Analysis and optimisation of a mixed fluid cascade (MFC) process

Accepted Manuscript Analysis and optimisation of a mixed fluid cascade (MFC) process He Ding, Heng Sun, Shoujun Sun, Cheng Chen PII: DOI: Reference:

S0011-2275(16)30114-X http://dx.doi.org/10.1016/j.cryogenics.2017.02.002 JCRY 2665

To appear in:

Cryogenics

Received Date: Revised Date: Accepted Date:

8 May 2016 30 January 2017 3 February 2017

Please cite this article as: Ding, H., Sun, H., Sun, S., Chen, C., Analysis and optimisation of a mixed fluid cascade (MFC) process, Cryogenics (2017), doi: http://dx.doi.org/10.1016/j.cryogenics.2017.02.002

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Analysis and optimisation of a mixed fluid cascade (MFC) process He Ding, Heng Sun *, Shoujun Sun, Cheng Chen National Engineering Laboratory for Pipeline Safety/MOE Key Laboratory of Petroleum Engineering /Beijing Key Laboratory of Urban Oil and Gas Distribution Technology, China University of Petroleum-Beijing, Beijing 102249, China Abstract: A mixed fluid cascade (MFC) process that comprises three refrigeration cycles has great capacity for large-scale LNG production, which consumes a great amount of energy. Therefore, any performance enhancement of the liquefaction process will significantly reduce the energy consumption. The MFC process is simulated and analysed by use of proprietary software, Aspen HYSYS. The effect of feed gas pressure, LNG storage pressure, water-cooler outlet temperature, different pre-cooling regimes, liquefaction, and sub-cooling refrigerant composition on MFC performance are investigated and presented. The characteristics of its excellent numerical calculation ability and the user-friendly interface of MATLAB™ and powerful thermo-physical property package of Aspen HYSYS are combined. A genetic algorithm is then invoked to optimise the MFC process globally. After optimisation, the unit power consumption can be reduced to 4.655 kWh/kmol, or 4.366 kWh/kmol on condition that the compressor adiabatic efficiency is 80 %, or 85 %, respectively. Additionally, to improve the process further, with regards its thermodynamic efficiency, configuration optimisation is conducted for the MFC process and several configurations are established. By analysing heat transfer and thermodynamic performances, the configuration entailing a pre-cooling cycle with three pressure levels, liquefaction, and a sub-cooling cycle with one pressure level is identified as the most efficient and thus optimal: its unit power consumption is 4.205 kWh/kmol. Additionally, the mechanism responsible for the weak performance of the suggested liquefaction cycle configuration lies in the unbalanced distribution of cold energy in the liquefaction temperature range.

Keywords: Mixed refrigerant; Genetic algorithm; Unit power consumption; Configuration optimisation.

1

1 Introduction Natural gas is a mixture of paraffinic hydrocarbons such as methane, ethane, propane, butane, etc., and the combustion of natural gas gives off lower emissions of CO 2 and other pollutants than the combustion of coal and oil [1]. Thus, natural gas has emerged as a preferred fuel due to its inherent environmental benignity, greater efficiency, and cost effectiveness [2]. When the distance between natural gas reservoirs to downstream markets is long enough, liquefying the natural gas to reduce its volume by a factor of approximately 600 for transportation has been identified as a practical solution. According to BP’s statistical review [3]: LNG accounts for 33.42 % of the global total natural gas traded in 2014, which increases by 6.13 % compared with that in 2013. However, natural gas liquefaction processes are energy-intensive and capital-intensive, so promoting the use of clean natural gas drives efforts to save process energy consumption and optimise the process configurations. Castillo [4] investigated the selection of a pre-cooling cycle for the LNG process in terms of technical advantages/disadvantages, the performance of using a pure propane, or mixed, refrigerant in the pre-cooling stage for C3MR and MFC processes was analysed, and the three stage propane pre-cooled cycle was found to be the most energetically efficient for both climate conditions. Khan [5] indicated the limitations of pure refrigerant and benefits of mixed refrigerant, and a practical method was proposed for selecting an appropriate refrigerant composition by using the deviated gain distribution of a component to analyse MR component gain distributions and component sensitivity over the exchanger length. Wang [6] identified the opportunities for C3MR process energy consumption minimisation through thermodynamic analysis and established an optimisation model with a sequential quadratic programming (SQP) solver as the chosen optimisation tool. Traditional deterministic optimisation methods may be easily be trapped in local optima. Khan [7] adopted a particle swarm paradigm algorithm to optimise the SMR process and used an augmented Lagrange penalty function to fold constraints into an objective function. Xu [8] optimised the SMR process by genetic algorithm and performed linear regression on the MR composition under different cold box inlet temperature conditions, the concentrations of methane, ethylene and propane will decrease at higher cold box inlet temperatures, and the amount of i-pentane generated will increase. Alabdulkarem [9] optimised a C3MR process by using HYSYS to develop a computer model and genetic algorithm from the MATLAB™ optimisation toolbox to search for a globally optimal solution. The mixed refrigerant cycle and propane pre-cooling cycle were optimised in sequence, and the unit power consumption was reduced to 5.14 kWh/kmol. He [10] optimised a parallel nitrogen expansion process by using a genetic algorithm, the flexibility of the process was tested under two feed gas conditions. Wang [11] optimised C3MR and DMR processes from both thermodynamic and economic points of view, and four different objective functions were selected and investigated. It was indicated that minimising the total capital cost of compressors and main cryogenic exchangers is more efficient than other objective functions, when aiming at reducing both shaft work and UA. Hatcher [12] improved the C3MR process by considering both design optimisation and operational optimisation. Eight objective functions were tested for their efficiency when searching for optimal conditions. Lim [13] focused on the cold energy recovery of LNG processes by considering using some of the natural gas as a fuel gas, or by taking the liquefaction ratio as the principal design factor. The proposed configuration was validated by simulation of C3MR, SMR, and single stage nitrogen expansion, and the specific work, refrigerant flow rate, and seawater cooling duties for all simulated process were reduced 2

