Simultaneous optimization of system structure and working fluid for the three-stage condensation Rankine cycle utilizing LNG cold energy

Applied Thermal Engineering 140 (2018) 120–130

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Research Paper

Simultaneous optimization of system structure and working fluid for the three-stage condensation Rankine cycle utilizing LNG cold energy Junjiang Bao, Ruixiang Zhang, Yan Lin, Ning Zhang, Xiaopeng Zhang, Gaohong He

T

⁎

State Key Laboratory of Fine Chemicals, School of Petroleum and Chemical Engineering, Dalian University of Technology, Panjin 124221, China

H I GH L IG H T S

cycles with different arrangements for compression and expansion process. • Nine cycle is recommended to improve the efficiency of the optimization. • AThesuperstructure superstructure contains the nine cycle structures. • Simultaneous optimization of cycle structure and working fluid is achieved. • The effect of the gasified pressure of LNG is studied. •

A R T I C LE I N FO

A B S T R A C T

Keywords: Compression arrangements Expansion arrangements LNG cold energy Superstructure Working fluid selection

For the power generation systems utilizing liquefied natural gas (LNG) cold energy, most researches paid attention to enhance the heat exchange process to improve the performance, but the compression and expansion process are less considered. The arrangements for compression and expansion process can affect the working conditions of turbines and pumps, respectively, thus affecting the system performance. Therefore, this paper optimizes the arrangements for compression and expansion process on the basis of the three-stage condensation Rankine cycle proposed in our previous work. For nine cycles with different structures, this paper proposes a superstructure that contains these possible cycle structures to improve the efficiency of the optimization. Firstly, the reliability of the superstructure optimization method is verified. Then, the effect of the gasified pressure of LNG on the optimum cycle structure is studied. Finally, the cycle parameters, structures and working fluids are simultaneously optimized through the proposed superstructure cycle. Results show that the arrangements for compression process have little effect on the cycle performance, while those for expansion process have a relatively significant effect. Furthermore, the optimum cycle structure is not affected by the gasified pressure of LNG and only depends on the used working fluid.

1. Introduction Natural gas (NG) is a clean fossil energy that is widely used in industrial production and residents’ life [1]. The world's gas reserves are huge and unevenly distributed, so that the demand is needed to be met by transport or trade [2]. Therefore, in order to facilitate the transportation, NG is cooled down to −162 °C at atmospheric pressure to obtain its liquid state, which is called liquefied natural gas (LNG) [3], and a large amount of electricity is consumed in this process. However, LNG must be re-gasified before being distributed to the NG users. The cold energy released in the re-gasification process is about 830–860 kJ/ kg [4]. Considering the vast consumption of producing LNG, utilizing its cold energy is very necessary for saving resources [5].

⁎

Corresponding author. E-mail addresses: [email protected], [email protected] (G. He).

https://doi.org/10.1016/j.applthermaleng.2018.05.049 Received 24 January 2018; Received in revised form 9 May 2018; Accepted 11 May 2018 1359-4311/ © 2018 Elsevier Ltd. All rights reserved.

The LNG cold energy can be used as the heat sink in some cryogenic processes, such as CO2-capture oxy-fuel power system [6–8] and cryogenic air separation process [9]. Mehrpooya et al. [10] also proposed a big integrated system, including air separation unit, coal gasification, solid oxide fuel cell, carbon dioxide transcritical cycle, steam cycle with liquefied natural gas (LNG) vaporization, in which all of the required refrigeration is provided by LNG. In general, besides cooling other substances directly, LNG cold energy is mostly used to generate electricity through thermodynamic cycles, so that it can also provide power for the power-consuming processes [11–14]. Organic Rankine cycle (ORC), as a simple and mature technology, is one of the effective methods for recovering LNG cold energy. In order to enhance power generation capacity, ORC is often

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conducted the simultaneous optimization for the cycle parameters and structures (or working fluids). Lampe et al. [31] proposed a framework of the simultaneous optimization for the cycle parameters and structure, which is achieved by exploiting the rich molecular picture underlying the PC-SAFT equation of state in a continuous-molecular targeting approach (CoMT-CAMD). Lee et al. [32] proposed a superstructure for ORC utilizing LNG cold energy that contains many possible structures and realized the simultaneous optimization for cycle parameters and structures. This simultaneous optimization method achieved by the superstructure is currently less used in the field of ORC and is commonly found in other fields such as CO2 capture [33,34]. Superstructure contains many possible structures and is able to optimize the cycle parameters and structures simultaneously, which will save the time for calculation. It is a very promising optimization method. According to the above review, it can be known that optimizing cycle structure and working fluid can enhance the efficiency of the power generation system utilizing LNG cold energy. However, to find the optimal cycle structure and the most suitable working fluid, they are usually optimized in two separate steps in traditional optimization method. In order to accomplish the optimization more efficiently, a one-step optimization method is proposed in this paper, which can optimize system structure and working fluid simultaneously with the superstructure and the working fluid selection coefficient. In addition, most previous studies focused on the improvement of heat exchange process and little attention is paid to the arrangements of compression and expansion process. The compression and expansion process are the power input and output process respectively in the power generation system and the arrangement for them will affect the working conditions of pump and turbine and thus affect the cycle performance. To this end, this paper focuses on the arrangements of compression and expansion process on the basis of the three-stage condensation Rankine cycle proposed in our previous work [23]. Nine different cycles are studied after combining three compression arrangements and three expansion arrangements. In order to find the optimal cycle structure and working fluid, a one-step optimization method with the superstructure that contains the 9 possible cycle structures is proposed and the selection coefficients are introduced for the studied working fluids. The superstructure is optimized through the genetic algorithm with the net power output as the objective function and the results are validated with the traditional optimization method. The effect of the gasified pressure of LNG on the optimum cycle structure is also studied. Finally, the cycle structures and working fluids are simultaneously optimized in one step at different vaporized pressures of LNG.

