Strengthening power generation efficiency utilizing liquefied natural gas cold energy by a novel two-stage condensation Rankine cycle (TCRC) system

Energy Conversion and Management 143 (2017) 312–325

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Strengthening power generation efficiency utilizing liquefied natural gas cold energy by a novel two-stage condensation Rankine cycle (TCRC) system Junjiang Bao, Yan Lin, Ruixiang Zhang, Ning Zhang, Gaohong He ⇑ State Key Laboratory of Fine Chemicals, School of Petroleum and Chemical Engineering, Dalian University of Technology, Panjin 124221, China

a r t i c l e

i n f o

Article history: Received 3 January 2017 Received in revised form 10 March 2017 Accepted 4 April 2017 Available online 12 April 2017 Keywords: Two-stage condensation Rankine cycle Liquefied natural gas Power generation efficiency Genetic algorithms

a b s t r a c t For the low efficiency of the traditional power generation system with liquefied natural gas (LNG) cold energy utilization, by improving the heat transfer characteristic between the working fluid and LNG, this paper has proposed a two-stage condensation Rankine cycle (TCRC) system. Using propane as working fluid, compared with the combined cycle in the conventional LNG cold energy power generation method, the net power output, thermal efficiency and exergy efficiency of the TCRC system are respectively increased by 45.27%, 42.91% and 52.31%. Meanwhile, the effects of the first-stage and second-stage condensation temperature and LNG vaporization pressure on the performance and cost index of the TCRC system (net power output, thermal efficiency, exergy efficiency and UA) are analyzed. Finally, using the net power output as the objective function, with 14 organic fluids (such as propane, butane etc.) as working fluids, the first-stage and second-stage condensation temperature at different LNG vaporization pressures are optimized. The results show that there exists a first-stage and second-stage condensation temperature making the performance of the TCRC system optimal. When LNG vaporization pressure is supercritical pressure, R116 has the best economy among all the investigated working fluids, and while R150 and R23 are better when the vaporization pressure of LNG is subcritical. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction With the development of economy, the contradiction between energy supply and demand is increasingly prominent, and environmental pollution is becoming more and more serious [1]. Natural gas (NG) has been receiving much more attentions in recent years as an environment-friendly energy source because of its high calorific value and less pollution [2,3], and it is widely used in various fields [4]. Under ambient temperature and pressure, NG is gaseous. For the purposes of transport and storage, it must be liquefied to LNG at the atmospheric pressure and temperature of about
162 °C and the volume of LNG is reduced as approximately 600 times than NG, which improves transport efficiency [5].The production of one ton of LNG by liquefying NG requires approximately 292–958 kW h of electric energy [6]. However, LNG must be regasified at the receiving site before it is utilized, and a great amount of cold energy in the LNG regasification process will be released, which is about 830–860 kJ/kg [7]. LNG cold energy is a kind of high ⇑ Corresponding author. E-mail address: [email protected] (G. He). http://dx.doi.org/10.1016/j.enconman.2017.04.018 0196-8904/Ó 2017 Elsevier Ltd. All rights reserved.

quality clean energy. If the efficiency of the LNG cold energy converted to electricity is 100%, one ton of LNG will produce about 240 kWh of electrical energy [2]. In the traditional LNG vaporization process, the LNG cold energy is usually transferred to sea water or air, which results in the extreme waste of energy, and has a great environmental impact on the sea near the regasification site [8]. The effective recovery of the LNG cold energy can not only achieve reasonable utilization of energy, but also reduce environmental pollution. Power generation is a conventional and effective way to utilize LNG cold energy [9]. At present, the traditional methods to generate electricity are the direct expansion (DE), organic Rankine cycle (ORC) and combined cycle (CC), which is the combination of previous two technologies [10]. The direct expansion cycle is simple, but its applications are limited, which is the result of the low LNG cold energy utilization efficiency and the high-pressure application background for NG users. However, organic Rankine cycle and combined cycle have been come into use, which are relatively mature. In early 1979 and 1982, Osaka Gas company in Japan respectively used propane as working fluid for organic Rankine cycle and combined cycle to generate electricity with LNG cold

J. Bao et al. / Energy Conversion and Management 143 (2017) 312–325

313

Nomenclature Q M h W

g

Ex Ex I T

heat transfer rate (kJ/h) mass flow rate (kg/h) mass enthalpy (kJ/kg) power (kW) efficiency (%) mass exergy (kW/kg) exergy (kW) irreversibility loss (kW) temperature (°C)

Abbreviations TCRC two-stage condensation Rankine cycle LNG liquefied natural gas NG natural gas DE direct expansion ORC organic Rankine cycle CC combined cycle Subscripts eva evaporator tur1 turbine 1 tur2 turbine 2

energy, and their power output were 1450 kW and 6000 kW respectively [11]. In view of the extensive application of organic Rankine cycle and combined cycle, the research on the influence factors of LNG power generation efficiency have attracted much attention. Kim et al. [12] analyzed the performance of organic Rankine cycle with seawater as heat source and LNG as cold source, and pointed out that it exists an optimal outlet temperature of the LNG condenser, which makes the system net power output maximized. Wang et al. [13] discussed the impact of condensation temperature, heat source temperature and evaporation pressure on exergy efficiency of organic Rankine cycle using LNG cold energy. When LNG vaporization pressure was 70 bar, Koku et al. [14] found that the thermal efficiency of the combined cycle was 6%, when used propane as working fluid and seawater and LNG cold energy as energy sources. In order to improve the power generation efficiency of LNG cold energy, many researchers have made some improvements in the perspective of the structure of thermodynamic cycle. Angelino et al. [15] and Rao et al. [16] respectively added a regenerator to the organic Rankine cycle and combined cycle to improve the system performance. In addition to this, Szargut and Szczygiel [17] discussed the utilization of LNG cold energy by the regenerative organic Rankine cycle with ethane as working fluid and seawater as the heat source. Two Rankine cycles in series is another method to improve the power generation efficiency of LNG cold energy. Two of these examples are Liu et al. [18] and Li et al. [19].The difference between them is the type of the top cycle. Liu et al. discussed the steam Rankine cycle as the top cycle while Li et al. researched organic Rankine cycle as the top cycle. Because of the large temperature range of LNG vaporization process, LNG cold energy utilization rate of the single-stage condensation process for ORC system is relatively low. In order to make full use of LNG cold energy, Meng et al. [20] proposed two Rankine cycles in parallel. The two parallel Rankine cycles have the same highest temperature but the different condensation temperatures. Shi and Che [21] proposed a combined power system, in which low-temperature waste heat can be efficiently recovered

con1 con2 con sp mix re p1 p2 p3 p4 p5 wf wf1 wf2 sw1 sw2 tot th in out 1–17

condenser 1 condenser 2 condensation splitter mixer reheater feed pump 1 feed pump 2 sea water pump 3 sea water pump 4 LNG pump 5 working fluid flow into evaporator working fluid flow into condenser 1 working fluid flow into condenser 2 sea water 1 sea water 2 total thermal inlet outlet The position of the number corresponding with in Fig. 1