respectively. Enhancement of C3MR process efficiency can be achieved by replacing conventional expansion process with expanders or by using an absorption chiller powered by gas turbine waste heat [14-15]. Jensen [16] indicated that determining the number of steady state degrees of freedom was important for optimal operation and plant-wide control, and methods to determine the potential degrees of freedom and actual degrees of freedom for C3MR and MFC processes were presented. Jensen [17] studied these degrees of freedom and how to adjust their number to achieve optimal steady-state operation with an MFC process used as an example. Mehrpooya [18] adopted an absorption refrigeration system that was powered by waste heat as an MFC process for research purposes. Mehrpooya [19] conducted advanced exergoeconomic analysis of C3MR, DMR, and MFC processes, and then a comparison was undertaken based on their exergy efficiencies, exergoeconomic factors, and total costs. Mehrpooya [20] used C3MR, DMR, and MFC refrigeration systems to supply the required refrigeration for the coproduction of LNG and NGL, and a high ethane recovery rate was achieved. The mixed fluid cascade (MFC) process was developed by Linde in collaboration with Statoil and was applied in the Snohvit LNG project. Compared with cascade processes, the MFC process has a higher efficiency as it uses three different mixed refrigerant compositions instead of three pure refrigerants [1]. Demand for larger LNG train capacity and lower unit cost can be achieved by the use of an MFC process. However, the MFC process is relatively complex with many design variables, the mixed refrigerant compositions differ in each refrigeration cycle in order to provide cold energy efficiently in each temperature range. The main aim of the study is to search globally optimal solutions for an MFC process by optimising the mixed refrigerant compositions and many design variables simultaneously, and then the process configuration is optimised with a view to further improving thermodynamic efficiency.

2 Process design 2.1 Liquefaction process Figure 1 shows a schematic representation of this MFC process: it entails three refrigeration cycles, and different refrigerant compositions are provided for each cycle in order to perform the pre-cooling, liquefaction, and sub-cooling duties respectively. As shown in Figure 1: natural gas (101) goes through the LNG heat exchangers (LNG-101, LNG-102, and LNG-103) and is liquefied when its temperature decreases to -150.1 °C. The pressure of the liquefied natural gas is reduced to the LNG storage pressure when passing through the throttling valve (VLV-101). In the pre-cooling cycle, the pre-cooling refrigerant that consists of ethylene, propane, and n-butane, first undergoes two-stage compression and is then water-cooled, the high pressure pre-cooling refrigerant is cooled by LNG-101, once expanded in the throttling valve (VLV-102), it vaporises and provides cold energy to cool the natural gas as well as for liquefaction purposes, thus sub-cooling the refrigerant to approximately -40 °C, then the super-heated pre-cooling refrigerant is returned to the compressor to complete the cycle. In the liquefaction cycle, propane, ethylene, and methane comprise the liquefaction refrigerant, the liquefaction refrigerant goes through two-stage compression, and a one-stage water-cooler, LNG-101 and LNG-102, respectively. After decreasing its pressure and temperature through the throttling valve (VLV-103), the low-pressure liquefaction refrigerant acts as the cold side in the liquefaction heat exchanger (LNG-102) to cool the natural gas and sub-cooling refrigerant to -92 °C. In the sub-cooling cycle, refrigerants with a lower boiling point, such as ethylene, methane, and nitrogen, make up the sub-cooling refrigerant. 3