combined with LNG direct expansion cycle as well, which is known as the combined cycle [15–18]. Due to its low efficiency for power generation, there are few studies for LNG direct expansion cycle [19,20]. Therefore, whether a single ORC or a combined cycle is used to recover LNG cold energy, most studies focused on how to improve the ORC system. In order to improve the cycle performance, many researchers proposed new cycle structures based on the traditional ORC. Choi et al. [21] proposed a new power generation cycle employing multiple organic Rankine cycles in series. Li et al. [22] reported a cascade cycle with solar energy as the heat source and liquefied natural gas as the heat sink. In the cascade cycle, the heat released from the top cycle is absorbed by the bottom cycle, which leads to lower volume ratio for each turbine than a single ORC and thus results in an easier design and manufacture for turbines. In addition, they also proposed a new index called equivalent efficiency to evaluate the performance of combination of solar collectors and LNG. Wang et al. [23] gave a similar cascade transcritical CO2 Rankine cycle and subcritical NH3 Rankine cycle for the discharge process of the pumped thermal energy storage system utilizing ambient thermal energy and LNG cold energy. A high round trip efficiency (139%) is realized by different levels of low temperatures in the charge and discharge processes. Cao et al. [24] described a novel GT (gas turbine)-cascade CO2 combined cycle which composed of a gas turbine, a supercritical CO2 Brayton cycle and a transcritical CO2 cycle. After the optimization through the new solving procedure proposed by them, the novel cycle performed better on thermodynamic performance than the conventional GT-steam Rankine combined cycles. Zhang et al. [4] proposed a combined system that consisted of three Rankine cycles. The results by a multi-objective optimization showed that the combined system had more net power output, lower total investment cost and larger heat availability factor than separated systems. Zhao et al. [25] also proposed a system combining two ORCs in parallel for utilizing LNG cold energy and heat from CO2 capture process. The system could reach an exergy efficiency of 57% and provide electric power of 119.42 kW, and meanwhile product liquid CO2. Garcia et al. [26] proposed and analyzed an efficient power plant composed of three paratactic Rankine cycles and a direct expansion process of LNG. It was proved to yield a high exergy efficiency. Bao et al. [27,28] successively proposed a two-stage condensation Rankine cycle and a three-stage condensation Rankine cycle. Great enhancement in performance was achieved compared with single ORCs due to that multi-stage condensation leads to a better temperature match between working fluid and LNG. All of these new cycles are proved to be superior to traditional ORC systems, showing that the development of the cycle structure is an important way to improve the cycle performance. Besides the cycle structure, working fluid selection also affects the cycle performance. Zhang et al. [3] involved 16 different working fluids when they studied three different systems that utilized LNG cold energy, and identified the optimum working fluid for each system. Bao et al. [27] identified the optimum working fluid among the 14 candidates for the two-stage condensation Rankine cycle at different gasified pressures of LNG. Ferreira et al. [29] researched the effect of different working fluids on the cycle performance when they compared the LNG direct expansion, ORC and combined cycle. The work of Lee et al. [30] found that working fluid selection had a significant effect on the maximum exergy efficiency and optimum turbine inlet pressure. Therefore, working fluid selection is an element that must be considered in the study of enhancing cycle performance. Optimization is an indispensable part when improving the cycle performance. In recent years, the optimization method has also been developed to improve the efficiency of the calculation. In the traditional optimization method, it is common to optimize cycle parameters under the specified cycle structure and working fluid firstly, and then optimize the cycle structures and working fluids. These two steps are independent, which often requires a large amount of calculations and are likely to obtain suboptimal solutions. Therefore, some studies

2. System descriptions The three-stage condensation Rankine cycle with different arrangements of compression and expansion process using LNG cold energy is shown in Fig. 1. The system consists of a three-stage condensation Rankine cycle and a LNG gasification system. In the threestage condensation Rankine cycle, the sea water SW-IN1 enters into the evaporator as the heat source to provide heat to the cycle for vaporizing the working fluid. The vaporized working fluid generates power through the expansion process. The working fluid is divided into three streams in the expansion process. They respectively flow into the firststage condenser Cond 1, the second-stage condenser Cond 2 and the third-stage condenser Cond 3 to be condensed by LNG. After they are condensed at different condensation temperatures, the three streams enter into the compression process. The three streams of the working fluid are converged to one stream in the compression process and then it flows into the evaporator to begin a new cycle. In the LNG gasification system, LNG is pressurized by the pump P-6 and then passes through the first-stage, second-stage and third-stage condensers in turn to be gasified by absorbing the heat from the working fluid. It is eventually heated to the distributed temperature by the seawater SW121

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16a

19a P-1a 17a

a

4A 5A

P-2a

18a

Sea Water (SW)

21a

SW-IN2

SW-IN1

LNG P-5

SW-1 16b

P-2b

19b

Arrangements for compress process

P-1b 20b

18b

5B

1

24

Arrangements for expansion process

G Turb-1B

SW-OUT1 SW-2

16c

19c

c

P-2c

L-1

LNG

21c 20c P-3c

23c

22c

P-1c P-6

L-2 13 14 15

G

Cond1

L-3

L-4

NG

Cond2 Cond3 Reheater SW-OUT2

8B

2C

4C

3C

6C G 5C Turb-1C

7C 8C G Turb-3C

a+A=Cycle 1 b+A=Cycle 4 c+A=Cycle 7

a+B=Cycle 2 b+B=Cycle 5 c+B=Cycle 8

7B

Turb-3B

Turb-2C

18c

B

Turb-2B

6B G

P-3b

17c

4B

2B 3B

Evap 22b

21b

A

8A P-4

17b

G

Turb-2A G Turb-3A 6A G 7A

Working Fluid (WF)

P-3a

b

3A Turb-1A

2A 22a

20a

C G 9C

a+C=Cycle 3 b+C=Cycle 6 c+C=Cycle 9

Fig. 1. The structure diagram for nine three-stage condensation Rankine cycles with different compression and expansion arrangements.

stage condenser and the other stream flows into the first-stage condenser after expanding in the turbine Turb-3C.