and cold energy of LNG can be fully utilized as well. By changing the condensation temperature and working fluid, the system performance achieves the best. Choi et al. [22] analyzed and optimized the cascade Rankine cycle for recovering LNG cold energy, and they found that the three-stage cascade Rankine cycle with propane had the highest net power output. When the LNG vaporization pressure is 60 bar, the thermal efficiency can reach 12.5%. Ramón Ferreiro García et al. [23] proposed and analyzed an efficient power plant composed of series Rankine cycles combined with a direct expansion cycle, where the rejected heat from each cascade power unit is used to heat the liquefied natural gas in a regasification plant. Zhang et al. [7] also proposed that the combined series and parallel Rankine cycle. They concluded that the performance of this cycle system was better than simple Rankine cycle system, and npentane emerged the best performance among eight working fluids. From the review of previous literature, for the simple organic Rankine cycle, the condensation process of working fluid is not well matched with the LNG vaporization process, which makes the thermal efficiency low. The combined series and parallel Rankine cycle could improve the heat transfer characteristic between working fluid and LNG, however, which is at the cost of increasing the system independent loop, the complexity of the system and control difficulty remarkably. Therefore, in order to reduce the irreversible loss in the condenser and improve the power generation system with liquefied natural gas (LNG) cold energy, without increasing the system independent loop and control difficulty greatly, this paper propose a novel two-stage condensation Rankine cycle (TCRC) system. Firstly, the TCRC system is simulated by Aspen Hysys software, and is compared with the conventional methods of generating electricity by LNG cold energy. Then the effects of the first-stage condensation temperature, second-stage condensation temperature and LNG vaporization pressure on the performance (net power output, thermal efficiency and exergy efficiency) and cost index UA of the TCRC system are analyzed. Finally, the net power output is used as the objective function, with 14 kinds of organic fluids (such as propane, butane etc.) as the

314

J. Bao et al. / Energy Conversion and Management 143 (2017) 312–325

working fluid, and the first-stage and second-stage condensation temperature at different LNG vaporization pressures are optimized.

3. Mathematical modeling 3.1. Assumption The energy and exergy analysis based on the first and second laws of thermodynamics are carried out for the two-stage condensation Rankine cycle (TCRC) system. In order to simplify the analysis, the following hypotheses have been made in this study:

2. System description 2.1. Traditional cycles At present, the traditional methods to generate electricity by LNG cold energy are the direct expansion (DE), organic Rankine cycle (ORC) and combined cycle (CC). In the direct expansion, LNG is pressurized by LNG pump and pumped into evaporator, where LNG is heated by sea water. Then it flows into turbine to the pipe network delivery pressure and then drive the generator to generate electricity. At last, LNG is fully vaporized to the expected temperature in the reheater by the sea water, as shown in Fig. 1. The organic Rankine cycle primarily utilizes cryogenic exergy of LNG. In the organic Rankine cycle, the working fluid usually goes through four processes, including condensation, compression, vaporization and expansion, to generate power, using LNG as its heat sink and sea water as its heat source, as presented in Fig. 2. The combined cycle is the integration of direct expansion and organic Rankine cycle, as illustrated in Fig. 3. The combined cycle can use the cryogenic and pressure exergy simultaneously and the connection between the two sub-cycles is realized through the condenser where the working fluid absorbs the cold energy released by LNG. The electricity is generated from both the working fluid turbine and the NG turbine.

(1) Pressure drops in all system components except pumps and turbines are negligible. (2) Heat losses and friction losses in all system components and connections are neglected. (3) All components operate under steady-state conditions. (4) The working fluid evaporates to a saturated vapor in the evaporator and condenses to a saturated liquid in the condenser. (5) Exergy loss during the separating process is neglected. 3.2. Energy analysis According to conservation of mass and energy, each components of the TCRC system can be performed by the following equations, which are shown in Table 1 and the calculation method of traditional cycles is similar to the TCRC system without presenting them. The net power output for the TCRC system:

W net ¼ W tur1 þ W tur2
W p1
W p2
W p3
W p4
W p5 The total heat absorption for the TCRC system:

Q tot ¼ Q ev a þ Q re

2.2. The TCRC system

ð1Þ ð2Þ

The thermal efficiency for the TCRC system: The schematic diagram of the proposed TCRC system is shown in Fig. 4. This system mainly consists of a mixer, an evaporator, a splitter, two turbines, two condensers and two feed pumps. LNG is pressurized by LNG pump and pumped into condenser 1, where LNG is heated by exhaust coming from turbine 1. Then LNG enters condenser 2 and is further heated by the exhaust at the outlet of turbine 2. At last, LNG is fully vaporized to the expected temperature in the reheater by the sea water. The cooled working fluids in condenser 1 and 2 are respectively pressurized by feed pump 1 and 2, and then converged in the mixer. After that, working fluid is boiled to vapor in the evaporator by sea water. Then it’s divide into two branches by splitter and they respectively flow into turbine 1 and 2 where the electricity is produced by the generator linked with them. The exhaust steams of the two turbines enter the condenser 1 and 2 where they release heat to LNG respectively and the new cycle recommences. Fig. 5 shows the T-s diagram of the TCRC system and it should be pointed that the state points labeled in Fig. 5 are the same as that in Fig. 4.

gth ¼ W net =Q tot

ð3Þ

3.3. Exergy analysis In this study, the specific exergy is defined using the classical definition (neglecting kinetic and potential exergy), which can be defined as:

ex ¼ h
h0
T 0 ðS
S0 Þ

ð4Þ

And the exergy flow rate is defined as the product of the mass flow rate and the specific exergy:

Ex ¼ m  ex

ð5Þ

The change for exergy of the LNG vaporization process:

ExLNG ¼ ExLNG

in


ExNG

ð6Þ

For sea water 1:

Sea water2

Sea water1

Pump3 Pump2

6

G

4

Turbine1

1

LNG

Heater

2 5

Pump1 Fig. 1. Schematic of the direct expansion.

3

NG Reheater 7

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J. Bao et al. / Energy Conversion and Management 143 (2017) 312–325

Sea water2

Sea water1

7 Pump4

Pump3 1 Evaporator

2

8

G Pump2

9

Turbine1 3

4

NG 5 LNG

Consender1

6

Heater 10

Pump1 Fig. 2. Schematic of the organic Rankine cycle.

Sea water2

Sea water1

Sea water3

9 Pump4

Pump3

Pump5

1 Evaporator

2

10

G

G Pump2

11

Turbine1

4

13

Turbine2

3 NG

5 LNG

Consender1

6

78

Heater

Reheater

12

Pump1

14

Fig. 3. Schematic of the combined cycle.