After undergoing two-stage compression, and one-stage water-cooler processing, the sub-cooling refrigerant is cooled in LNG-101, LNG-102, and LNG-103 by the previous two, and this, refrigeration cycles, then the flow enters the throttling valve (VLV-104) to reduce its pressure and temperature to provide sub-cooling energy for cooling the natural gas to -150.1 °C.

Fig. 1. Schematic representation of the mixed fluid cascade process

2.2 Parameter setting Before investigating the performance of the MFC process, some essential parameters, and certain detailed assumptions, are made: the pressure of the feed gas P101 is set at 5 MPa, the temperature for T101 is 30 °C, and the flow rate is set at 52010.62 kmol/h (8 MPTA). It is assumed that any impurities in the natural gas have been removed before the natural gas enters the liquefaction unit. The Peng-Robinson equation is adopted to calculate the enthalpy, entropy, and other thermo-physical parameters. The molar fraction of feed gas and other key equipment operating parameters are listed in Table 1. Table1 Known parameters for MFC process simulation Items

Parameter

Adiabatic compressor efficiency

80 %

Superheat temperature at inlet to first stage compressor (K)

≥ 10

Minimum temperature approach in the LNG heat exchangers (K)

3

LNG storage pressure (kPa)

200

Temperature after the water-cooler (K)

30

Pressure drop in the water-cooler (kPa)

30

Pressure drop in the LNG heat exchangers (kPa)

0

Liquefaction rate

95 %

Molar composition of natural gas

4

CH4

91.6 %

C2H6

4.5 %

C3H8

1.1 %

i-C4H10

0.5 %

n-C4H10

0.3 %

N2

2.0 %

3 Parametric analysis Key parameters have great influence on the process performance, so it’s necessary to conduct parameters investigation to have deep insight into the MFC process performance.

3.1. Effect of feed gas pressure on the process performance Feed gas pressure has great effect on MFC liquefaction process performance, as shown in Figure 2, the unit power consumption w decreases along with feed gas pressure increasing, the flow rate of pre-cooling, liquefaction, sub-cooling refrigerant decrease at the same time. Figure 3 indicates that the higher of feed gas pressure is, the less cooling duty of the process requires, and the slope of cooling curves in liquefaction range (-60℃~-100℃) increases with feed gas pressure increasing, this implies that the demand for cold energy that is supplied by liquefaction refrigerant cycle (LRC) is reduced, so the MFC process consumes less power. The slope of w is large at first, then the slope declines, finally the slope increases again. The trend of w is almost as same as that of sub-cooling refrigerant flow rate, this results from the characteristic of MFC process, SRC is the upstream of PRC and LRC, once the flow rate of sub-cooling refrigerant changes, the flow rate of liquefaction, sub-cooling refrigerant has to change in response in order to ensure the process to work stably and efficiently. Just as the cooling duty of natural gas in sub-cooling temperature range declines slowly in Figure 3, the flow rate of sub-cooling refrigerant declines slowly when feed gas pressure ranges from 4000kPa to 8000kPa.At the same time, the flow rate of liquefaction refrigerant (LR) decreases due to the decline of cooling duty in liquefaction temperature range. Apart from pre-cooling natural gas, the pre-cooling refrigerant provides cold energy for liquefaction, sub-cooling refrigerant, so with flow rate of liquefaction, sub-cooling refrigerant decreasing, the flow rate of pre-cooling refrigerant decreases monotonically as well.

Unit power consumption PR flow rate LR flow rate SR flow rate

6.50 6.00

85,000 75,000 65,000

5.50

55,000 5.00 45,000 4.50

35,000

4.00

25,000

3.50 3.00 2500

3500

4500

5500

6500

7500

8500

15,000 9500

Feed gas pressure (kPa) Fig.2. Effect of feed gas pressure on the process performance

5

Flow rate of refrigerant (kmol/h)

Unit power consumption (kWh/kmol)