IN2 in the reheater. In the above mentioned system, three different compression arrangements and three different expansion arrangements are proposed, respectively. Combining the different compression and expansion arrangements can obtain nine different three-stage Rankine cycle power generation systems, as shown in Fig. 1. The arrangements for compression process include the parallel arrangement (a), the partial parallel arrangement (b), and the serial arrangement (c). In the parallel arrangement (a), the three streams of the working fluid from the three condensers are pressurized by the pumps P-1a, P-2a and P-3a, respectively, and then enter into the evaporator after being mixed by the mixer. In the partial parallel arrangement (b), the two streams of the working fluid from the first-stage and second-stage condensers are pressurized by the pumps P-3b and P-2b, respectively, and after that they are mixed with the working fluid from the third-stage condenser. The converged stream is compressed by the pump P-1b and then flows into the evaporator. In the serial arrangement (c), the working fluid from the first-stage condenser is pressured by the pump P-3c and then it is mixed with the working fluid from the second-stage condenser. The stream converged by the first mixer is pressured by the pump P-2c and then is mixed with the working fluid from the third-stage condenser. The stream converged by the second mixer is pressured by the pump P1c and then flows into the evaporator to be vaporized. Similarly, the arrangements for expansion process also include the parallel arrangement (A), the partial parallel arrangement (B), and the serial arrangement (C). In the parallel arrangement (A), the working fluid vaporized by the evaporator is divided into three streams by the splitter, which respectively enter into the turbines Turb-1A, Turb-2A and Turb-3A to expand, and then flow into the condensers. In the partial parallel arrangement (B), the working fluid firstly expands in the turbine Turb-1B to generate power and then is divided into three streams by the splitter. One of them flows into the third-stage condenser and the other two flow into the second-stage and first-stage condensers after generating power in the turbines Turb-2B and Turb-3B, respectively. In the serial arrangement (C), the working fluid firstly expands in the turbine Turb-1C and then it is divided into two streams by the first splitter. One of them enters into the third-stage condenser and the other is divided into two streams again by the second splitter after expanding in the turbine Turb-2C. One of these two streams flows into the second-

3. Methods In order to compare the system performance of 9 cycles mentioned above, the working fluids and system parameters should be optimized. The traditional optimization process is a two-step process where the first step is to optimize the parameters and working fluids for each cycle, and the second step is to compare the nine cycles under their best conditions. If there are n candidates for working fluids, the 9 cycles will be optimized for 9n times in total. The optimum cycle structure and the optimum working fluid can be obtained by comparing the results. The traditional optimization process needs lots of calculations which is time-consuming. Therefore, this paper proposes a superstructure cycle and introduces the working fluid selection coefficients to improve the computational efficiency. Based on this, simultaneous optimization of cycle parameters, structures and working fluids can be achieved. 3.1. Superstructure The superstructure of the three-stage condensation Rankine cycle contains the nine cycles with different structures that are described in Section 2, as shown in Fig. 2. In this superstructure, the arrangements for compression and expansion process are optimized by the selection modules SP1 and SP2, respectively. The selection module SP1 is a ternary variable whose value set is {(1, 0, 0), (0, 1, 0), (0, 0, 1)}. The three values correspond to the parallel (a), partial parallel (b) and serial arrangement (c) for compression process, respectively. Similarly, the selection module SP2 is also a ternary variable with a value set of {(1, 0, 0), (0, 1, 0), (0, 0, 1)}. The three values correspond to the parallel (A), partial parallel (B) and serial arrangement (C) for expansion process, respectively. It should be noted that SP1 includes three sub-modules and the streams selected by the sub-modules of SP1 must have the same letter suffixes (such as the streams 16a, 17a, and 18a in Fig. 2) to achieve the selection of the compression arrangements. Thus, the values of all the three sub-modules are set to the same value, which is just the value of SP1. In summary, different values of SP1 and SP2 represent different 122

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17a 18a

P-1a

G

P-4

SP1=(1,0,0)

Turb-1A

Turb-2A

Turb-3A

A

SP2=(1,0,0) SW-1

16b 17b 18b

21b

19b P-2b

Evap

22b 24

P-1b

20b

b

19c 21c

18c P-3c

P-2c

20c

6B

Turb-1B

SP2

G

Turb-2B 8B

Turb-3B

B

SP2=(0,1,0)

4C

2C 3C

23c

G

P-1c

22c

7B G

G

SP1=(0,1,0)

16c 17c

4B 5B

3B

2B

1

SW-OUT1

P-3b

c

G

8A

5A

21a

G

4A 7A

2A

SW-IN1

P-3a

a

SP1

22a

20a

P-2a

6A

3A

19a

16a

5C

Turb-1C

6C

SW-IN2

G

Turb-2C

SP1=(0,0,1)

7C 9C

8C

G

Turb-3C

C

SP2=(0,0,1)

10

11

L-1

LNG

Cond1

13 14 15

P-6

Sea Water (SW)

L-2 Cond2

12 L-3

SW-2 L-4

P-5 NG

Cond3 Reheater SW-OUT2

Streams for working Fluid (WF)

LNG

L

Fig. 2. The superstructure of the three-stage condensation Rankine cycle.

17a 18a

P-1a

G

P-4

SP1=(1,0,0)

G

Turb-1A

Turb-2A

Turb-3A

A

SP2=(1,0,0) SW-1

16b 17b 18b

21b

19b P-2b

Evap

22b 24

P-1b

20b

18c P-3c

19c 21c 20c

P-2c

22c

3B

4B 5B 6B

Turb-1B

SP2

7B G

G

SP1=(0,1,0)

16c 17c

2B

1

SW-OUT1

P-3b

b

SP1

8A

5A

21a

G

4A 7A

2A

SW-IN1

P-3a

a

c

22a

20a

P-2a

6A

3A

19a

16a

G

Turb-2B 8B

Turb-3B

B

SP2=(0,1,0)

4C

2C 3C

23c

G

P-1c

Turb-1C

5C

6C

Turb-2C

SP1=(0,0,1)

SP2=(0,0,1)

G

7C 9C

8C

SW-IN2

G

Turb-3C

C 10

L-1

LNG

Cond1

13 14 15

P-6

Sea Water (SW)

11 L-2 Cond2

12 L-3

SW-2 L-4

P-5 NG

Cond3 Reheater SW-OUT2

Streams selected by SP1 and SP2

Streams not be selected

LNG L

Fig. 3. The system structure when SP1 = (0, 1, 0) and SP2 = (0, 0, 1).

