key simulation results are described in this paragraph. The net power output of the gas turbine cycle is 2  150 MW. In this analysis, the isentropic efficiencies of the gas turbine and the air compressor are considered to be 87% and 89%, respectively. The compressor pressure ratio (PR) and the gas turbine inlet temperature (TIT) are decision variables. For the PWR cycle, the isentropic efficiencies of the steam turbine and pumps are considered to be 87% and 89%, respectively. The effectiveness of the superheater is considered constant at 92%. For the PWR, the total input thermal power is 2640 MW (Sayyadi and Sabzaligoll, 2009). The steam mass flow rate is calculated by an energy balance of the steam generator (SG). The temperature of the superheated

Table 1 Energy and exergy rate balance equations for components. No. of component

Component

Energy rate balance

Exergy rate balance

1

AC

2

CC

_ AC ¼ m _ air ðh2  h1 Þ W _ f LHV ¼ m _ 3 h3 _ 2 h2 þ gCC m m

3

GT

_ AC E_ D;AC ¼ ðE_ 1  E_ 2 Þ þ W E_ D;CC ¼ E_ 2 þ E_ 7  E_ 3 _ GT E_ D;GT ¼ ðE_ 3  E_ 4 Þ  W

4

SH

5

Stack

6

Reactor

7

SG

_ GT ¼ m _ gas ðh3  h4 Þ W _ steam ðh19  h18 Þ _ gas ðh4  h5 Þ ¼ m m _ 5 h5 _ 6 h6 ¼ m m

E_ D;SH ¼ ðE_ 4  E_ 5 Þ þ ðE_ 18  E_ 19 Þ E_ D;Stack ¼ E_ 5  E_ 6

_ 12 ðh12  h11 Þ Q_ R ¼ m _ 18 ðh18  h17 Þ _ 12 ðh12  h10 Þ ¼ m m

E_ D;Reactor ¼ Q_ R þ ðE_ 11  E_ 12 Þ E_ D;SG ¼ ðE_ 12  E_ 10 Þ þ ðE_ 17  E_ 18 Þ

_ Pump ¼ m _ 10 ðh11  h10 Þ W _ P1 ¼ m _ 14 ðh15  h14 Þ W _ P2 ¼ m _ 16 ðh17  h16 Þ W

_ Pump E_ D;Pump ¼ ðE_ 10  E_ 11 Þ þ W _ P1 E_ D;P1 ¼ ðE_ 14  E_ 15 Þ þ W _ P2 E_ D;P2 ¼ ðE_ 16  E_ 17 Þ þ W

8

Pump

9

P1

10

P2

11

ST

12

Deaerator

_ ST ¼ m _ 19 ðh19  h20 Þ þ m _ 21 ðh20  h21 Þ W _ 20 h20 ¼ m _ 16 h16 _ 15 h15 þ m m

_ ST E_ D;ST ¼ ðE_ 19  E_ 20  E_ 21 Þ  W E_ D;Deaerator ¼ E_ 15 þ E_ 20  E_ 16

13

Condenser

_ 25 ðh26  h25 Þ _ 21 ðh21  h14 Þ ¼ m m

E_ D;Cond ¼ ðE_ 21  E_ 14 Þ þ ðE_ 25  E_ 26 Þ

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740

700

680

660

640

620

PR for various values of TIT is presented in Fig. 2. The net power output of the combined cycle is seen to decline _ net increases with increasing PR for each TIT. For a constant PR, W

600

4

6

8

10

12

14 PR

16

18

20

22

24

Fig. 3. Temperature of superheat steam with respect to pressure ratio (PR) for various values of turbine inlet temperature (TIT).

First law efficiency (%)

37

36

35

34

Second law efficiency (%)

with increasing of TIT. The superheated steam temperature (temperature of stream 19 in Fig. 1) with respect to PR for various values of TIT is presented in Fig. 3. The figure shows that the superheated steam temperature decreases with increasing PR for each TIT, but for a constant PR, it increases with increasing of TIT. Fig. 4 shows the first and second law efficiency for the combined cycle with respect to pressure ratio (PR) for various values of TIT (see Eqs. (1) and (2)). The figure shows that there is a maximum value for the first and second law efficiency corresponding to the optimum value of PR for each TIT. The optimum values of PR are 8, 9 and 11 for TIT = 1300 K, TIT = 1400 K and TIT = 1500 K, respectively. This figure demonstrates that the first and second law efficiency increases with increasing of TIT. Fig. 5 presents the total exergy destruction rate for the combined cycle with respect to pressure ratio (PR) for various values of TIT. This figure shows that there is an optimum PR for each TIT. These values are 16, 19 and 23 for TIT = 1300 K, TIT = 1400 K and TIT = 1500 K, respectively. Therefore, the optimum PR is increased by increasing TIT. Fig. 6 presents the total cost rate for the combined cycle with respect to pressure ratio (PR) for various values of TIT (see Eq. (5)). The figure illustrates that there is an optimum PR for each TIT. This value is 14, 15 and 17 for TIT = 1300 K, TIT = 1400 K, and