7.00

Fig. 3. Natural gas cooling curves

3.2 Effect of LNG storage pressure on the process performance It’s well known that if the lowest evaporate temperature of refrigerant increases, the refrigeration system will consume less power. Higher LNG storage pressure will result in higher required refrigerating temperature, meanwhile which increases lowest evaporate temperature of mixed refrigerant indirectly. Therefore, the LNG storage pressure has great influence on the MFC process performance. The changes of unit power consumption w with different LNG storage pressure are shown in Figure 4, as LNG storage pressure increases, w declines monotonically, the flow rate of pre-cooling, liquefaction, sub-cooling refrigerant decrease as well. It’s because that higher LNG storage pressure will increase lowest evaporate temperature of refrigerant, and the flow rate of sub-cooling refrigerant decreases more rapidly than that of pre-cooling or liquefaction refrigerant. 70,000

65,000 5.00

60,000

4.80

Unit power consumption

55,000

SR flow rate

50,000

PR flow rate

4.60

45,000

LR flow rate

40,000 4.40

35,000

30,000

4.20

25,000 4.00

20,000 150

200

250

300

350

400

450

500

550

LNG storage pressure (kPa) Fig. 4. Effect of LNG storage pressure on the process performance

6

Flow rate of refrigerant (kmol/h)

Unit power consumption (kWh/kmol)

5.20

3.3 Effect of water-cooler outlet temperature on the process performance The MFC process actually is to transfer natural gas cooling duty to the cooling water through the three individual refrigeration cycles at the expense of compressor system power. So, the outlet temperature of water-coolers has great effect on process performance. Figure 5 indicates that the unit power consumption w increases along with water-cooler outlet temperature increasing. Generally, for pre-cooling refrigerant, there’re three reasons for why colder water-coolers outlet temperature will lead to less process energy consumption. Firstly, water-coolers take the responsibility of completely condensing the pre-cooling refrigerant, colder water-coolers outlet temperature could lower condensing pressure, namely compressor discharge pressure, which in turn reduces compressor system energy consumption. Secondly, for centrifugal and axial compressor, for a given mass flow rate and pressure ratio, a colder inlet temperature will reduce compressor power. Finally, colder water-coolers outlet temperature decreases the inlet temperature of cold box, which lowers the cooling duty of the MFC process, which in turn decreases the flow rate of pre-cooling refrigerant and unit power consumption. However, based on previous literatures, there’s still lack of comprehensive reports on effect of above-mentioned three factors on the process performance. A mathematic model for the power of a compressor can be defined based on thermodynamics laws, isentropic process and added a correction for no ideal gas, the formulation is given as below [21]:

z1  z2 k 1 k P 2 （ m [  2 - 1） ] k 1 P 1 MW k W η T1

(1)

where W is the power (kW); m is mass gas per unit time (kg/s); T1 is the suction temperature; z1, z2 are compressibility factors at suction and discharge respectively; k is the isentropic exponent; P1, P2 is the suction and discharge pressure (kPa); MW is the gas molecular weight (kg/kmol); η is the efficiency. From the equation, pressure ratio, flow rate of pre-cooling refrigerant, compressor suction temperature can be recognized as primary factors. With hotter inlet temperature of LNG-101, more higher boiling point refrigerant should be charged into pre-cooling refrigerant in order to keep the minimum approach in LNG-101 larger than 3K, which might lower the condensing pressure of PR. However, the compressor discharge pressure increases significantly due to higher water-coolers outlet temperature. In addition, the change of evaporate pressure of pre-cooling refrigerant is negligible, so the pressure ratio is dominated by compressor discharge pressure, namely condensing pressure of PR. Compressor power consumption is proportional to the compressor suction temperature T1 and mass flow rate of PR m. To compare the effect of the above-mentioned three factors on the process performance more directly, and power consumption is proportional to rd, thus rd is identified as a factor instead of pressure ratio, which is given as followings:

P rd  2 P1 7

k 1 k

-1

(2)

Commuted unit power consumption is acquired with keeping a factor as a variable and others as constant. The effect of derivative pressure ratio rd, mass flow rate of PR m, compressor suction temperature T1on the process performance is shown in Figure 5, the commuted unit power consumption of the three factors are all increasing along with the water-cooler outlet temperature increasing. In particular, the commuted unit power consumption due to higher pressure ratio increases more rapidly than others, which indicates that the condensing pressure has major influence on the power consumption. While the effect of reducing compressor power by lowering compressor suction temperature is weakest, since there’s only one compressor in pre-cooling cycle is affected by this factor. The commuted unit power consumption due to more PR flow rate increases slowly than that of higher pressure ratio with higher water-cooler outlet temperature, but more rapidly than that of higher compressor suction temperature.