taken as the variables as well as the condensation temperatures in the optimization process. In this way, the optimization of cycle parameter and cycle structure can be simultaneously achieved. Detailed implementation process is described in Section 4.

compression and expansion arrangements, respectively. For example, the corresponding cycle structure when SP1 is (0, 1, 0) and SP2 is (0, 0, 1) is as shown in Fig. 3. The values of SP1 and SP2 indicate that the partial parallel compression arrangement (b) and serial expansion arrangement (C) are selected. The selected arrangements for compression and expansion process are in green, and the other arrangements in grey are not selected. The selection modules SP1 and SP2, as ternary variables, can be

3.2. Selection coefficient for working fluid With the optimization of superstructure mentioned above, the 123

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the weather. (7) The isentropic efficiency of the pump and the turbines is assumed to be a constant value of 80%. (8) The pressures of all the interfaces of each mixer are the same. The thermodynamic properties of all the interfaces of each splitter are also the same. In this paper, the energy analysis is based on the first law of thermodynamics. The net power output is used as the performance index and it is equal to the difference between the sum of the power output of all turbines and the sum of the power consumption of all pumps, which is expressed as follows [35]: 3

Wnet =

i= 1

i= 4

(2)

Wnet = WTurb-1C + WTurb-2C + WTurb-3C−WP-1a−WP-2a−WP-3a−WP-4−WP-5 −WP-6

(3)

The power output of the turbines and the power consumption of the working fluid pumps can be calculated by Eqs. (4) and (5) [22]:

n

ai = 1

6

where WTurb-ij is the power output of the turbine Turb-ij, WP-ik is the power consumption of the working fluid pump P-ik, and WP-i is the power consumption of the seawater pump or LNG pump P-i. The value of j is a, b or c, which means the corresponding compression arrangement. And the value of k is A, B or C which means the corresponding expansion arrangement, as shown in Fig. 1. For example, the parallel compression arrangement (a) and the serial expansion arrangement (C) indicate that j = a and k = C, respectively, and therefore the net power output of this system obtained from Eq. (3) is calculated as follows:

corresponding optimum cycle parameter and system structure can be obtained simultaneously for each working fluid. However, if there are n working fluid candidates, it still needs to be optimized for n times. Is it possible to get the optimum cycle parameter, cycle structure and working fluid optimized through only one optimization step? To this end, the selection coefficient ai (i = 1, 2, … , n) for working fluid selection is introduced in this paper, as shown in Fig. 4. All selection coefficients are binary variables with the value set {0, 1}. If ai = 1, it means that the working fluid i that corresponds to this coefficient is used in the cycle. In contrast, if ai = 0, it means that the working fluid i is not used. Since only pure working fluids are involved in this study, which means only one working fluid can be selected every time, the selection coefficient should be constrained as follows:

i= 1

3

WTurb-ik− ∑ WP-ij− ∑ WP- i

i= 1

Fig. 4. The schematic of selection coefficient.

∑

∑

WTurb -ik = ηTurb- ik mTurb - ik ΔhTurb-ik,is

(1)

In this way, it can be known which working fluid is used according to the value of ai and the optimization of working fluids can be achieved by optimizing the selection coefficients. If system parameters, selection modules SP1 and SP2, and selection coefficients ai for working fluids are all taken as the optimization variables, the optimum cycle parameter, structure and working fluid can be obtained through only one optimization step. Detailed implementation process will be discussed in Section 4.

WP-ij =

(4)

mP-ijΔhP-ij,is ηP-ij

(5)

The power consumption of the seawater or LNG pumps can be calculated by Eq. (6) [22]:

WP-ij =

mP- i ΔhP-i,is ηP- i

(6)

In Eqs. (4)–(6), η is the isentropic efficiency of the turbines or pumps, m is the mass flow rate of the working fluid and Δh is the specific enthalpy change when the working fluid passes through the turbines or pumps. The subscript ‘is’ means ‘isentropic’. In this paper, Aspen Hysys is used to simulate the superstructure of the three-stage condensation Rankine cycle, and there are physical properties calculation packages in this software. The built-in PengRobinson equation in the software is used to calculate the physical properties during the simulation process. In the actual simulation, the selection modules SP1 and SP2 that control the cycle structure are realized by the splitters in Aspen Hysys. The splitter is able to decide which path of compression or expansion the working fluid can enter by adjusting its flow ratios, and the corresponding compression or expansion process arrangement could be determined. The selection module SP1 mentioned above includes three sub-modules and they correspond to the three splitters in Hysys. The value of first sub-module is specified to equal to that of the module SP1, corresponding to the flow ratios of the first splitter. The other two splitters have the same flow ratios with the first splitter, which is ensured by the module Set in Hysys. In this way, the three sub-modules are ensured to have the same values. The selection coefficient can change the molar fraction of the corresponding working fluid in Hysys to realize the selection of working fluid. The molar fraction xi of the working fluid i is obtained as follows:

4. Implementation details In order to simplify the analysis, the following assumptions are made: (1) The whole system runs under a steady state, that is, the parameters of each state point do not change with time. (2) Except for the pumps and turbines, the pressure drops of the heat exchangers, splitters and mixers and pipelines in the system are negligible. (3) Each stage condenser of the system condenses the working fluid to the saturated liquid that corresponds to its condensation temperature. The evaporator heats the working fluid to saturated vapor and the evaporation temperature is fixed to 10 °C. (4) The heat released to the environment by the components and pipelines is negligible. It means that there is no extra heat loss caused by the ambient temperature in the components and the temperature is constant in the same pipeline without the effect of its distance. (5) The mechanical losses for the pumps and turbines are negligible. That is, the conversion rate between the mechanical work and electricity is 100%. (6) The environment temperature and pressure are assumed to be 15 °C and 100 kPa, respectively. And they are assumed not to change with 124

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Table 1 The physical parameters of the working fluids [36].

Table 4 The optimization variables and their ranges.