TIT = 1300 K TIT = 1400 K TIT = 1500 K

720 Temperature 0f superheat steam (K)

steam can be calculated using the superheater (SH) energy balance equation. The inlet pressure of the steam turbine, the deaerator pressure, and the condenser pressure are 10 MPa, 1.0 MPa and 10 kPa, respectively. Thus the net power output of steam cycle (nuclear power plant) is a dependent variable that is a function of the superheat temperature of the steam. Recall that the objective of this paper is to investigate the effects of PR and TIT on the total power output, the efficiency, the total cost flow rate and the specific cost of the produced work (cw), for the combined cycle. The computational algorithm for the thermodynamic and exergoeconomic calculations is presented in Appendix C. Using the algorithm in Appendix C, various results are obtained. _ net Þ with respect to The net power output of the combined cycle ðW

TIT = 1300 K TIT = 1400 K TIT = 1500 K 4

6

8

10

12

14 PR

16

18

20

22

24

10

12

14 PR

16

18

20

22

24

38 37.5 37 36.5

TIT = 1300 K TIT = 1400 K TIT = 1500 K

36 35.5

4

6

8

Fig. 4. First and second law efficiency for combined cycle with respect to pressure ratio (PR) for various values of turbine inlet temperature (TIT).

Net power output of combined cycle (MW)

1550 TIT = 1300 K TIT = 1400 K TIT = 1500 K

1500

1450

1400

1350

1300

1250

4

6

8

10

12

14 PR

16

18

20

22

24

Fig. 2. Net power output of steam cycle with respect to pressure ratio (PR) for various values of turbine inlet temperature (TIT).

TIT = 1500 K, respectively. It is seen in the figure that the optimum PR is increased by increasing TIT. The specific cost of the produced work (see Eq. (9)) as a function of PR for various values of TIT is illustrated in Fig. 7. The figure shows that for each TIT there is an optimum PR. These optimum values increase with increasing TIT, and are 11, 12 and 13 for TIT values of 1300 K, 1400 K and 1500 K, respectively. A comparison between the Figs. 4–7 shows that the optimum PR is not same based on the first or second law efficiency, the total exergy destruction rate, the total cost rate and the specific cost of the produced work for each TIT. For example, the values of the optimum PR are 8, 16, 14 and 11 based on these parameters, for TIT = 1300 K, respectively. Thus the selection of the PR depends on the goal of the designer. If the first law efficiency is deemed to be more important than the total exergy destruction rate, the total cost rate and the specific cost of the produced work, PR = 8 should be selected. If the total cost rate is more important than others, PR = 14 should be selected and so on. For better comparison, the optimum pressure ratios are represented in Table 3.

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S.M. Seyyedi et al. / Annals of Nuclear Energy 115 (2018) 161–172 2600

36 TIT = 1300 K TIT = 1400 K TIT = 1500 K

2550

35 Specific cost ($ / (MW.h)

Exergy destruction (MW)

2500 2450 2400 2350 2300

34.5 34 33.5 33

2250

32.5

2200

32

2150

TIT = 1300 K TIT = 1400 K TIT = 1500 K

35.5

4

6

8

10

12

14 PR

16

18

20

22

24

Fig. 5. Total exergy destruction rate for combined cycle with respect to pressure ratio (PR) for various values of turbine inlet temperature (TIT).

31.5

4

6

8

10

12

14 PR

16

18

20

22

24

Fig. 7. Specific cost of the produced work for combined cycle with respect to pressure ratio (PR) for various values of turbine inlet temperature (TIT).

4

5.4

x 10

Table 3 Optimum pressure ratio (PR) for various objective functions at different TIT.

TIT = 1300 K TIT = 1400 K TIT = 1500 K

5.2

Total cost rate ($ / h)

5

4.8

Objective function

TIT = 1300 K

TIT = 1400 K

TIT = 1500 K

First or second law efficiency ðgI orwÞ Total exergy destruction rate ðE_ D;T Þ

8 16

9 19

11 23

Total cost rate ðC_ T Þ Specific cost of the produced work ðcW Þ

14

15

17

11

12

13

4.6

4.4

cost of the produced work as the objective function, i.e. optimum conditions at Fig. 7). Table 6 shows the investment cost rate ðZ_ T Þ, the nuclear fuel

4.2

4

4

6

8

10

12

14 PR

16

18

20

22

24

Fig. 6. Cost rate for combined cycle with respect to pressure ratio (PR) for various values of turbine inlet temperature (TIT).

Table 4 lists the values of exergy destruction rate, fuel exergy rate, product exergy rate and exergy efficiency for each component at TIT = 1500 K and PR = 13 (optimum pressure ratio in Fig. 7, i.e. the specific cost of the produced work is selected as the objective function). Fig. 8 shows the values of fossil fuel cost rate ðC_ F Þ, nuclear fuel

cost rate ðC_ Q Þ, investment cost rate ðZ_ T Þ and the sum of these values, i.e., the total cost rate ðC_ T Þ, at the optimum PR for each TIT (based on the total cost rate as the objective function). Fig. 9 presents the values of the specific cost of the produced work at the optimum PR for each TIT (based on the total cost rate as the objective function, too). The figure shows that the specific cost of the produced work decreases with increasing PR and TIT at the optimum conditions. Table 5 presents the total input thermal power, the mass flow rate of fossil fuel, the net power output of the gas turbine cycle, the net power output of the steam turbine cycle, the net power output of combined cycle, and the first and second law efficiencies for the combined cycle at TIT = 1500 K and PR = 13 (based on the specific