5.60

Commuted unit power consumption due to higher pressure ratio Commuted unit power consumption due to more PR flow rate Commuted unit power consumption due to higher compressor suction temperature

5.50 5.40 5.30 5.20 5.10

30.00

32.00

34.00

36.00

38.00

40.00

Unit power consumption (kWh/kmol)

5.70 Unit power consumption

5.00 42.00

Water-cooler outlet temperature (℃)

Fig. 5. Effect of water-cooler outlet temperature on the process performance

3.4 Effect of mixed refrigerant composition on the process performance Optimal or near-optimal mixed refrigerant composition will drive the hot and cold composites curves matching better in LNG exchangers, which lowers the entropy generation and improve overall energy efficiency of MFC process. Because the MFC process has three individual mixed refrigerant cycles, it’s necessary to investigate the effect of mixed refrigerant composition for each cycle on the process performance. Sub-cooling cycle has effect on each refrigeration cycle of MFC process, liquefaction cycle has effect on pre-cooling cycle and itself, while the pre-cooling cycle only has influence on itself, so the sequence of this investigation is from sub-cooling cycle to pre-cooling cycle. Mixed refrigerant compositions of sub-cooling, liquefaction, pre-cooling cycle are set and presented in Table 2-4, effect of mixed refrigerant on the process performance is illustrated in Figure 6-8. Sub-cooling refrigerant composition has great effect on the MFC process, as illustrated in Figure 6, the unit power consumption w increases with the increase of the methane molar fraction (with decrease of the ethylene molar fraction), w decreases with the decline of nitrogen molar fraction. To prevent liquids existing in compressors inlet, compressors suction superheat degree is another important performance index. As shown in Figure 6, the superheat degree of SR6 increases with the increase of methane content in SR, then it decrease with the decline of nitrogen 8

content in SR, the reason is that methane has lower boiling point than that of ethylene, the boiling point of SR will decrease with more methane content, which will result in the increase of the SR6 superheat degree. Similarly, nitrogen has lower boiling point and is more difficult to be liquefied than methane, the boiling point of SR with less nitrogen molar fraction will increase, which in turn decreases the superheat degree of SR6. The superheat degree of LR5 decreases with the increase of methane content in SR, while increases with the decline of nitrogen molar fraction in SR. The reason is that the mass specific capacity of ethylene is higher than that of methane, so the liquefaction cycle could provide less cold energy with less ethylene content in SR. The flow rate of LR is set as constant in this case, therefore the outlet temperature of LR at hot end of LNG-102 will decrease, namely the temperature of LR5 will decrease and the superheat degree of LR5 will also decrease with fixed LR composition. Similarly, the mass specific capacity of nitrogen is lower than that of methane, which means that methane is more difficult to be cooled down to desired temperature (-92℃), so the liquefaction cycle has to provide more cooling energy with methane content increasing in SR, the outlet temperature of LR at hot end of LNG-102 is supposed to increase in order to complete the cooling duty of liquefaction cycle, namely, superheat degree of LR5 will increase. The changing of sub-cooling refrigerant composition has little influence on the superheat degree of PR4, the superheat degree of PR4 almost remains the same. To guarantee that the MFC process can operate safely and stably, the minimum approach in LNG exchangers should be kept positive, as illustrated in Figure 6, the minimum approach in LNG-103 decreases with the decrease of ethylene content in SR, while it increases first and then decreases with lower nitrogen molar fraction in SR. The minimum approach in LNG-102 firstly increases with the decrease of ethylene content in SR, then decreases along with the decrease of nitrogen content in SR. The minimum approach in LNG-101 almost keeps the same and is little affected by the varying composition of SR. Note that there’re negative minimum approach values in LNG-102, LNG-103 when the nitrogen molar fraction is below 8%.Nitrogen takes the responsibility of providing cold energy at the cold end of LNG-103, and the SR is less efficient to provide enough cold energy at cold end with less nitrogen content in SR, which will leads to a negative minimum approach in LNG-103. Less nitrogen content in SR means more methane molar fraction, as above-mentioned, methane requires more cooling energy in the liquefaction cycle, and the liquefaction cycle couldn’t provide enough cold energy with nitrogen content in SR decreasing to 8%, which results in negative minimum approach in LNG-102. Table 2 Different sub-cooling refrigerant composition Molar composition

SA

SB

SC

SD

SE

SF

SG

SH

SI

SJ

CH4 (%)

63.50

64.00

64.50

65.00

65.50

66.00

68.00

70.00

72.00

74.00

C2H4 (%)