Working fluids

Chemical name

Tcrit (°C)

Pcrit (bar)

Optimization variables

R290 R600 R600a R601 R601a R123 R245ca R245fa R236ea R227ea R32 R152a

Propane N-butane I-butane N-pentane I-pentane 2,2-dichloro-1,1,1-trifluoroethane 1,1,2,2,3-pentafluoropropane 1,1,1,3,3-pentafluoropropane 1,1,1,2,3,3-hexafluoropropane 1,1,1,2,3,3,3-heptafluoropropan Difluoromethane 1,1-difluoroethane

96.7 152.0 134.7 196.6 187.2 183.7 174.4 154.0 139.3 101.8 78.1 113.2

42.5 38.0 36.3 33.7 33.8 36.6 39.3 36.5 35.0 30.0 57.8 45.1

The The The The The The The The The The The The The The The The The

R601a

195

R123 R245ca

R601 R245fa

°C

R600

130

R600a

The mole fraction of the working fluid obtained from Eq. (7) can be inputted to the system by using the spreadsheet in Aspen Hysys. 12 kinds of working fluids are involved in this work, whose physical parameters and T-s diagrams are shown as Table 1 and Fig. 5, respectively. It can be seen from Fig. 5 that the slopes of the saturated vapor curves of these working fluids are negative when temperature is low. Since the inlet temperatures of some turbines in the partial parallel and serial expansion arrangements are low and the working fluid is easy to enter into the two-phase zone after expanding, additional constraint should be set in the optimization process. If the inlet of turbine has liquid phase, the net power output is specified as a very small value (such as 0 kW). By this way, the situations that the inlet of turbine has liquid will be eliminated. The specific implementation is achieved by the syntax “if” of Matlab: if the gas phase fraction of a certain turbine inlet is 1, the output value of the net power output is the calculated value, and otherwise it is 0 kW. The temperature of LNG used in the simulation is −162 °C and its pressure is 1 bar. The mass flow rate of LNG is 1 kg/s. The molar fractions of the compositions of the LNG are 91.33% of methane, 5.36% of ethane, 2.14% of propane, 0.47% of n-butane, 0.46% of isobutane, 0.01% of n-pentane, 0.01% of isopentane and 0.22% of nitrogen. The other input parameters are shown in Table 2. To finish the optimization of the superstructure, Matlab is connected with Aspen Hysys by ActiveX technology. ActiveX is a standard protocol based on the COM (Component Object Model) technology. It can establish a connection between two software modules so that the two software modules can communicate through an “interface”. As a client in ActiveX, Matlab can also connect to the other softwares. The built-in function “actxserver” can create a COM server running Aspen Hysys, and Matlab can be connected as a controller with Hysys through ActiveX. In this way, the spreadsheet in Hysys can be controlled by the Matlab programs so that the cells can be written or read. The spreadsheet in Hysys can connect to the data in the simulated process. So, Matlab programs can use ActiveX technology to input or read the system parameters in the simulated process, and then these system parameters be optimized by algorithm involved in Matlab. The problem in this paper is optimized by genetic algorithm, which is achieved by the built-in genetic algorithm toolbox of Matlab. Genetic algorithm is based on natural selection and genetic theory. It is an efficient global search algorithm that combines the rule of survival of the fittest in biological evolution process with the mechanism of random information exchange of internal chromosomes in the groups. It is widely used in process optimization issues. The parameters input in genetic algorithm are shown in Table 3. The variables of the optimization process are the first-stage, second-stage and third-stage condensation temperatures, the selection modules SP1 and SP2, and the

R227ea

R290

R32

0 -65 -130

-9

-8

-7

-6

-5

-4

-3

Specific Entropy(kJ kg-1 °C -1)

-2

-1

Fig. 5. T-s diagram of the working fluids. Table 2 The input parameters for the simulation. Parameters

Values

Isentropic efficiency of pumps Isentropic efficiency of turbines Evaporation temperature of the working fluid Pinch point of the condensers Temperature of sea water Pressure of sea water Temperature of sea water at the outlet of evaporator and reheater Pressure of sea water at the outlet of evaporator and reheater Temperature of NG Pressure of NG

80% 80% 10 °C 5 °C 15 °C 1 bar 10 °C 3 bar 10 °C 70 bar

Table 3 The parameters input in genetic algorithm. Parameters

Values

Crossover fraction Migration interval Migration fraction Initial penalty Penalty factor Population size for simultaneous optimization Population size for structure optimization Generations Function tolerance

0.8 20 0.2 10 100 800 100 100 1 × 10−6

n

x i = ai

∑ i= 1

ai

[−130, −100] [−99, −60] [−55, −15] {(1, 0, 0), (0, 1, 0), (0, 0, 1)} {(1, 0, 0), (0, 1, 0), (0, 0, 1)} {0, 1} {0, 1} {0, 1} {0, 1} {0, 1} {0, 1} {0, 1} {0, 1} {0, 1} {0, 1} {0, 1} {0, 1}

R236ea

R152a

65

first-stage condensation temperature second-stage condensation temperature third-stage condensation temperature selection module SP1 selection module SP2 selection coefficient a1 for R290 selection coefficient a2 for R600 selection coefficient a3 for R600a selection coefficient a4 for R601 selection coefficient a5 for R601a selection coefficient a6 for R123 selection coefficient a7 for R245fa selection coefficient a8 for R245ca selection coefficient a9 for R236ea selection coefficient a10 for R227ea selection coefficient a11 for R32 selection coefficient a12 for R152a

Ranges

(7)

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Table 5 The optimization results of the superstructure. The optimum compression arrangement

The optimum expansion arrangement

a

A

b

c

B

Tcond1 (°C)

Tcond2 (°C)

Tcond3 (°C)

The net output power (kW)

Time (min)

−118.46

−77.58

−38.29

107.4676

57.3

C

▴

△

Table 6 The optimization results with the traditional method. Cycles

Cycle Cycle Cycle Cycle Cycle Cycle Cycle Cycle Cycle

1 2 3 4 5 6 7 8 9

The corresponding compression arrangement

The corresponding expansion arrangement

a

A

b

c

▴ ▴ ▴

B

△ △ △ △ △ ▴ ▴ ▴

△ △ △

Gasified pressure of LNG (bar)