cost rate ðC_ Q Þ, the fossil fuel cost rate ðC_ F Þ, the total cost rate ðC_ T Þ and specific cost of the produced work ðcW Þ for the combined cycle at TIT = 1500 K and PR = 13. In Appendix D, thermodynamic properties of the combined cycle (the state of each stream) are shown for PR = 13 and TIT = 1500 K (1226.9 °C). These are corresponding to optimum conditions based on the minimum of the specific cost of the produced work. As seen in Table 6, the specific cost of the produced work ðcW Þ is equal to 31.63 $/MWh. For the base case design (nuclear power plant without superheater), this value is cW ¼ 8:527 $=GJ ¼ 30:697 $=MWh (see the last row of Table VII in Sayyadi and Sabzaligoll, 2009). But the net power output is 1024 MW and 1324.3 MW for the base case design and the combined cycle (present work), respectively. Therefore, the net power output increases 29.33% while the specific cost of the produced work increases only 3.04%. It should be noted that the first law efficiency and the specific cost of gas turbine cycle are 30.77% and 50.013 $/MWh, respectively. But, the first law efficiency for combined cycle is 36.63% (see Table 5). Fig. 10 presents the values of the superheated steam temperature at two values of PR (PR = 13 and PR = 17) for TIT = 1500 K at different values of gas turbine power. The figure shows that the superheated steam temperature increases with increasing of gas turbine power. In this figure, the saturation temperature is 584 K (corresponding to PB = 10 MPa). Fig. 11 presents the values of the specific cost of the produced work and the net power output of the combined cycle at two

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S.M. Seyyedi et al. / Annals of Nuclear Energy 115 (2018) 161–172 Table 4 Rates of exergy destruction, fuel exergy and product exergy and exergy efficiencies for components at TIT = 1500 K and PR = 13. No. of component

Component

Fuel Rate (MW)

Product Rate (MW)

Exergy Destruction Rate (MW)

Exergy Efficiency (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 Total combined cycle

AC CC GT SH Stack Reactor SG Pump P1 P2 ST Deaerator Condenser

165.75 662.41 354.03 232.26 102.36 2640 1318.5 23.48 1.17 15.59 1234.1 246.51 126.66 3517.3

156.89 521.34 315.75 178.07 100.78 1301 1238.3 17.51 0.93 14.49 1064.5 175.45 33.09 1324.3

8.86 141.07 38.28 54.19 1.58 1339 80.2 5.97 0.24 1.10 169.6 71.06 93.57 2193a

94.65 78.70 89.19 76.67 98.45 49.28 93.92 74.57 78.90 92.93 86.26 71.18 26.12 37.65

a: To obtain the total exergy destruction (that is equal to sum of the exergy destruction for each component, too), the exergy destruction of AC, CC and GT must be multiplied P by 2. E_ D;Total ¼ E_ F;Total  E_ P;Total ¼ ni¼1 E_ D;k

4.5

x 10

4

CQ CF

4

ZT 3.5

CT

Cost rate ($ / h)

3 2.5 2 1.5 1

to increasing of the net power output of the combined cycle from 971.4 MW to 1324.3 MW (36.33% increasing) while the specific cost of the produced work increase from 28.97 $/MWh to 31.63 $/MWh (only 9.18% increasing). Fig. 12 shows the values of the specific cost of the produced work at two values of PR (PR = 13 and PR = 17) for TIT = 1500 K at different values of inlet pressure of steam turbine (PB). The figure shows that the specific cost of the produced work decreases with increasing inlet pressure of steam turbine. The value of 6.85 MPa for inlet pressure of steam turbine has been selected from Sayyadi and Sabzaligoll (2009).

0.5

4. Conclusion 0

1 1: TIT = 1300 K and PR = 14

2 2: TIT = 1400 K and PR = 15

3 3: TIT = 1500 K and PR = 17

Fig. 8. Fossil fuel cost rate ðC_ F Þ, nuclear fuel cost rate ðC_ Q Þ, investment cost rate ðZ_ T Þ and total cost rate ðC_ T Þ at optimum pressure ratio (PR) for each turbine inlet temperature (TIT).

34

Specific cost ($ / (MW.h)

33.5

33

32.5

32

31.5

31 1 1: TIT = 1300 K and PR = 14

2 2: TIT = 1400 K and PR = 15

3 3: TIT = 1500 K and PR = 17

Fig. 9. Specific cost of the produced work at the optimum pressure ratio (PR) for each turbine inlet temperature (TIT).

values of PR (PR = 13 and PR = 17) for TIT = 1500 K at different values of gas turbine power. The figure shows that for a constant PR, (for example PR = 13) increasing of gas turbine power from 30 MW to 150 MW, leads