22.50

22.00

21.50

21.00

20.50

20.00

20.00

20.00

20.00

20.00

N2 (%)

14.00

14.00

14.00

14.00

14.00

14.00

12.00

10.00

8.00

6.00

9

4.78

40.00

LR5

35.00

PR4

30.00

Unit power consumption

4.76 4.74

25.00 20.00

4.72

15.00

4.70

10.00

5.00

4.68

0.00 -5.00 B

C

D

E

F

G

H

I

4.00 3.00 2.00 1.00 Minimun approach in LNG-103

0.00

Minimun approach in LNG-102 Minimun approach in LNG-101

-1.00 -2.00

4.66 A

5.00 Minimum approach (℃)

SR6

Degree of superheat (℃)

6.00

4.80

45.00

Unit power consumption (kWh/kmol)

50.00

A

J

B

C

D

E

F

G

H

I

J

Fig. 6. Effect of different sub-cooling refrigerant composition on process performance

As illustrated in Figure 7, liquefaction refrigerant composition has great significant on the process performance, the unit power consumption w decreases along with the increase of the ethylene content in LR, and it decreases with more propane molar fraction in LR. The superheat degree of LR5 decreases with less methane molar fraction in LR, the reason lies in that the boiling point of ethylene or propane is higher than that of methane, the molar fraction of ethylene or propane will increase with the decline of methane content in LR, which will increase the LR boiling point and then lowers the superheat degree of LR5. The superheat degree of PR4 increases with the increase of ethylene content in LR and increases with the increase of propane molar fraction in LR, the reason lies in that mass specific capacity of ethylene is higher than that of methane, thus the pre-cooling cycle has to provide more cold energy for LR to reaching desired refrigeration temperature, which leads to the increase of PR outlet temperature in LNG-101 on the condition that the flow rate of PR is set as constant, thus the superheat degree of PR4 will increase with more ethylene content in LR. Similarly, the mass specific capacity of methane is higher than that of propane, but propane occurs phase change in this temperature range. As a consequence, the pre-cooling cycle has to provide more cold energy to liquefy propane than that of cooling methane to -40℃. As indicated in Figure 7, the minimum approach in LNG-102 increases rapidly with increase of ethylene content in LR, and then decreases slowly with the increase of propane content in LR. The minimum approach in LNG-101 increases slowly with increase of ethylene content in LR, and then decreases rapidly along with higher propane molar fraction in LR. The liquefaction cycle can’t provide enough cold energy when the molar fraction of ethylene is below 75.60%, which results in negative minimum approach in LNG-102. Table 3 Different liquefaction refrigerant composition Molar composition

LA

LB

LC

LD

LE

LF

LG

LH

LI

LJ

CH4 (%)

13.00

12.80

12.60

12.40

12.20

12.00

11.90

11.80

11.70

11.60

C2H4 (%)

75.00

75.20

75.40

75.60

75.80

76.00

76.00

76.00

76.00

76.00

C3H8 (%)

12.00

12.00

12.00

12.00

12.00

12.00

12.10

12.20

12.30

12.40

10

4.79

45.00

4.78

40.00

4.77 LR5 PR4 Unit power consumption

35.00 30.00

4.76

4.75

25.00 4.74

20.00

4.73

15.00 10.00

4.72

5.00

4.71

0.00

5.00 4.00

Minimum approach (℃)

4.80

50.00

Unit power consumption (kWh/kmol)

Degree of superheat (℃)

55.00

B

C

D

E

F

G

H

I

2.00 1.00 0.00 -1.00

-2.00

Minimum approach in LNG-102

-3.00

Minimum approach in LNG-101

-4.00 -5.00

4.70

A

3.00

A

J

B

C

D

E

F

G

H

I

J

Fig. 7 Effect of different liquefaction refrigerant composition on process performance

Pre-cooling refrigerant composition has great effect on the MFC process, as illustrated in Figure 8, the unit power consumption w increase with the increase of propane content in PR, and increases with the increase of ethylene content in PR. The variation trend of superheat degree of PR4 is as same as that of w. The minimum approach in LNG-101 increases slowly with the increase of propane content in PR, but it decreases rapidly with more ethylene molar fraction in PR. When the n-butane molar fraction is below 14.60%, the minimum approach in LNG-101 is negative, this is because n-butane has the highest boiling point and mainly provides cold energy for LNG-101 at hot end. With less n-butane molar fraction in PR, the pre-cooling cycle can’t provide enough cold energy at the higher temperature range, even if the cold energy of PR is excessive at low temperature range. Table 4 Different pre-cooling refrigerant composition Molar composition