Long distance transmission Local distribution Combined cycle stations Steam power stations

70 30 25 6

Tcond3 (°C)

The net output power (kW)

Time (min)

−118.26 −118.26 −118.21 −118.20 −118.32 −118.35 −118.20 −118.27 −118.35

−77.15 −77.35 −77.33 −77.08 −77.38 −77.34 −77.08 −77.38 −77.44

−38.11 −38.62 −38.26 −38.14 −38.63 −38.27 −38.14 −38.65 −38.27

103.9412 106.4266 107.4669 103.9430 106.4269 107.4675 104.0345 106.4276 107.4695

16.6 14.8 14.2 13.9 17.1 14.0 13.9 15.5 12.7

C). The maximum net power output reaches 107.4676 kW. As for the traditional optimization method, these 9 cycles needed to be optimized respectively, as shown in Table 6. It can be seen that the maximum net power output of Cycle 9 is 107.4695 kW and is the highest of the nine cycles, which means the corresponding compression and expansion arrangements of Cycle 9 are the optimum. Therefore, the credibility of the optimization results of the superstructure is verified. In addition, to obtain the optimum cycle structure, the superstructure only needs one-step optimization, which takes 57.3 min. While the traditional method needs nine times of optimization, which takes 132.7 min totally. This illustrates that using the superstructure to optimize the three-stage condensation Rankine cycle can not only get credible results, but also greatly improve the optimization efficiency. From Table 6, it can also be found that when the expansion arrangement is the same, the compression arrangement has little effect on the cycle performance. The difference in net power output between the optimum (the serial compression arrangement) and the worst (the parallel compression arrangement) cases is less than 0.1%, which can even be negligible. And when the expansion arrangement is the same, the expansion arrangement has relatively significant effect on the cycle performance. The difference in net power output between the optimum (the serial expansion arrangement) and the worst (the parallel expansion arrangement) cases is about 3.4%. However, the above conclusions can’t be obtained from Table 5, which indicates that the proposed superstructure optimization also has its deficiency: only the optimal cycle structure can be obtained, but the specific characteristics of the different structures cannot be known exactly.

Table 7 The gasified pressures of LNG at different applications [1] Applications

Tcond2 (°C)

C

△

▴ ▴ ▴

Tcond1 (°C)

selection coefficients for working fluids. The condensation temperatures are continuous variables and the other variables are discrete variables. The optimization variables and their ranges are shown in Table 4. 5. Results and discussions 5.1. Verification for the superstructure optimization In order to verify the credibility of the optimization results for the superstructure and compare the consumed time of the calculations, the results of superstructure optimization are compared with that of the traditional optimization method. R601 is used as the working fluid in the verification process, so the optimization of working fluid is not involved, which means that the optimization variables are only three condensing temperatures and selection modules SP1 and SP2. The values and ranges of these variables in the optimization process are shown in Table 3. The optimization results of the superstructure are shown in Table 5. The optimized values of SP1 and SP2 are (0, 0, 1) and (0, 0, 1), respectively. It indicates that the optimum arrangements of the compression and expansion process are both the serial arrangement (c and

5.2. The effect of the gasified pressure The gasified pressure of LNG depends on its application [1], as

Table 8 The optimization results of the superstructure with R601 as the working fluid. Gasified pressure of LNG (bar)

70 30 25 6

The optimum compression arrangement

The optimum expansion arrangement

a

A

b

c

B

▴ ▴ ▴ ▴

Tcond2 (°C)

Tcond3 (°C)

The net output power (kW)

−118.46 −119.99 −122.52 −122.00

−77.58 −79.46 −85.03 −85.23

−38.29 −43.70 −46.93 −49.33

107.4676 167.4233 178.9290 266.6601

C △ △ △ △

126

Tcond1 (°C)

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Table 9 The optimization results of the superstructure with R600 as the working fluid. Gasified pressure of LNG (bar)

The optimum compression arrangement

The optimum expansion arrangement

a

A

b

c

B

Tcond2 (°C)

Tcond3 (°C)

The net output power (kW)

−118.43 −120.03 −122.54 −122.27

−77.63 −79.47 −84.89 −89.69

−38.28 −43.63 −46.70 −52.35

105.9816 165.4413 176.7605 263.9833

Tcond1 (°C)

Tcond2 (°C)

Tcond3 (°C)

The net power output (kW)

−119.31 −120.54 −122.80 −122.84

−79.06 −79.82 −85.32 −93.87

−38.83 −44.91 −47.76 −52.35

107.5763 168.1781 180.9446 271.5661

C

▴ ▴ ▴ ▴

70 30 25 6

Tcond1 (°C)

△ △ △ △

Table 10 The optimization results of the superstructure with R245ca as the working fluid. Gasified pressure of LNG (bar)

The optimum compression arrangement

The optimum expansion arrangement

a

A

b

c

B

▴ ▴ ▴ ▴

70 30 25 6

C

△ △ △ △

Table 11 Optimization results of the superstructure with different working fluids when the gasified pressure of LNG is 70 bar. Working fluids

R290 R600 R600a R601 R601a R123 R245ca R245fa R236ea R227ea R152a R32

The optimum compression arrangement

The optimum expansion arrangement

a

A

b

c ▴ ▴ ▴ ▴ ▴ ▴ ▴ ▴ ▴ ▴ ▴ ▴

B

Tcond1 (°C)

Tcond2 (°C)

Tcond3 (°C)

The net power output (kW)

−118.21 −118.44 −118.60 −118.56 −118.57 −118.83 −119.31 −118.10 −119.02 −118.24 −118.07 −117.92

−77.31 −77.63 −77.99 −77.78 −77.72 −78.26 −79.06 −77.29 −78.37 −77.28 −77.27 −77.07

−38.49 −38.28 −38.41 −38.41 −38.44 −38.72 −38.83 −38.17 −38.39 −38.15 −38.34 −38.24

101.9122 105.9816 105.4488 107.4690 108.0532 106.5898 107.5763 105.1741 105.3942 105.1586 102.1695 102.3984