A novel configuration is proposed of a gas turbine cycle combined with a pressurized water reactor nuclear power plant. The effects of compressor pressure ratio and gas turbine inlet temperature on the net power output, the first and second law efficiencies and the total cost rate are investigated. The results show that each gas turbine inlet temperature is proportional to an optimum pressure ratio. For the specific cost of the produced work, the values of the optimum pressure ratio are found to be 11, 12 and 13 for turbine inlet temperatures of 1300 K, 1400 K, and 1500 K, respectively. The optimum pressure ratio increases with increasing of turbine inlet temperature. Also, the total cost rate and the specific cost of the produced work for the combined cycle for a turbine inlet temperature of 1500 K and a pressure ratio of 13 are found to be 41,882 $/h and 31.63 $/MWh, respectively. The results of the exergoeconomic analyses show that the integration of a PWR power plant with a gas turbine cycle can potentially improve the competitiveness of nuclear energy compared to the single gas turbine power plants. In future, the study can be extended to analyses the combination of generation-IV nuclear power plants with different thermodynamic cycles (i.e. Organic Rankine cycle, hydrogen production, desalination, etc). Appendix A. Physical and thermodynamic models Here we present the equations that constitute the physical model of the combined cycle. The specific energy and exergy of the air, gas, water and steam streams are calculated with Eqs (A.59)–(A.63). Table A1 presents some of the properties of the air and fuel.

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Table 5 Total input thermal power, mass flow rate of fossil fuel, net power output of gas turbine cycle, net power output of steam turbine cycle, net power output of combined cycle, and first and second law efficiencies for combined cycle at TIT = 1500 K and PR = 13. Q_ Reactor ðMWÞ

_ Fuel ðkg=hrÞ m

_ net;GT ðMWÞ W

_ net;ST ðMWÞ W

_ net ðMWÞ W

gI ð%Þ

w ð%Þ

2640

2  35098.92

2  150

1024.3

1324.3

36.63

37.65

Table 6 Investment cost rate ðZ_ T Þ, nuclear fuel cost rate ðC_ Q Þ, fossil fuel cost rate ðC_ F Þ, total cost rate ðC_ T Þ and specific cost of the produced work ðcW Þ for combined cycle at TIT = 1500 K and PR = 13. Z_ T ð$=hÞ

C_ Q ð$=hÞ

C_ Fuel ð$=hÞ

C_ T ð$=hÞ

cW ð$=MWhÞ

24,041

3801.6

14,040

41882.6

31.627

ðA:1Þ

gAC

P2 kair  1 and cair ¼ kair P1

ðA:2Þ

P1 ¼ P0 and T 1 ¼ T 0

ðA:3Þ

_ AC ¼ m _ air cp;air ðT 2  T 1 Þ W

ðA:4Þ

Combustion Chamber (CC):

2×30 MW 2×50 MW 2×150 MW 2×250 MW

_ air þ m _ fuel _ gas ¼ m m

ðA:5Þ

680

_ fuel ) m _ gas ¼ ð1 þ AFÞm _ fuel _ air =m AF ¼ m

ðA:6Þ

660

_ air h2 þ m _ fuel LHV ¼ m _ gas h3 þ Q_ CC m

700 Superheat Temperature (K)

  1 T2 ¼ T1 1 þ ½PRcair  1

where PR ¼

TIT = 1500 K 720

Air Compressor (AC):

where LHV

¼ 50; 000 kJ=kg

640

ðA:7Þ

620

_ fuel LHVð1  gCC Þ where gCC ¼ 0:98 Q_ CC ¼ m

ðA:8Þ

600

AF ¼ ðgCC LHV  h3 Þ=ðh3  h2 Þ

ðA:9Þ

k ¼ n_ fuel =n_ air ¼ ðM air =M fuel Þ=AF

ðA:10Þ

P2 ¼ P1  PR

ðA:11Þ

P3 ¼ P2 ð1  DPcc Þ where DPcc ¼ 0:05 bar

ðA:12Þ

P6 ¼ P0

ðA:13Þ

580 1

2 2: PR = 17

1: PR = 13

Fig. 10. Superheat temperature at PR = 13 and PR = 17 for various gas turbine power and TIT = 1500 K.

Net power output (MW)

Specific cost ($ / MWh)

TIT = 1500 K 34 2 × 30 MW 2 × 50 MW 2 × 150 MW 2 × 250 MW

32 30 28 26

1 1: PR = 13

2 2: PR = 17

1 1: PR = 13

2 2: PR = 17

1600 1400 1200 1000

Fig. 11. Specific cost and net power output at PR = 13 and PR = 17 for various gas turbine power and TIT = 1500 K.

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S.M. Seyyedi et al. / Annals of Nuclear Energy 115 (2018) 161–172

Deaerator:

TIT = 1500 K 34 PB = 6.85 MPa PB = 8 MPa PB = 10 MPa

Specific cost ($ / MWh

33.5

33

_ 20 h20 ¼ m _ 16 h16 _ 15 h15 þ m m

ðA:26Þ

_ 19 ¼ m _ steam and xD ¼ m _ 20 =m _ 19 ) m _ 20 ¼ xD m _ steam m

ðA:27Þ

_ 16 ¼ m _ 17 ¼ m _ 18 ¼ m _ 19 ¼ m _ steam and m _ 14 ¼ m _ 15 ¼ m _ 21 m _ steam ¼ ð1  xD Þm

32.5

ðA:28Þ

_ steam h15 þ xD m _ steam h16 _ steam h20 ¼ m ð1  xD Þm

ðA:29Þ

xD ¼ ðh16  h15 Þ=ðh20  h15 Þ

ðA:30Þ

32

31.5

31

Steam Turbine (ST):

1 1: PR = 13

2 2: PR = 17

Fig. 12. Specific cost at PR = 13 and PR = 17 for different values of inlet pressure of steam turbine (PB). and TIT = 1500 K.