PA

PB

PC

PD

PE

PF

PG

PH

PI

PJ

C2H4 (%)

7.00

7.00

7.00

7.00

7.00

7.00

7.20

7.40

7.60

7.80

C3H8 (%)

68.00

70.00

72.00

74.00

76.00

78.00

78.00

78.00

78.00

78.00

n-C4H10(%)

25.00

23.00

21.00

19.00

17.00

15.00

14.80

14.60

14.40

14.20

60.00

4.80

4.78

50.00

Temperature (℃)

45.00 4.76

40.00 35.00

4.74

30.00

Minimum approach in LNG-101

25.00

Superheat degree of PR4

20.00

Unit power consumption

4.72

15.00

4.70

10.00 5.00

4.68

Unit power consumption (kWh/kmol)

55.00

0.00 -5.00

4.66 A

B

C

D

E

F

G

H

I

J

Fig. 8. Effect of different sub-cooling refrigerant composition on process performance

11

4 Optimisation 4.1 Optimisation approach Genetic algorithm is a random searching algorithm that refers to natural selection and genetic mechanism in biosphere. Genetic algorithm doesn’t depend on gradient or other auxiliary information. It searches the optimal solution by imitating natural evolution, such as reproduction, crossover and mutation. Additionally, it has the potential of reaching a global optimum, especially in the design of an LNG plant that is highly non-linear problem with many local optima. MATLABTM has the characteristic of excellent numerical calculation and user-friendly interface, it also has an optimisation toolbox, in which genetic algorithm, pattern search, quadratic programming and other methods are involved. ActiveX components are used to access to HYSYS COM server by writing codes in MATLABTM, then MATLABTM can read simulation variables and objective function values in MFC liquefaction process, and optimises them by GA. The typical tuning parameters of the GA are shown in Table 5. Table 5 Typical tuning parameters for the genetic algorithm Tuning parameters

Value

Number of population

200

Selection method

Stochastic uniform

Mutation

Adaptive feasible

Crossover function

Scatter

Fraction of migration

0.2

Number of generations

200

Because of characteristic of the MFC process, the optimisation procedure is divided into three stages, each refrigeration cycle is optimised individually, the sequence of optimisation is from sub-cooling cycle to pre-cooling cycle. Simulation variables for each refrigeration cycle is 5, it includes condensing pressure, evaporation pressure, molar flow rate of three different refrigerants in each cycle. This paper focuses on the thermodynamic performance of the MFC process when producing unit LNG, so unit power consumption is selected as objective function.

Min　f (X)  w 

W q

COM

(3)

LNG

Where X is a matrix of simulation variables, Wcom (kW) is the sum of the compressor power consumption, qLNG (kmol/h) is the mole flow rate of liquefied natural gas.

4.2 Constrains and penalty function To ensure that the MFC process works stably and the genetic algorithm can achieve reasonable results, several constraints must be satisfied. Different constraints in process optimisation result in definitely different results. The more constraints conform to actual engineering conditions, the more meaningful is the optimisation results, the constraints adopted in this case are presented as below: 1) In pre-cooling cycle, sum of the molar fraction of ethylene, propane, n-butane must be 12

equal to unity.

xC2H4  xC3H8  xnC4H10  1

(4)

2) In liquefaction cycle, sum of the molar fraction of methane, ethylene, propane must be equal to unity.

xCH4  xC2H4  xC3H8  1

(5)

3) In sub-cooling cycle, sum of the molar fraction of nitrogen, methane, ethylene must be equal to unity.

xN2  xCH4  xC2H4  1

(6)

4) The minimum approach in pre-cooling exchanger (LNG-101), liquefaction exchanger (LNG-102), sub-cooling exchanger (LNG-103) should be larger than 3K. LNG 101 Tmin 3

(7)

LNG 102 Tmin 3

(8)

LNG 103 Tmin 3

(9)

5) The superheat degree of first-stage compressor suction temperature should be larger than 10K.