Sea water1

Sea water2

11

13

Pump3

1

Pump4

2

Splitter

10 Mixer Pump2

6

Evaporator

Sea water 7

3

12

Working fluid

G 9

Pump1

Turbine 1

LNG

G

Turbine 2

8 5

4

15

LNG

16 Condenser 1

Pump5 Fig. 4. Schematic diagram of the TCRC system.

17

NG

Condenser 2 Reheater

14

Temperature (

)

316

J. Bao et al. / Energy Conversion and Management 143 (2017) 312–325

90

4. Results and discussion

60

4.1. Comparison between the TCRC system and conventional power generation method

Sea water

30

2

0

10 9

-30

8 17

6 5

-60

4 16

16

-90 -120

LNG

-150

15

1.0

1.5

2.0

2.5

3.0

3.5

Entropy (kJ/(kg· ) Fig. 5. T-s diagram of the TCRC system.

Table 1 The equation applied to energy analysis of the TCRC. Components

Equation

Evaporator Turbine 1 Turbine 2 Condenser 1 Condenser 2 Feed pump 1 Feed pump 2 Sea water pump 3 Sea water pump 4 LNG pump 5 Reheater

Q ev a ¼ mwf  ðh2
h1 Þ ¼ msw1  ðh11
h12 Þ W tur1 ¼ mwf 1  ðh3
h4 Þ W tur2 ¼ mwf 2  ðh7
h8 Þ Q con1 ¼ mLNG  ðh16
h15 Þ ¼ mwf 1  ðh4
h5 Þ Q con2 ¼ mLNG  ðh17
h16 Þ ¼ mwf 2  ðh8
h9 Þ W p1 ¼ mwf 1  ðh6
h5 Þ W p2 ¼ mwf 2  ðh10
h9 Þ W p3 ¼ msw1  ðh11
hsw1 in Þ W p4 ¼ msw2  ðh13
hsw2 in Þ W p5 ¼ mLNG  ðh15
hLNG in Þ Q re ¼ mLNG  ðhNG out
h17 Þ ¼ msw2  ðh14
h13 Þ

Exsw1 ¼ Exsw1

in


Ex12

ð7Þ

For sea water 2:

Exsw2 ¼ Exsw2

in


Ex14

ð8Þ

The total exergy of the TCRC system is calculated by:

Extot ¼ ExLNG þ Exsw1 þ Exsw2

ð9Þ

According to the exergy balance equation, the exergy loss of each component is described in Table 2.The exergy efficiency of the TCRC system:

gex ¼ W net =Extot

ð10Þ

Table 2 The equation applied to exergy analysis of the TCRC. Components

Equation

Sea water 1 Sea water 2 Evaporator Turbine 1 Turbine 2 Condenser 1 Condenser 2 Splitter Mixer Reheater Feed pump1 Feed pump 2 Sea water pump 3 Sea water pump 4 LNG pump 5

Exsw1 ¼ Exsw1 in
Ex12 Exsw2 ¼ Exsw2 in
Ex14 Iev a ¼ Ex11
Ex12 þ Ex1
Ex2 Itur1 ¼ Ex3
Ex4
W tur1 Itur2 ¼ Ex7
Ex8
W tur2 Icon1 ¼ Ex4
Ex5 þ Ex15
Ex16 Icon2 ¼ Ex8
Ex9 þ Ex16
Ex17 Isp ¼ Ex2
Ex3
Ex7 Imix ¼ Ex10 þ Ex6
Ex1 Ire ¼ Ex17
ExNG out þ Ex13
Ex14 Ip1 ¼ Ex9
Ex10 þ W p1 Ip2 ¼ Ex5
Ex6 þ W p2 Ip3 ¼ Exsw1 in
Ex11 þ W p3 Ip4 ¼ Exsw2 in
Ex13 þ W p4 Ip5 ¼ ExLNG in
Ex15 þ W p5

The previously mentioned traditional power generation methods using LNG cold energy are the Rankine cycle and combined cycle with the single-stage condensation to vaporize LNG. This paper has proposed a TCRC system to improve the utilization of LNG cold energy by the two-stage condensation process. In order to determine whether the new proposed cycle has a better performance, the novel system is compared with the conventional methods under the same conditions. The composition of LNG is listed in Table 3 [24]. The LNG are
162 °C for initial temperature, 0.1 MPa for initial pressure, 3600 kg/h for handling capacity and 7 MPa for vaporization pressure, while the temperature of NG is 10 °C. The systems are simulated using Aspen Hysys software. This software is able to cope with most of the petroleum, gaseous, oil and other such industrial processes [25]. User friendly interface, integrated steady state and dynamic modeling capabilities are motivations for using Aspen Hysys [26]. The Peng-Robinson equation of state is used to calculate the thermodynamic states of the process streams. In this paper, the condensation temperatures of four kinds of power generation system are chosen with net output power as the objective function, and the all other state parameters remain constant. By the genetic algorithm, the condensation temperature is optimized. When the net output power is maximum, the related operating conditions are listed in Table 4 and the detailed thermodynamic datas of four different cycle are shown in Appendix A. Fig. 3 shows the net power output, thermal efficiency and exergy efficiency of the four power generation methods. It can be seen from Fig. 6 that the utilization of LNG cold energy is remarkably improved for the TCRC system in terms of net power output, thermal efficiency and exergy efficiency compared with the traditional power generation methods. When finishing the same LNG vaporization process, the combined cycle system has the best performance among the traditional methods. Compared with the combined cycle, the net power output, thermal efficiency and exergy efficiency of the TCRC system are respectively increased by 45.27%, 42.91% and 52.31%. With the purpose of revealing the reason why the TCRC system is superior to the traditional methods, the exergy analysis is made for the organic Rankine cycle and TCRC systems. The irreversible losses for various components of the organic Rankine cycle and TCRC systems are shown in Fig. 7. From Fig. 7 it can be found that the total irreversible loss of the TCRC system is lower than that of the ORC system. Although the irreversible losses of the turbine, evaporator and pump increase slightly, the irreversible losses of the condenser and the reheater are much lower than that of the ORC system, which results in the reduction of the lower total irreversible loss of the TCRC system than that of the ORC system and improves the system performance of the TCRC system. Fig. 8 shows the heat transfer characteristics between working fluid and LNG for the ORC and TCRC systems. From Fig. 8, it can be known that the ORC system has a larger heat transfer irreversibility between the LNG and working fluid than that of the

Table 3 Composition of LNG. Component

Mole fraction (%)

Component

Mole fraction (%)

CH4 C3H8 n-C4H10 n-C5H12

91.33 2.14 0.46 0.01

C2H6 i-C4H10 i-C5H12 N2

5.36 0.47 0.01 0.22

317

J. Bao et al. / Energy Conversion and Management 143 (2017) 312–325 Table 4 The operation conditions of four power generation methods by LNG cold energy. Parameters