P5 ¼ P6 =ð1  DPStack Þ where DPStack ¼ 0:02bar

ðA:14Þ

P4 ¼ P5 =ð1  DPgasHRSG Þ where DPgasHRSG ¼ 0:03 bar

ðA:15Þ

s20s ¼ s19

ðA:32Þ

     8 > < ifs20s < sg P20 ) x20s ¼ ðs20s  sf P20 Þ=sfg P20 ) h20s ¼ hf P20 þ x20s hfg P20   P 20 superheat steam tables > ¼¼¼¼¼¼¼¼¼¼¼¼¼¼¼¼¼¼¼¼¼) h20s : if sg P20 < s20s ) s20s ðA:33Þ  Note: sg P means specific entropy of saturated steam must be

calculated in pressure of 20th stream.

   cgas  P4 kgas  1 where cgas ¼ T 4 ¼ T 3 1  gGT 1  kgas P3

ðA:16Þ

_ GT ¼ m _ gas cp;gas ðT 3  T 4 Þ W

ðA:17Þ

_ net;GT ¼ 150 MW where W

ðA:18Þ

_ GT  W _ AC ¼ ð1 þ AFÞm _ net;GT ¼ W _ fuel cp;gas ðT 3  T 4 Þ W _ fuel cp;air ðT 2  T 1 Þ  AF m

ðA:19Þ

_ net;GT =½ð1 þ AFÞcp;gas ðT 3  T 4 Þ  AFcp;air ðT 2  T 1 Þ _ fuel ¼ W m

ðA:20Þ

Superheater (SH):

_ gas cp;gas ðT 4  T 5 Þ ¼ m _ steam ðh19  h18 Þ 2m

ðA:21Þ

_ gas cp;gas ðT 4  T 5 Þ Q_ SH ¼ 2  m

SH ¼

ðA:31Þ

20

Gas Turbine (GT):

_ GT  W _ AC _ net;GT ¼ W W

_ ST ¼ m _ 19 ðh19  h20 Þ þ m _ 21 ðh20  h21 Þ W

ðA:22Þ

h20 ¼ h19  gST ðh19  h20s Þ

ðA:34Þ

s21s ¼ s19

ðA:35Þ

8 > < if

s21s < sg

> : if

sg

 P 21

 P 21

< s21s

    ) x21s ¼ ðs21s  sf P Þ=sfg P ) h21s ¼ hf P þ x21s hfg P 21 21 21 21  P 21 superheat steam tables ) ¼¼¼¼¼¼¼¼¼¼¼¼¼¼¼¼¼¼¼) h21s s21s ðA:36Þ

h21 ¼ h19  gST ðh19  h21s Þ

ðA:37Þ

_ ST =m _ 19 ¼ ðh19  h20 Þ þ ð1  xD Þðh20  h21 Þ wST ¼ W

ðA:38Þ

Pump:

_ Pump ¼ m _ 10 ðh11  h10 Þ W

ðA:39Þ

P1:

T4  T5 T 4  T 18

ðA:23Þ

_ P1 ¼ m _ 14 ðh15  h14 Þ W

ðA:40Þ

T 5 ¼ T 4  eSH ðT 4  T 18 Þ

ðA:24Þ

ws;P1 ¼ v 14 ðP15  P14 Þ

ðA:41Þ

_ steam þ h18 h19 ¼ Q_ SH =m

ðA:25Þ

h15;s ¼ ws;P1 þ h14

ðA:42Þ

Table A1 Properties of air and fuel. Atmospheric pressure

P 0 ¼ 1:013 bar

Atmospheric temperature Mole fractions of reference substances for air (with relative humidity = 60%)

T 0 ¼ 25 C x0O2 ¼ 0:2059; x0N2 ¼ 0:7748; x0CO2 ¼ 0:0003; x0H2 O ¼ 0:019 ef ¼ 51; 850 kJ=kg and hf ¼ LHV ¼ 50; 000 kJ=kg

Specific energy and exergy of fuel (methane): Air properties

c

Rair ¼ 0:287kJ=kgK and Rair ¼ cp;air  cv ;air and kair ¼ cvp;air ;air cp;gas cv ;gas

Combustion gas properties

Rgas ¼

Molecular weights of methane and air Reaction of complete combustion:

MCH4 ¼ M f ¼ 16:043 kJ=kmol and M air ¼ 28:648 kJ=kmol

kJ 0:29 kg K

and Rgas ¼ cp;gas  cv ;gas and kgas ¼







kCH4 þ x0O2 O2 þ x0N2 N2 þ x0CO2 CO2 þ x0H2 O H2 O ) k þ x0CO2 CO2 þ 2k þ x0H2 O H2 O þ x0O2  2k O2 þ x0N2 N2

Specific heat capacity of air and combustion products (hot gases) are considered to be functios of temperature that are as follows: (T is in Kelvin) 4 cp;air ¼ 1:04841  3:8371 T þ 9:4537 T 2  5:49031 T 3 þ 7:9298 4 10 14 T 107 10