C

△ △ △ △ △ △ △ △ △ △ △ △

structure of the three-stage condensation Rankine cycle, the superstructure with different working fluids when the gasified pressure of LNG is 70 bar is optimized and the results are shown in Table 11. Furthermore, the optimum arrangements for compression process are always the serial arrangement (c) when different working fluids are used. However, the optimal arrangements for expansion process are different. Among 12 studied working fluids, the optimum expansion arrangements of most working fluids are serial arrangements (C), while the optimum expansion arrangements of R290, R123 and R245ca are partial parallel arrangements (B) and the optimum expansion arrangements of R152a and R32 are parallel arrangements (A). The different optimum expansion arrangements of the working fluids are caused by the additional constraint that mentioned in Section 4, which is that if the inlet of turbine has liquid phase, the net power output is specified as a very small value (such as 0 kW). Theoretically, the order of three expansion arrangements are C, B and A according to their performance. However, the inlet temperatures of some turbines in the partial parallel (B) and serial (C) expansion arrangements are low and the working fluid is easy to enter into the two-phase zone after expanding, which is not allowed technically. Therefore, the working fluids may correspond to different optimum expansion arrangements. To explain the reason more clearly, T-s diagrams of the infeasible expansion arrangements for R290, R123, R245ca, R152a and R32 are shown in Fig. 6, where the condenser temperatures are the optimum that corresponds to their actual optimum expansion arrangements. When the expansion arrangements for R290, R123 and R245ca are serial arrangements (C), it can be seen that from Fig. 6a–c that the state

shown in Table 7. Therefore, it is necessary to study the optimum compression and expansion arrangements at different gasification pressures of LNG. R601 is still used as the working fluid. The optimization results of the superstructure at different gasified pressures are shown in Table 8. The results show that when the working fluid is specified, the gasified pressure of LNG has no influence on the optimum compression and expansion arrangements in the three-stage condensation Rankine cycle, and the optimum arrangements for them are both the serial ones (c and C). Furthermore, the net power output of three-stage condensation Rankine cycle is increased with the reduction of the gasified pressure of LNG. In order to avoid the accidental effect of using only one working fluid, the superstructure is also optimized with R600 and R245ca as working fluids. The results are shown in Tables 9 and 10, respectively. The results prove that the previous conclusion is credible, that is, the optimum cycle structure is not affected by the gasified pressure of LNG when the working fluid of the three-stage condensation Rankine cycle is specified. Furthermore, as seen from Table 10, the optimum arrangement for expansion process is the partial parallel arrangement (B) with R245ca as the working fluid, which is different from that of R601 and R600. It implies that working fluids have influence on the optimum structure of the three-stage condensation Rankine cycle and it will be discussed in detail in Section 5.3. 5.3. The effect of the working fluid on the cycle structure In order to explore the effect of working fluid on the optimal 127

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a)

R290 10

b)

2C

3C/4C/5C

-30

-50

Saturationcurve Arrangement C

3C/4C/5C

-50

-70

-70

6C/7C/8C

-90

6C/7C/8C

-90

-110

-110

9C

-130 -7.00

-6.75

-6.50

-6.25

-6.00

-5.75

2C

2B(2C)

3C/4C/5C

-30

-70

-70

6C/7C/8C

-1.00

3B/4B/5B/6B (3C/4C/5C)

-50

-50

-1.25

Saturation curve Arrangement B Arrangement C

-10 °C

-30

-1.50

R152a 10

Saturationcurve Arrangement C

-10

-1.75

Specific Entropy(kJ kg-1 °C-1)

d)

R245ca 10

9C

-130 -2.00

-5.50

Specific Entropy(kJ kg-1 °C -1)

c)

°C

2C

-10 °C

°C

-30

10

Saturation curve Arrangement C

-10

R123

7B(6C/7C/8C)

-90

-90 -110

-110

9C

-130 -3.00

-2.75

-2.50

-2.25

-2.00

-1.75

-1.50

Specific Entropy(kJ kg-1 °C -1)

e)

-3.25

-3.00

-2.75

-2.50

Specific Entropy(kJ kg-1 °C -1)

-2.25

R32 10

2B(2C)

Saturation curve Arrangement B Arrangement C

-10 °C

9C 8B

-130 -3.50

-30 -50

3B/4B/5B/6B (3C/4C/5C)

-70

7B(6C/7C/8C)

-90 -110 -130 -2.50

9C 8B

-2.25

-2.00

-1.75

-1.50

-1.25

Specific Entropy(kJ kg-1 °C -1)

-1.00

Fig. 6. T-s diagrams of the infeasible expansion arrangements for (a) R290, (b) R123, (c) R245ca, (d) R152a and (e) R32.

Furthermore, it can be found from Table 11 that R601a is the optimum working fluid with the maximum net power output of 108.05 kW, which is about 6% more than the worst working fluid R290. Therefore, the influence of the working fluid on the cycle performance is significant and obtaining the optimal working fluid and system structure under different gasified pressures of LNG is necessary, which is studied in Section 5.4.

point (8C) at the inlet of Turb-3C is always in the two-phase zone. Thus the optimum expansion arrangements of them are partial parallel ones (B). Similarly, when the expansion arrangements for R152a and R32 are partial serial arrangements (B), they are in the two-phase zone at the inlets of Turb-2B and Turb-3B (4B and 5B, respectively), and when the expansion arrangements for them are serial ones (C), they are in the two-phase zone at the inlets of Turb-2C and Turb-3C (5C and 8C, respectively). Thus, the optimum expansion arrangements of them only can be parallel ones (A). 128

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Table 12 Simultaneous optimization results of the superstructure. Gasified pressure of LNG (bar)

The optimum working fluid

The optimum compression arrangement a

70 30 25 6

R601a R601a R245ca R245ca

b

The optimum expansion arrangement

c

C

▴ ▴ ▴ ▴

△ △ △ △

Tcond1 (°C)

Tcond2 (°C)

Tcond3 (°C)

The net power output (kW)

−118.57 −120.17 −123.04 −123.03

−77.73 −79.47 −85.21 −96.67

−38.43 −43.64 −47.52 −52.50

108.0532 168.1549 180.9446 271.5661

output between the optimum and worst cases is about 3.4%. (2) When the working fluid is specified, the corresponding optimum cycle structure is not affected by the gasified pressure of LNG. (3) The optimum compression arrangements for all working fluids are the serial arrangements, while the optimum expansion arrangements may be different. This is affected by the technical constraint of turbines that the working fluid is not allowed to be the two-phase state at the inlets of the turbines at low inlet temperatures. (4) The results of simultaneous optimization show that when the LNG gasification pressure is 70 or 30 bar, the optimum working fluid is R601a and the optimum compression and expansion arrangements are both serial. When the LNG gasification pressure is 25 or 6 bar, the optimum working fluid is R245ca and the optimum compression and expansion arrangement is serial and partial parallel, respectively. The maximum net power output can reach 108 kW, 168 kW, 180 kW and 271 kW when the LNG gasified pressure is 70 bar, 30 bar, 25 bar and 6 bar, respectively.