DE

ORC

CC

TCRC

Cold source Working fluid Heat source Inlet temperature of heat source (°C) Outlet temperature of heat source (°C) Adiabatic efficiency of the pump (%) Adiabatic efficiency of the turbine (%) Minimum approach temperature in the condenser (°C) Minimum approach temperature in the heater and reheater (°C) Evaporation temperature (°C) Inlet pressure of LNG turbine (kPa) Condensation temperature (°C) Discharged pressure of seawater pump (bar)

– – Sea water 15 10 80 80 – 5 11 15,850 – 3

LNG Propane Sea water 15 10 80 80 5 5 11 –
52 3

LNG Propane Sea water 15 10 80 80 5 5 11 13,070
47 3

LNG Propane Sea water 15 10 80 80 5 5 11 –
99.6,
41.7 3

(b)

85.93

8

59.15

60

ηth (%)

Wnet (kW)

80 51.03

40 20 0

(c)

10.07

10

20

7.13 6.24

6 4

ORC

CC

14.59

12

4

0.19

0

DEC

16.97 16

8

2

1.48

24.62

24

ηex (%)

(a)

TCRC

DEC

0

ORC

CC

0.43

DEC

TCRC

ORC

CC

TCRC

Fig. 6. System performance of the four power generation methods. (a) Net power output, (b) thermal efficiency, (c) exergy efficiency.

TCRC system mainly because of the two-stage condensation process for the TCRC system instead of the single-stage condensation process of the ORC system, which reduces the irreversible loss of the condenser and improves the system performance.

320

240 200

4.2. The influences of the first-stage and second-stage condensation temperature

160 120 80 40 0 ORC

TCRC

Fig. 7. Comparison of irreversible losses for various components between the ORC and TCRCSystems.

From Fig. 7 in Section 4.1, it can be found that the irreversible loss of the condenser is the largest among the components. The first-stage condensation temperature is related to the condensation temperature in the condenser 1 while the second-stage condensation temperature is the condensing temperature of condenser 2, which are both labeled in Fig. 8. For the TCRC system, it can be seen from Fig. 8(b) that the first-stage and second-stage condensation temperature will affect the temperature matching

(b)

(a) Temperature (䉝)

-20

-20

Tcon

-40

Tcon2

-40

-60 -80 -100

working fluid LNG

-120 -140

Temperature (䉝)

Irreversible loss (kW)

280

-60 -80 -100

working fluid LNG

Tcon1

-120 -140 -160

-160 0

3

6

9

12

15

18

Heat Duty(×105 kJ/h)

21

0

3

6

9

12

15

18

Heat Duty(×105 kJ/h)

Fig. 8. Heat transfer characteristics between working fluid and LNG (a) ORC, (b) TCRC.

21

J. Bao et al. / Energy Conversion and Management 143 (2017) 312–325

between working fluid and LNG, and therefore it is necessary to analysis the influence of the first-stage and second-stage condensation temperature on the system performance. Keeping the working fluid and other system parameters remain unchanged, the basic conditions of LNG is the same as Section 4.1, and the first-stage and second-stage condensation temperature are changed only. Fig. 9 illustrates the variation of net power output, thermal efficiency, exergy efficiency and UA with respect to the various firststage and second-stage condensation temperatures. From Fig. 9 (a), the net power output increases firstly and then decreases with the increase of the first-stage condensation temperature when the second-stage condensation temperature is fixed, which means that there exists an optimal first-stage condensation temperature making the system net power output maximum. Fig. 10 shows the effect of the first-stage condensation temperature on the power output and input for turbines and pumps at the second-stage condensation temperature of
60 °C. From that it could be found that the first-stage condensation temperature has no serious effects on the power input for all the pumps, positive effect on the turbine 1 and negative effect on turbine 2. The power output of the turbine is related to the flow rate of the working fluid and the enthalpy of the inlet and outlet of the turbine. When the first-stage condensation temperature decreases, the enthalpy in the outlet of turbine reduces so specific power of turbine 1 increases. The heat absorption of LNG in the first condenser reduces and the working fluid 1 vaporization latent heat increases, so the mass flow rate of working fluid 1 decreases. Due to the increment of working fluid 1 mass flow is much greater than the reduction of the power output of turbine 1, Therefore, with the increase of the first-stage condensation temperature, the W_turbine1 increases. When condition of the inlet and outlet of

80 70

40 30

10 0 -120

-100

-90

-80

-70

Fig. 10. When the second-stage condensation temperatures is
60 °C, the influence of the first-stage condensation temperature on the power output and input for turbines and pumps.

the turbine 2 remain unchanged, the enthalpy difference of turbine 2 is constant. Therefore, the power output of turbine 2 is mainly related to the mass flow of the working fluid. When the secondstage condensation temperature is constant and the first-stage condensation temperature increases, the heat absorption of LNG in the second condensation cycle decreases. Due to the vaporization latent heat of working fluid is unchanged, the mass flow of working fluid decreases. Therefore, when the first-stage condensation temperature increases, the power output of turbine 2 reduces.

(b) 10 9.5

75

9.0

70

ηth (%)

80

Tcon2=-60

65

Tcon2=-52 Tcon2=-44

60

Tcon2=-36 Tcon2=-28

55 -110

-100

Tcon2=-60 Tcon2=-52 Tcon2=-44

8.0 7.5

Tcon2=-36 Tcon2=-28

7.0

Tcon2=-20

-120

8.5

Tcon2=-20

6.5

-90

-80

-70

-120

-110

Tcon1(ć)

(d) 20

24.0

5 UA (×10 kJ/(h·ć ))

22.5 21.0 Tcon2=-60 Tcon2=-52

18.0

Tcon2=-44 Tcon2=-36

16.5

Tcon2=-28 Tcon2=-20

15.0 -120

-110

-100

-90

Tcon2=-60

18

19.5

-100

-80

-70

Tcon1(ć)

(c)

ηex (%)

-110

Tcon1 (ć)

85

Wnet (kW)

50

20

(a)

50

WTurbine2 WTurbine1 Wpump_LNG Wpump_wf Wpump_sw

60

Power (kW)

318

Tcon2=-52

Tcon2=-36 Tcon2=-28

Tcon2=-44

Tcon2=-20

16 14 12 10 8

-90

Tcon1(ć)

-80

-70

-120

-110

-100

-90

-80

-70

Tcon1(ć)

Fig. 9. The effects of the first-stage condensation temperature on system performance (a) net power output, (b) thermal efficiency, (c) exergy efficiency, and costs indices (d) UA, at the different second-stage condensation temperature.