10

10

cp;gas ¼ 0:991615 þ 6:99703 T þ 2:7129 T 2  1:22422 T3 10 105 107 10

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h15 ¼ h14 þ ðh15;s  h14 Þ=gP1

ðA:43Þ

wP1 ¼ ðh15  h14 Þ

ðA:44Þ

Appendix B. Cost balance equations and purchased equipment cost for each component B.1. Economic model

P2:

_ P2 ¼ m _ 16 ðh17  h16 Þ W

ðA:45Þ

ws;P2 ¼ v 16 ðP17  P 16 Þ

ðA:46Þ

h17;s ¼ ws;P1 þ h16

ðA:47Þ

h17 ¼ h16 þ ðh17;s  h16 Þ=gP2

ðA:48Þ

wP2 ¼ ðh17  h16 Þ

ðA:49Þ

Steam Generator (SG):

_ 18 ðh18  h17 Þ _ 12 ðh12  h10 Þ ¼ m m

ðA:50Þ

_ 12 ðh12  h10 Þ=ðh18  h17 Þ _ 18 ¼ m m

ðA:51Þ

Condenser:

_ 25 ðh26  h25 Þ _ 21 ðh21  h14 Þ ¼ m m

ðA:52Þ

Total Combined Cycle

The principal costs of a thermal system are the capital investment, the operation and maintenance, and the fuel costs. Based on the capital recovery factor (CRF) a simplified economic model can be applied. The total capital investment (TCI) in a plant is given by the sum of all the purchased equipment costs (PEC) multiplied by a constant factor b (Bejan et al., 1996). The total capital investment in a plant is thus given by

TCI ¼

X X X TCIk ¼ bPECk ¼ b PECk k

k

ðB:1Þ

k

The investment cost rate for each component ðZ_ IN k Þ is expressed by

CRFTCIk Z_ IN k ¼

ðB:2Þ

s

n

CRF ¼

ið1 þ iÞ n ð1 þ iÞ  1

ðB:3Þ

where i is the interest rate, n is the useful system life (years), and s is the operating hours in a year. The operation and maintenance cost rate for each component ðZ_ OM Þ can now be expressed by k

wnet;ST ¼ wST  ð1  xD ÞwP1  wP2

ðA:53Þ

_ net;ST ¼ m _ Pump _ steam wnet;ST  W W

ðA:54Þ

_ net;GT þ W _ net;ST _ net ¼ 2  W W

ðA:55Þ

cCRFTCIk Z_ OM ¼ k s

ðB:4Þ

where c is the maintenance factor, here assumed constant. _ is the sumThe system total cost rate, excluding fuel costs ðZÞ IN _ mation over all components of ðZ Þ from Eq. (B.2), and ðZ_ OM Þ from k

Eq. (B.4):

_ net;GT þ W _ net;ST 2W gI ¼ _ f LHV þ Q_ R 2m

ðA:56Þ X X _ OM Z_ T ¼ Z_ k ¼ ðZ_ IN k þ Zk Þ ¼

_ net;GT þ W _ net;ST 2W W¼ _ _ _ f ef þ Q R  ðELoss;Stack þ E_ Los;Cond Þ 2m

k

E_ D;T ¼1 _ _ 2  mf ef þ Q R  ðE_ Loss;Stack þ E_ Los;Cond Þ cW ¼

ðA:57Þ

C_ T _ _ net;ST 2  W net;GT þ W

ðA:58Þ

_ i ei Exergy : ei ¼ ðhi  h0 Þ  T 0 ðsi  s0 Þ and Ei ¼ m

for i

¼ 10  12; 14  21; 25; 26 Here,

the

reference

state

ðA:59Þ is

saturated

liquid

with

kJ kJ and s0 ¼ 0:2244 kg:K . T 0 ¼ 288:75 K; h0 ¼ 63:08 kg

Specific energy and exergy of the air streams (i = 1 and 2):

Energy : hi ¼ cp;air ðT i  T 0 Þ  Exergy : ei ¼ cp;air T i  T 0  T 0 ln

ðA:60Þ 

Ti Pi þ Rair T 0 ln T0 P0

ðA:61Þ

Specific energy and exergy of the gas streams (i = 3,4, 5 and 6) (Kotas, 1995):

Energy : hi ¼ cp;gas ðT i  T 0 Þ

ðA:62Þ

  Ti Pi þ Rgas T 0 ln Exergy : ei ¼ cp;gas T i  T 0  T 0 ln T0 P0 X xij þ Rgas T 0 xij ln 0 where j ¼ O2 ; N2 ; CO2 ; H2 O: ðA:63Þ xj j

k

k

X CRFbð1 þ cÞPECk k

s

ðB:5Þ

The purchased-equipment cost for component k (PECk) can be expressed by

  ek nk _ mk EP;k PECk ¼ Bk expðBk1 TIT þ Bk2 Þ 1  ek

ðB:6Þ

where ek is the component exergetic efficiency and E_ P;k is the product exergetic flow rate of kth component. In Eq. (B.6), TIT is gas turbine inlet temperature, while Bk , Bk1 , Bk2 , nk and mk are component specific constants that are shown in Table B1 (Vieira et al., 2004, 2005, 2006). Note that in this paper the values of the interest rate (i), the useful system life (n), the yearly plant operating hours (s), the maintenance factor (cÞ and constant factor (b) in Eq. (B.5) are considered to be 12.7%, 20 years, 8000 h, 0.06 and 2, respectively (Vieira et al., 2004, 2005, 2006). Also, regarding Eq. (B.3), the capital recovery factor (CRF) is equal to 13.98%. B.2. Cost balance equations Cost balance equations and auxiliary exergoeconomic equations based on the average cost theory (ACT) method (Bejan et al., 1996) for each component are presented in Table B2. Appendix C. Algorithm for thermodynamic and exergoeconomic calculations The algorithm used here for thermodynamic and exergoeconomic calculations is presented.