5.4. Simultaneous optimization It is known from Section 5.3 that the net power output of R601a is maximum in the several working fluids involved when the gasified pressure of LNG is 70 bar. However, the optimization method used in Section 5.3 will be very cumbersome if there are too many working fluids taken into account because of each working fluid needs an optimization process. In order to further improve the optimization efficiency, the selection coefficient ai is introduced. The methodology and implementation details of the selection coefficients have been described in Sections 3.2 and 4. In this section, all the variables in Table 3 need to be optimized simultaneously. The simultaneous optimization results of at different gasified pressures of LNG are shown in Table 12. When the gasified pressure of LNG is 70 bar or 30 bar, the optimum working fluid is R601a and the corresponding optimum arrangements for compression and expansion process are both the serial arrangements (c and C). When the gasified pressure of LNG is 25 bar or 6 bar, the optimum working fluid is R245ca and the corresponding optimum arrangements for compression and expansion process are the serial arrangement and the partial parallel arrangement respectively (c and B). In addition, when the gasified pressure of LNG is 25 bar or 6 bar, R245ca performs the best though the serial expansion arrangement is unfeasible for it. This result also implies that whether the serial expansion arrangement is feasible for the working fluids or not can’t be taken as a criterion for judging the working fluid’s performance. Generally, it is necessary to optimize working fluids and system structure at different gasified pressure of LNG and the proposed optimization method with superstructure and selection coefficients provides an efficiency approach to solve this problem.

Acknowledgements This research was financially supported by the National Natural Science Foundation of China (No. 51606025), MOST innovation team in key area (No. 2016RA4053), the Fundamental Research Funds for the Central Universities (Grant No. DUT17RC (4)29), Liaoning Province S & T Department (Grant No. 201601034) and Education Department (LT2015007). References [1] B.B. Kanbur, L. Xiang, S. Dubey, F.H. Choo, F. Duan, Cold utilization systems of LNG: a review, Renew. Sustain. Energy Rev. 79 (2017) 1171–1188. [2] Petrol B. BP energy outlook; 2017 [Online]. [3] M.G. Zhang, L.J. Zhao, Z. Xiong, Performance evaluation of organic Rankine cycle systems utilizing low grade energy at different temperature, Energy 127 (2017) 397–407. [4] M.-G. Zhang, L.-J. Zhao, C. Liu, Y.-L. Cai, X.-M. Xie, A combined system utilizing LNG and low-temperature waste heat energy, Appl. Therm. Eng. 101 (2016) 525–536. [5] H. Liu, L. You, Characteristics and applications of the cold heat exergy of liquefied natural gas, Energy Convers. Manage. 40 (1999) 1515–1525. [6] M. Mehrpooya, M. Rajabi, M. Aghbashlo, M. Tabatabai, S. Hosseinpour, S. Ramakrishna, Design of an integrated process for simultaneous chemical looping hydrogen production and electricity generation with CO2 capture, Int. J. Hydrogen Energy 42 (2017) 8486–8496. [7] M. Mehrpooya, M.A. Rosen, Energy and exergy analyses of a novel power cycle using the cold of LNG (liquefied natural gas) and low-temperature solar energy, Energy 95 (2016) 324–345. [8] M. Mehrpooya, A novel integration of oxy-fuel cycle, high temperature solar cycle and LNG cold recovery- energy and exergy analysis, Appl. Therm. Eng. 114 (2017) 1090–1104. [9] M. Mehrpooya, M.A. Rosen, Optimum design and exergy analysis of a novel cryogenic air separation process with LNG (liquefied natural gas) cold energy utilization, Energy 90 (2015) 2047–2069. [10] M. Mehrpooya, Conceptual and basic design of a novel integrated cogeneration power plant energy system, Energy 127 (2017) 516–533. [11] Y. Song, J. Wang, Y. Dai, E. Zhou, Thermodynamic analysis of a transcritical CO2 power cycle driven by solar energy with liquified natural gas as its heat sink, Appl. Energy 92 (2012) 194–203. [12] J.F. Wang, Z.Q. Yan, M. Wang, Y.P. Dai, Thermodynamic analysis and optimization of an ammonia-water power system with LNG (liquefied natural gas) as its heat sink, Energy 50 (2013) 513–522. [13] H. Sun, H.M. Zhu, F. Liu, H. Ding, Simulation and optimization of a novel Rankine

6. Conclusion This paper proposes different arrangements for the compression and expansion process of the three-stage condensation Rankine cycle. Combination of the different compression and expansion arrangements can obtain nine cycles with different structures. To improve the efficiency of the optimization, the superstructure that contains 9 possible structures are proposed. The reliability of the optimization results of the superstructure is verified at first. Then the effect of the gasified pressure LNG on the optimum cycle structure is studied. Finally, the optimum cycle parameter, structure and working fluid are simultaneously optimized by introducing the selection coefficients. It can be concluded as follows: (1) For the three-stage condensation Rankine cycle, when using R601 as the working fluid, the compression arrangement has little effect on the cycle performance and the serial arrangement performs slightly better than the other two arrangements. The difference in net power output between the optimum and the worst cases is less than 0.1%. However, the influence of expansion arrangements on cycle performance is relatively obvious, where the serial arrangement is the best, the partial parallel arrangement is the next and the parallel arrangement is the worst. The difference in net power 129

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