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J. Bao et al. / Energy Conversion and Management 143 (2017) 312–325

As the first-stage condensation temperature increases, the increasing rate of power output for turbine 1 tends to be gentle, while the reduction rate for power output of turbine 2 changes linearly. Their combined effects lead to the existence of the optimal first-stage condensation temperature which makes net power output have the largest value. As shown in Fig. 9(b) and (c), the change trend of thermal efficiency and exergy efficiency are the same as that of net power output. The relationship between thermal efficiency and net power output is as follows:

g¼

W net W net 1 ¼ ¼ Q con Q ev a W net þ Q con 1 þ W net

ð11Þ

According to Eq. (11), the thermal efficiency of the TCRC system is mainly related to the net power output and heat release Qcon of the system. The heat release Qcon of the system is constant at the fixed second-stage condensation temperature. Hence, when the first-stage condensation temperature increases, the thermal efficiency and net power output have the same change trends. According to Eq. (3), the exergy efficiency is mainly affected by the net power output of the system and exergy input of the system. Due to the constant values of the inlet and outlet temperature of the LNG and seawater, with the first condensation temperature changes, the exergy input of system keeps basically unchanged. Therefore, the change trend of exergy efficiency with the increase of the first condensation temperature is the same as that of net power output. UA values can be calculated by Eq. (12):

UA ¼

Q DT

ð12Þ

ðUAÞtotal ¼ ðUAÞev a þ ðUAÞcon1 þ ðUAÞcon2 þ ðUAÞre

(b)

84

10

81

9.6

78 75

Tcon1= -120 Tcon1= -112 Tcon1= -104 Tcon1= -96 Tcon1= -88 Tcon1= -80

72 69 66

9.2 Tcon1= -120 Tcon1= -112 Tcon1= -104 Tcon1= -96 Tcon1= -88 Tcon1= -80

8.8 8.4 8.0 7.6

63 -60

-55

-50

-45

-40

-35

-30

-25

-60

-20

-55

-50

Tcon2( )

-45

-40

-35

-30

-25

-20

Tcon2( )

(c) 25

(d) 18 Tcon1= -120 Tcon1= -112 Tcon1= -104 Tcon1= -96 Tcon1= -88 Tcon1= -80

UA (×105 kJ/(h· ))

24 23

ηex (%)

ð13Þ

In this paper, the simple weight model of the heat exchanger model in Aspen Hysys software is chosen. This method is suitable for dealing with nonlinear thermal curve problems. In the weight model, the heating curve is divided into several intervals and the energy balance calculation is performed in each interval. So the logarithmic temperature difference and the UA value of each section of the heat transfer curve are calculated, and then the sum of UA value is calculated. The effects of the first-stage condensation temperature on UA at different second-stage condensation temperatures are shown in Fig. 9(d). When the second-stage condensation temperature is lower than
44 °C, the first condensation temperature has no significant effect on UA, while the second-stage condensation temperature is higher than
48 °C, the UA decreases with the increase of the first-stage condensation temperature. The variations of system performance (net power output, thermal efficiency, exergy efficiency and UA) as the second-stage condensation temperature changes at different first-stage condensation temperatures are illustrated in Fig. 11. From Fig. 11 (a)–(c), it could be found that the effect of the second-stage condensation temperature on net power output, thermal efficiency and exergy efficiency is similar to that of Fig. 9(a)–(c). The reason is the same as the previous discussions and it won’t be explained again here for simplicity.

ηth (%)

Wnet (kW)

(a) 87

where U and A stand for the heat transfer coefficient and the area, respectively.UA is the thermal conductance, Q is the heat transfer of the system and DT is the log mean temperature difference. The total UA value of the system is equal to the sum of the UA values for each heat exchanger, shown as Eq. (13).

22 Tcon1= -120 Tcon1= -112 Tcon1= -104 Tcon1= -96 Tcon1= -88 Tcon1= -80

21 20 19 18

16 14 12 10 8 6

-60

-55

-50

-45

-40

-35

Tcon2( )

-30

-25

-20

-60

-55

-50

-45

-40

-35

-30

-25

-20

Tcon2( )

Fig. 11. The effects of the second-stage condensation temperature on system performance (a) net power output, (b) thermal efficiency, (c) exergy efficiency, and costs indices (d) UA, at the different first-stage condensation temperature.

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J. Bao et al. / Energy Conversion and Management 143 (2017) 312–325

The influence of the second-stage condensation temperature on UA at different first-stage condensation temperatures is shown in Fig. 11(d). When the first-stage condensation temperature keeps fixed, UA increases significantly as the augment of the secondstage condensation temperature, which indicates that the second-stage condensation temperature has more obvious influence on the system economy than that of the first-stage condensation temperature. Fig. 12 shows the effect of the second-stage condensation temperature on the UA of various heat exchangers at the first-stage condensation temperature of
100 °C. It can be seen that the second-stage condensation temperature has little effect on the UA of the condenser and reheater, while the UA of the evaporator increases significantly with the increase of the second-stage condensation temperature, which is much larger than the UA value of other heat exchangers. The reason why the UA of the evaporator increases significantly with the increase of the second-stage condensation temperature is explained as the following. When the second-stage condensation temperature increases, the temperature of working fluid entering into the evaporator increases, which result the decrease of the logarithmic mean temperature difference between working fluid and the sea water in the evaporator.

Q ¼ UADt

ð14Þ

According to Eq. (14), UA will go up with the increase of the secondstage condensation temperature in the case of the basically unchanged total heat absorption. 4.3. The effect of LNG different vaporization pressure In the practical application, the LNG vaporization pressure is determined according to different applications. Therefore, it is necessary to analysis the influence of LNG vaporization pressure on the performance and parameters of the TCRC system. The vaporization pressure of LNG corresponding to different applications is shown in Table 5 [27]. From Section 4.2 it can be seen that the change tendencies of net power output, thermal efficiency and exergy efficiency at different first-stage and second-stage condensation temperatures are similar. In this section, the influence of the first-stage and second-stage condensation temperatures on the net power output and UA of system for different vaporization pressures are analyzed. The composition, inlet temperature, inlet pressure and flow rate of the LNG are the same as those in Section 4.1. Other system

16

5 UA (×10 kJ/(h·ć ))

14 12 10 UAEvaporator UAReheater

8 6

UACondenser1 UACondenser2

4 2 0 -60

-50

-40

-30

-20

Tcon2 (ć) Fig. 12. Effects of the second-stage condensation temperature on the UA of various heat exchangers at the first-stage condensation temperature of
100 °C.