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S.M. Seyyedi et al. / Annals of Nuclear Energy 115 (2018) 161–172 Table B1 Values of parameters for purchased equipment cost equation (Eq. (B.6)).

a

Componenta

Bk

Bk1

Bk2

nk

mk

AC CC GT SH P1 P2 ST Deaerator Condenser

51.9 299.9 181.3 244435.9 3727.1 23749.0 290591.3 93605.6 1115819.2

– 0.014 0.035 – – – – – –

– -19.898 -53.799 – – – – – –

2.499 1.038 1.450 0.108 2.032 1.269 0.000 0.028 0.074

1.002 1.002 1.004 0.962 0.547 0.554 0.916 0.791 0.962

Fixed values for this factor for the reactor and the remainder of the primary loop are assumed, at 2.15 $/s and 1.62 $/s, respectively (Sayyadi and Sabzaligoll, 2009).

b. Read saturation pressure ðPex Þ corresponding to T ex c. Set P 20 ¼ P ex Step 16. Read values of v f and hf corresponding to PCond and set v 14 ¼ v f and h14 ¼ hf Step 17. Set P 15 ¼ P 16 ¼ P20 Step 18. Calculate ws;P1 ; h15;s ; h15 andwP1 from Eqs. (A.41)–(A.44), respectively Step 19. Read values of v f and hf corresponding to P ex and set v 16 ¼ v f and h16 ¼ hf Step 20. Calculate ws;P2 ; h17;s ; h17 andwP2 from Eqs. (A.46)–(A.49), respectively Step 21. Read the enthalpy and entropy of saturation steam corresponding to P 18 and set these values as h18 and s18 , respectively _ steam _ 18 from Eq. (A.51) and set as m Step 22. Calculate m Step 23. Calculate T 5 from Eq. (A.24) Step 24. Calculate Q_ SH and h19 from Eq. (A.22) and (A.25),

Step 1. Define constant values such as:

_ net;GT ; Q_ Reactor ; . . . P0 ; T 0 ; gAC ; gGT ; gST ; gP1 ; gP2 ; gPump ;SH ; W Step 2. Set P1 ¼ P0 andT 1 ¼ T 0 Step 3. Set PR ¼ 2 and TIT ¼ 1300 K Step 4. Calculate T 2 from Eq. (A.1) Step 5. Calculate h2 and h3 from Eq. (A.60) and Eq. (A.62), respectively Step 6. Calculate AF from Eq. (A.9) Step 7. Calculate P2 , P3 ; P4 , P 5 and P 6 from Eqs. (A.11)–(A.15), respectively Step 8. Calculate T 4 and h4 from Eqs. (A.16) and (A.62), respectively _ fuel and k from Eqs. (A.20) and (A.10), Step 9. Calculate m respectively _ gas from Eq. (A.6) _ air and m Step 10. Calculate m Step 11. Calculate e1 and e2 from Eq. (A.61) and e3 and e4 from Eq. (A.63) Step 12. Set P17 ¼ P18 ¼ P 19 ¼ P B andP14 ¼ P 21 ¼ P Cond Step 13. Read values of saturation temperature corresponding to PB andP Cond from steam tables and set these values as T B andT Cond , respectively. Step 14. Set T 18 ¼ T B Step 15. Calculate⁄ or select P 20 ⁄ A proper value of the pressure of extraction steam ðP20 Þ can be selected between PB and PCond or it can be appropriately calculated as follows: a. Set T ex ¼ ðT B þ T Cond Þ=2

respectively Step 25. Read the temperature and entropy of superheated steam by P 19 and h19 and set these values as T 19 and s19 , respectively Step 26. Calculate h20 and h21 using Eqs. (A.32)–(A.37), respectively Step 27. Calculate xD from Eq. (A.30) _ net;ST ; g andw using Eqs. (A.53)– Step 20. Calculate wnet;ST ; W I

(A.58), respectively Step 21. Calculate exergy for streams 10–12, 14–21, 25 and 26 using Eq. (A.59)

Table B2 Auxiliary exergoeconomic equations and cost rate balance equations based on ACT method. No. of component

Component

Cost rate balance equation

Auxiliary exergoeconomic equations based on ACT method (Bejan et al., 1996)

1

AC

2

CC

C_ 1 ¼ 0 _ f cf ef where cf ¼ 0:004 $=MJ C_ 7 ¼ m

3

GT

C_ 2 ¼ C_ 1 þ C_ 8 þ Z_ AC C_ 3 ¼ C_ 2 þ C_ 7 þ Z_ CC C_ 4 þ C_ 8 þ C_ 9 ¼ C_ 3 þ Z_ GT