Table 5 Required pressure for several uses of NG. Application

Pressure (bar)

Steam power stations Combined cycle stations Local distribution Long-distance distribution

6 25 30 70

parameters remain unchanged and the working fluid is still propane. Only the first-stage and second-stage condensation temperature as well as the vaporization pressure of the LNG are changed. When the first-stage and second-stage condensation temperature changes, the change trend of the net power output at different LNG vaporization pressures (70 bar, 30 bar, 25 bar, 6 bar) is shown in Fig. 10. It can be found from Fig. 13(a) that there is an optimal firststage and second-stage condensation temperature making the net power output maximum at the LNG vaporization pressure of 70 bar, which corresponds to the result of Section 4.2. While the LNG vaporization pressure is 30 bar, as plotted in Fig. 13(b), the contours of the net output power will have an inflection point, which also exists in Fig. 13(c) and can’t be found in Fig. 13 (a) and (d). From Fig. 13 it also can be known that with the decrease of LNG vaporization pressure, the optimum range of the first-stage condensation temperature firstly increases and then decreases. The T-s diagram of the LNG vaporization process at different vapor pressures is shown in Fig. 14. The critical pressure of LNG is 65.41 bar at the given composition. It can be observed that with the supercritical state of the LNG for the vaporization pressure of 70 bar, there is no inflection point in the vaporization process of LNG, while the pressure is lower than 70 bar, LNG vaporization curves have inflection points. Taking the LNG vaporization pressure of 30 bar as an example, from Fig. 14 it can be seen that it has an inflection point at about
94 °C in the vaporization process of LNG, while in Fig. 13(b) the inflection point occurs at the first-stage condensation temperature of about
89 °C. The temperature difference between them is set 5 °C which corresponds to the heat exchanger pinch temperature, so the contour of net power output will appear an inflection point. This is the reason why there exist no any inflection points on the contour of net power output at the LNG gasification pressure of 70 bar and appear an inflection point for the LNG vaporization pressure of 25 bar. However, when the LNG vaporization pressure is 6 bar, there exist an inflection point in the LNG vaporization process, but the net power output contour doesn’t show up an inflection point. This is because of the minimum condensation temperature of
119 °C at the LNG vapor pressure of 6 bar which is higher than the inflection point temperature of
134 °C. The existence of the inflection point will change the temperature matching between working fluid and LNG in the heat transfer process, which leads to the shift of the corresponding optimal firststage condensation temperature range when LNG vaporization pressure changes from 70 to 30 bar. With the decrease of the vaporization pressure for the subcritical state of LNG, the corresponding temperature of inflection point in the LNG vaporization process will reduce, which makes the first-stage condensation temperature corresponding to the maximum net power output drop accordingly. The change tendencies of the total UA is plotted in Fig. 15 at the LNG vaporization pressure of 70 bar, 30 bar, 25 bar and 6 bar. When LNG is in the supercritical state, the effect of the firststage condensation temperature on UA value is stronger than that of the second-stage condensation temperature, which is in accor-

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J. Bao et al. / Energy Conversion and Management 143 (2017) 312–325

(a)

-40

-50

(kW)

Inflection point

-115 -110 -105 -100 -95 -90 -85 -80 -75

Tcon1 (ć)

(c)

(d) net

-30

-40 Inflection point

-50

(kW) 151.4 146.6 138.3 130.1 121.8 113.5 105.2 96.95 88.68 80.40

-115 -110 -105 -100 -95 -90 -85 -80 -75

Tcon1 (ć)

W (kW) net 233.2 226.5 218.0 209.5 201.0 192.5 184.0 175.5 167.0 158.5 150.0

-20

Tcon2 (ć)

W

-20

Tcon2 (ć)

-40

-60

-115 -110 -105 -100 -95 -90 -85 -80 -75

net

138.2 131.5 124.8 118.1 111.4 104.7 98.05 91.37 84.68 78.00

-30

-50

Tcon1 (ć)

-60

W

-20

Tcon2 (ć)

Tcon2 (ć)

-30

-60

(b)

W (kW) net 86.00 82.50 79.00 75.50 72.00 68.50 65.00 61.50 58.00 54.50

-20

-30

-40

-50

-60

-115 -110 -105 -100 -95 -90 -85 -80 -75

Tcon1 (ć)

Fig. 13. Contour of net power output when the first-stage and the second-stage condensation temperature simultaneously changes at different vaporization pressures (a) 70 bar, (b) 30 bar, (c) 25 bar, (d) 6 bar.

4.4. Parameters optimization and working fluids comparison 20 0

Temperature (ć)

-20 -40

70bar 30bar 25bar 6bar

-60 -80 -100 -120

Inflection point

-140 -160 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5

Entropy (kJ/(kg·ć )) Fig. 14. The T-s diagram of the LNG vaporization process under different pressures.

dance with the results of Section 4.2. At the LNG vaporization pressure of 30 and 25 bar in Fig. 15(b) and (c), the contours of the UA values are both linear before the emergence of inflection point and non-linear after the inflection point. The main reason is implicit in Fig. 14, which is the linear vaporization curve of LNG before the inflection point and the non-linear vaporization curve after the inflection point. When the LNG vaporization pressure is 6 bar, the minimum first-stage condensation temperature always higher than the inflection point temperature of
134 °C, which results in the non-linear UA contour as shown in Fig. 12(d).

The high-efficiency operation of the TCRC system mainly depends on the system parameters and the choice of working fluids. Based on the analysis of Section 4.3, it can be concluded that there is an optimal first-stage and second-stage condensation temperature which makes the system performance best for different LNG vaporization pressures and it’s vital to optimize the system parameters. The choice of working fluids is the key factor that influences the temperature matching between working fluid and LNG, so that it is necessary to explore the effect of different working fluids on the performance of the TCRC system. The previous analysis uses propane as the working fluid, which is a common choice in other literatures. Based on the above principles, other 13 kinds of organic fluids have been selected for comparison [10]. Their basic physical properties is listed in Table 6. In order to determine the optimal system parameters for different working fluids at various vaporization pressures of LNG, choosing the net power output as the objective function, by combining the Hysys and Matlab, genetic algorithms is used to optimize. The optimization results are shown in Table 7. The optimum net power output and UA corresponding to the optimal net power output for different working fluids at various LNG vaporization pressures are shown in Fig. 16. From Fig. 16(a) it can be seen that the optimal net power output increases significantly for various working fluids with decrease of LNG vaporization pressure. This is because of the reduction of the LNG vaporization pressure as well as the average release heat temperature of the TCRC system. According to the Carnot theorem, it can be known that the thermal efficiency of the system increases as well as the net power output.

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J. Bao et al. / Energy Conversion and Management 143 (2017) 312–325

(a)

5 UA (×10 kJ/(h·

-20

23.35 23.10 21.50 19.90 18.30 16.70 15.10 13.50 11.90 10.30 8.700 7.100

-40

-50

5 UA (×10 kJ/(h·

-20

-40

Inflection point

-50

-60

-115 -110 -105 -100 -95 -90 -85 -80 -75

-115 -110 -105 -100 -95 -90 -85 -80 -75

Tcon1 (ć)

Tcon1 (ć)

(c)

5 UA (×10 kJ/(h·

(d) ))

Tcon2

-30

-40 Inflection point

-50

-40

-50

-60

-115 -110 -105 -100 -95 -90 -85 -80 -75

))

15.50 15.11 14.70 14.29 13.87 13.46 13.05 12.64 12.23 11.81 11.40

-30

Tcon2

28.40 26.96 25.20 23.44 21.69 19.93 18.18 16.42 14.66 12.91 11.15

5 UA (×10 kJ/(h·

-20

-20

-60

))

28.55 27.16 25.35 23.54 21.74 19.93 18.13 16.32 14.51 12.71 10.90

-30

Tcon2

Tcon2

-30

-60

(b) ))

-115 -110 -105 -100 -95 -90 -85 -80 -75

Tcon1 (ć)

Tcon1 (ć)

Fig. 15. Contour of UA when the first-stage and the second-stage condensation temperature simultaneously changes at different vaporization pressures (a) 70 bar, (b) 30 bar, (c) 25 bar, (d) 6 bar.

Table 6 Physical properties of working fluids. Working fluids Abbreviations

Chemical formula

R290 R150 R170 R1270 R600 R41 R32 R152a R23 R143a R134a R125 R116 R218

C3H8 C2H4 C2H6 C3H6 C4H10 CH3F CH2F2 C2H4F2 CHF3 C2H3F3 C2H2F4 C2HF5 C2F6 C3F8

Critical temperature (°C)

Critical pressure (bar)

Normal boiling point (°C)

96.74 9.2 32.17 91.06 151.98 44.13 78.10 113.26 26.14 72.71 101.06 66.02 19.88 71.87

42.51 50.12 48.72 45.55 38.00 58.97 57.82 45.17 48.32 37.61 40.59 36.18 30.48 26.40


42.11
103.77
88.82
47.62
0.55
78.13
51.65
24.02
82.09
47.27
26.07
48.09
78.09
36.79

The working fluid corresponding to the least net power output is R150, followed by R23 at different LNG vaporization pressures. At the LNG vaporization pressure of 70 bar and 6 bar, R152a has the largest net power output, followed by R32. While the vaporization pressure is 30 bar and 25 bar, the net power output of R32 is maximum. This indicates that the vaporization pressure of LNG has a great influence on the selection of working fluid, and the optimum working fluid will alter with the change of LNG vaporization pressure. The net power output can evaluate the revenue of the whole system, while UA value can weigh the investment cost of the system. The net power output of R150 is lower and R152a and R32 are

larger than other working fluids as shown in Fig. 16(b), while the UA of R150 is least and R152a and R32 are the largest, which means the investment cost is contradiction with the revenue of the whole system. In order to evaluate the economy of the whole system, UA per unit net power output of different working fluids at various vaporization pressures are illustrated in Fig. 17. It can be seen from Fig. 17 that when LNG vaporization pressure is supercritical pressure, R116 has the best economy of all the investigated working fluid, while R150 and R23 are better when the vaporization pressure of LNG is subcritical. If choosing R152a and R32 as the working fluid at different LNG vaporization pressure, the system performance is poor.

323

J. Bao et al. / Energy Conversion and Management 143 (2017) 312–325 Table 7 Optimization results of system parameters and performance for different working fluids at various LNG vaporization pressures. C2H4

C2H6

C3H6

C3H8

C4H10

CH3F

CH2F2

C2H4F2

CHF3

C2H3F3

C2H2F4

C2HF5

C2F6

C3F8

70 bar

Tcon1 (°C) Tcon2 (°C) Wnet (kW) gth (%) gex (%) UA (105kJ/ °Ch)


101
43.88 54.78 6.67 15.67 3.046


99.88
42 74.61 8.86 21.37 6.970


99.26
41.83 87.05 10.19 24.95 11.44


99.64
41.74 85.93 10.07 24.62 10.84


100.4
41.83 88.5 10.34 25.36 11.67


99.74
41.79 82.12 9.67 23.52 8.832


98.89
41.77 88.54 10.34 25.37 12.44


98.92
41.68 88.84 10.38 25.46 12.81


99.99
41.92 73.49 8.74 21.04 3.286


98.91
41.67 83.28 9.79 23.86 9.381


99.46
41.78 87.01 10.18 24.93 10.95


97.27
41.05 81.13 9.56 23.24 8.585


100.5
42.55 65 7.81 18.60 4.692


103.9
45.64 84.79 9.95 24.29 7.288

30 bar

Tcon1 (°C) Tcon2 (°C) Wnet (kW) gth (%) gex (%) UA (105kJ/ °Ch)


115.9
72.5 96.31 10.45 21.58 3.042


114.8
71.14 119.9 12.68 26.89 6.487


114.2
70.91 136.3 14.16 30.58 10.29


114.4
70.51 134.5 14.01 30.19 9.796


114.6
70.03 137.5 14.27 30.87 10.46


81.39
46.27 133.0 13.87 29.84 10.30


81.35
46.24 141.9 14.66 31.86 14.19


113.9
70.55 138.5 14.36 31.08 11.27


81.55
46.04 121.2 12.80 27.18 7.515


114.5
70.36 130.7 13.66 29.31 8.598


113.9
69.39 135.6 14.11 30.44 9.941


114.4
70.02 127.8 13.40 28.68 7.857


114.6
71.42 108.2 11.58 24.24 4.522


118
69.98 135.7 14.11 30.46 7.504

25 bar

Tcon1 (°C) Tcon2 (°C) Wnet (kW) gth (%) gex (%) UA (105kJ/ °Ch)


119.1
78.45 103.8 11.09 22.15 3.021


118
76.5 128 13.32 27.34 6.385


86.65
48.7 153.1 15.52 32.73 12.98


86.63
48.36 151.3 15.37 32.34 12.34


117.1
74.94 146 14.91 31.21 10.26


86.66
48.65 145.8 14.89 31.17 10.27


86.71
48.85 155.4 15.71 33.22 13.97


116.5
76.13 147.3 15.02 31.49 10.98


86.84
49.44 133.2 13.78 28.45 7.451


117
76.12 139 14.30 29.71 8.412


117.4
79.02 144.1 14.74 30.79 9.660


117
74.89 136 14.03 29.05 7.731


116.8
75.91 115.9 12.22 24.75 4.484


124.7
76.39 144.7 14.80 30.94 7.354

6 bar

Tcon1 (°C) Tcon2 (°C) Wnet(kW) gth (%) gex (%) UA (105kJ/ °Ch)