_

_

_

_

c3 ¼ c4 ) CE_ 3 ¼ CE_ 4 and c8 ¼ c9 ) CE_ 8 ¼ CE_ 9 3

4

8

4

SH

C_ 5 þ C_ 19 ¼ C_ 4 þ C_ 18 þ Z_ SH

c4 ¼ c5 ) CE_ 4 ¼ CE_ 5

5

Stack

6

Reactor

C_ 6 ¼ C_ 5 þ Z_ Stack C_ 12 ¼ C_ 11 þ C_ Q þ Z_ Reactor

7

SG

C_ 10 þ C_ 18 ¼ C_ 12 þ C_ 17 þ Z_ SG

– C_ Q ¼ cQ Q_ R where cQ ¼ 4  107 $=kJ

8

Pump

C_ 11 ¼ C_ 10 þ C_ 13 þ Z_ Pump

c13 ¼ c24 )

9

P1

C_ 15 ¼ C_ 14 þ C_ 22 þ Z_ P1

c22 ¼ c24 ) CE_ 22 ¼ CE_ 24

10

P2

C_ 17 ¼ C_ 16 þ C_ 23 þ Z_ P2

c23 ¼ c24 ) CE_ 23 ¼ CE_ 24

11

ST

12

Deaerator

13

Condenser

C_ 20 þ C_ 21 þ C_ 24 ¼ C_ 19 þ Z_ ST C_ 16 ¼ C_ 15 þ C_ 20 þ Z_ Deaerator C_ 14 þ C_ 26 ¼ C_ 21 þ C_ 25 þ Z_ Cond

_

9

_

4

5

_

_

c10 ¼ c12 ) CE_ 10 ¼ CE_ 12 10

12

C_ 13 E_ 13

¼ CE_ 24

_

_

24

_

22

_

24

_

23

_

24

_

_

_

c19 ¼ c20 ) CE_ 19 ¼ CE_ 20 and c19 ¼ c21 ) CE_ 19 ¼ CE_ 21 19

20

19

21

– _ _ c14 ¼ c21 ) CE_ 14 ¼ CE_ 21 and C_ 25 ¼ 0 14

21

a. In this system, the number of components and streams are 13 and 26, respectively. Therefore, there are 13 equations; so we need 26–13 = 13 auxiliary equations.

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S.M. Seyyedi et al. / Annals of Nuclear Energy 115 (2018) 161–172

Table D1 Thermodynamic properties of the combined cycle at PR = 13 and TIT = 1500 K (1226.9 °C). No. Stream

T(°C)

P(kPa)

_ mðkg=sÞ

hðkJ=kgÞ

sðkJ=kg:KÞ

exðkJ=kgÞ

ExðMWÞ

1A&1B 2A&2B 3A&3B 4 5 6 7 10 11 12 14 15 16 17 18 19 20 21 25 26

25 387.3 1226.9 673.2 340 340 25 302.5 302.8 326.1 45.8 45.9 179.9 181.4 311 365.7 180 45.8 15 25

101.3 1316.9 1251 107 103 101.3 101.3 15,350 15,800 15,800 10 1000 1000 10,000 10,000 10,000 1000 10 100 100

444.86 444.86 454.6 909.2 909.2 909.2 9.75 19,158 19,158 19,158 1033 1033 1353 1353 1353 1353 320 1033 46,361 46,361

0.0 372.6 1415.5 720.9 336.74 336.74 50,000 1351.7 1353 1490.8 191.8 192.94 762.5 774.1 2725.5 2983.7 2598.5 2072.3 62.92 104.8

0.0 0.11 1.369 1.368 0.793 0.799 0.0 3.2504 3.2515 3.4859 0.649 0.650 2.1381 2.1408 5.6160 6.0406 6.1907 6.5449 0.2244 0.3673

0.0 352.67 1146.8 368.02 112.57 110.85 51,850 386.43 387.35 455.26 2.073 2.97 128.88 139.59 1054.9 1186.6 756.53 124.74 0.0 0.711

0.0 156.89 512.34 167.31 51.178 50.392 505.52 7403.2 7420.7 8721.7 2.141 3.066 174.35 188.84 1427.1 1605.2 242.34 128.80 0.0 33.09

Step 22. Calculate fuel exergy, product exergy, exergy destruction and exergy efficiency for each component using equations in Tables 2 and 3 and Eq. (3) Step 23. Calculate purchased equipment cost (PEC) for each component using Eq. (B.6) and Table B1 Step 24. Calculate CRF from Eq. (B.3) Step 25. Calculate investment cost rate ðZ_ T Þ with Eq. (B.5) Step 26. Calculate exergy cost for each stream, fuel exergy cost and product exergy cost for each component using equations in Table D1 Step 27. Calculate fossil fuel cost rate ðC_ F Þ, nuclear fuel cost rate

ðC_ Q Þ and total cost rate ðC_ T Þ using Eqs. (5) and (6) Step 28. Repeat this procedure for PR = 3, 4,. . ., 24 and TIT = 1400 K and TIT = 1500 K. Appendix D. Calculation of thermodynamic properties

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