121
73.07 177.7 17.16 27.30 3.762


120.6
68.45 211.1 19.71 32.47 7.736


120.8
68.14 236.9 21.60 36.46 12.02


120.6
66.87 233.6 21.36 35.95 11.49


120.7
66.29 237.8 21.66 36.59 12.18


120.5
67.76 226.1 20.82 34.78 9.731


120.6
67.2 239.4 21.77 36.84 12.80


120.6
67.83 239.6 21.78 36.87 12.93


120.7
67.67 208.4 19.51 32.04 7.185


120.6
67.67 226.8 20.87 34.90 10.14


120.6
65.77 233.2 21.33 35.88 11.48


120.6
65.18 220.9 20.44 33.98 9.291


120.1
69.99 191.7 18.23 29.46 5.413


120.6
60.22 224.6 20.71 34.55 8.553

C2H4

240

CHF3

210

C2F6

180

C3F8

C2H6 C2HF5

150

CH3F C2H3F3

120

C3H8

90

C2H2F4 C3H6

60

C4H10

30 0

CH2F2 C2H4F2

70bar

30bar

25bar

6bar

(b)

C2H4

14

5 UA (×10 kJ/(h· ))

W net (kW)

(a)

CHF3 C2F6

12

C2H6

10

C3F8

8

CH3F

C2HF5 C2H3F3

6

C3H8

4

C2H2F4

2

C4H10

C3H6 CH2F2

0 70bar

LNG vaporization pressure

30bar

25bar

6bar

C2H4F2

LNG vaporization pressure

UA/Wnet (1/ )

Fig. 16. (a)The optimal net power output and (b) UA corresponding to optimal net power output for different working fluids at various LNG vaporization pressures.

4.0

C 2 H4

3.5

C2F6 C 2 H6

3.0

C3F8 C2HF5

2.5

CH3F

2.0

C2H3F3

1.5

C 3 H8

1.0

C 3 H6

C2H2F4 C4H10

0.5 0.0

5. Conclusions

CHF3

CH2F2 C2H4F2

6bar

25bar

30bar

70bar

LNG vaporization pressure Fig. 17. UA/Wnet of various working fluids at different LNG vaporization pressures.

In order to improve the performance of the conventional power generation system utilizing LNG cold energy, this paper proposed a novel TCRC system. Through the system simulation, parameters analysis and optimization, the following conclusions can be drawn: (1) When finishing the same LNG vaporization process, the combined cycle system has the best performance among the traditional methods. Compared with the combined cycle, the net power output, thermal efficiency and exergy efficiency of the TCRC system are respectively increased by 45.27%, 42.91% and 52.31%. (2) There is a first-stage and second-stage condensation temperature that makes net power output, thermal efficiency and energy efficiency of the TCRC system optimal. And the second-stage condensation temperature has more obvious

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J. Bao et al. / Energy Conversion and Management 143 (2017) 312–325

influence on the system economy than that of the first-stage condensation temperature. (3) The vaporization pressure of LNG has an obvious effect on the optimal first-stage and second-stage condensation temperature range. At the LNG vaporization pressure of 25 bar and 30 bar, the net power output and UA contour line exist inflection points. (4) When LNG vaporization pressure is supercritical pressure, R116 has the best economy of all the investigated working fluids, while R150 and R23 are better when the vaporization pressure of LNG is subcritical.

Acknowledgement This research was financially supported by the National Natural Science Foundation of China (No. 51606025).

Appendix A The thermodynamic data of the four kinds of power generation system are shown in following tables (see Tables A1–A4).

Table A1 The thermodynamic data of the direct expansion. State

T (°C)

P (kPa)

h (kJ/kg)

s (kJ/kg °C)

m (kg/h)

1 2 3 4 5 6 7 NG LNG Sea water 1 Sea water 2


154.7 11
34.63 15.01 10 15.01 10 10
162 15 15

15,800 15,800 7000 300 300 300 300 7000 100 100 100


5131
4518
4568
15,860
15,880
15,860
15,880
4417
5174
15,860
15,860

4.346 7.496 7.548 0.2245 0.1510 0.2245 0.1510 8.131 4.238 0.2244 0.2244

3600 3600 3600 52,580 52,580 25,860 25,860 3600 3600 52,580 25,860

Table A2 The thermodynamic data of the organic Rankine cycle. State

T (°C)

P (kPa)

h (kJ/kg)

s (kJ/kg°C)

m (kg/h)

1 2 3 4 5 6 7 8 9 10 NG LNG Sea water 1 Sea water 2


46.43 11
46.76
46.76
158.8
51.76 15.01 10 15.01 10 10
162 15 15

653.9 653.9 82.57 82.57 7000 7000 300 300 300 300 7000 100 100 100


2897
2399
2471
2898
5155
4674
15,860
15,880
15,860
15,880
4417
5174
15,860
15,860

1.388 3.194 3.274 1.387 4.286 7.083 0.2245 0.1510 0.2245 0.1510 8.131 4.238 0.2244 0.2244

4055 4055 4055 4055 3600 3600 96,100 96,100 44,100 44,100 3600 3600 96,100 44,100

Table A3 The thermodynamic data of the combined cycle. State

T (°C)

P (kPa)

h (kJ/kg)

s (kJ/kg°C)

m (kg/h)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 NG LNG Sea water 1 Sea water 2 Sea water 3


69.28 11
69.60
69.60
156.2
74.60 11
26.24 15.01 10 15.01 10 15.01 10 10
162 15 15 15

653.9 653.9 25.45 25.45 13,069 13,069 13,069 7000 300 300 300 300 300 300 7000 100 100 100 100


2944
2399
2506
2946
5139
4864
4492
4533
15,860
15,880
15,860
15,880
15,860
15,880
4417
5174
15,860
15,860
15,860

1.168 3.194 3.326 1.166 4.327 6.086 7.648 7.690 0.2245 0.1510 0.2245 0.1510 0.2245 0.1510 8.131 4.238 0.2244 0.2244 0.2244

2248 2248 2248 2248 3600 3600 3600 3600 58,360 58,360 63,750 63,750 19,960 19,960 3600 3600 58,360 63,750 19,960

325

J. Bao et al. / Energy Conversion and Management 143 (2017) 312–325 Table A4 The thermodynamic data of the TCRC system. State

T (°C)

P (kPa)

h (kJ/kg)

s (kJ/kg°C)

m (kg/h)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 NG LNG Sea water 1 Sea water 2


59.67 11 11
99.05
99.05
98.76 11
41.65
41.65
41.32 15.01 10 15.01 10
158.8
104.0
46.65 10
162 15 15

653.9 653.9 653.9 3.323 3.323 653.9 653.9 103.7 103.7 653.9 300 300 300 300 7000 7000 7000 7000 100 100 100


2925
2399
2399
2557
3002
3001
2399
2464
2887
2886
15,860
15,880
15,860
15,880
5155
4974
4634
4417
5174
15,860
15,860

1.262 3.194 3.194 3.422 0.8649 0.8667 3.194 3.264 1.435 1.437 0.2245 0.1510 0.2245 0.1510 4.286 5.577 7.261 8.131 4.238 0.2244 0.2244

4355 4355 1470 1470 1470 1470 2885 2885 2885 2885 109,000 109,000 37,260 37,260 3600 3600 3600 3600 3600 109,000 37,260

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