Ti  Ti dew  10

i  ( PR4, LR5, SR6)

(10)

6) The pressure ratio of compressors should be less than 5. m Pout r  m  5 m  ( K  100, K  101, K  102, K  103, K  104, K  105) Pin m

(11) To allow a more direct optimisation, all of aforementioned inequality constraints are applied with a penalty function:

 n 2  p(X, h)  f (X)  h    max 0, g i  X    i 1 

(12)

Where h is the penalty factor, P(X,h) is minimized for each refrigeration cycle instead of f(X) by GA. The number of equality for each refrigeration cycle is 4, take sub-cooling cycle optimisation as an example, g(X) is presented as below: LNG 103 g1 (X)  3  Tmin

(13)

g2 (X)  10  (TSR 6  TSRdew6 )

(14)

g3 (X)  r K 104  5

(15)

g4 (X)  r K 105  5

(16)

13

5 Results and discussion 5.1 Optimisation results After optimizing the mixed refrigerant composition, condensing and evaporation pressure by genetic algorithm, the unit power consumption is 4.655kWh/kmol, which is 13.15% less than that of base case. The unit water-cooler load is water-cooler duty when producing unit LNG. After optimisation, the unit water-cooler load is 8.649kWh/kmol that is reduced by 7.60% compared to base case. Assuming that the compressor adiabatic efficiency can be improved to 83%, 85%, the unit power consumption can be reduced to 4.477kWh/kmol, 4.366kWh/kmol, meanwhile, the corresponding unit water-cooler duty is reduced to 8.516kWh/kmol, 8.405kWh/kmol respectively. When a large-scale LNG plant is being designed, generally more effort is paid to enhancing process thermodynamic performance, and improving compressors adiabatic efficiency can directly and significantly save power consumption. The optimisation results are presented in Table 6, propane accounts for the majority molar fraction of mixed refrigerant in pre-cooling cycle, ethylene for liquefaction cycle and methane for sub-cooling cycle, the three aforementioned refrigerants are identical with the selection of conventional cascade process. Additionally, the flow rate of liquefaction refrigerant, sub-cooling refrigerant is near or less than the feed gas flow rate, volumetric flow rate of mixed refrigerant at each compressors suction is reduced due to the three refrigeration cycle configuration of MFC process, which makes greatly increased capacity feasible and lowers the unit power consumption. The composite curves of MFC process before and after optimisation by GA are illustrated in Figure 9. The temperature difference between cold and hot composite curves is reduced significantly in sub-cooling and liquefaction temperature range, which decreases the irreversibility of the entire process. Meanwhile, the minimum approach temperature of LNG-101, LNG-102 and LNG-103 are decreased to 3.000K, 3.001K and 3.000K respectively after optimisation. However, the temperature difference in pre-cooling temperature range is still large, as indicated in Table 6, propane accounts for the majority molar fraction of pre-cooling refrigerant. Generally, propane in C3MR process is throttled 3~4 times, therefore, increasing the throttling times of pre-cooling refrigerant in MFC process might further enhance the thermodynamic efficiency. The detailed simulation results for overall optimised MFC are presented in Table 7. Table 6 MFC process optimisation results CH4(%)

C2H4(%)

C3H8(%)

n-C4H10(%)

N2(%)

Flow rate (kmo/h)

PH(kPa)

PL(kPa)

PRC

——

7.26

77.43

15.31

——

60884.06

1316

153

LRC

10.55

78.29

11.16

——

——

53452.92

2063

372

SRC

69.28

21.09

——

——

9.62

29383.59

4119

419

Table 7 Detailed simulation results for overall optimised MFC Temperature

Pressure

Molar flow

Mass enthalpy

Mass entropy

(℃)

(kPa)

(kmol/h)

(kJ/kg)

(kJ/(kg·K))

101

30.00

5000.00

52010.62

-4294.97

8.65

102

-40.00

5000.00

52010.62

-4483.50

7.94

103

-92.00

5000.00

52010.62

-4866.90

6.05

Node

14

104

-150.08

5000.00

52010.62

-5081.74

4.64

105

-154.74

200.00

52010.62

-5081.74

4.72

BOG

-154.74

200.00

2600.531

-3605.95

7.85

LNG

-154.74

200.00

49410.09

-5163.28

4.55

PR1

30.00

1286.38

60884.06

-2478.89

2.08

PR2

-40.00

1286.38

60884.06

-2651.00

1.43

PR3

-44.19

153.32

60884.06

-2651.00

1.44

PR4

27.00

153.32

60884.06

-2129.15

3.55

PR5

66.21

388.70

60884.06

-2063.84

3.59

PR6

30.00

358.70

60884.06

-2129.46

3.40

PR7

88.25

1316.38

60884.06

-2041.19

3.45

PR8

30.00

1286.38

60884.06

-2478.89

2.08

LR1

30.00

2032.89

53452.92

723.24

5.41

LR2

-40.00

2032.89

53452.92

267.61

3.61

LR3

-92.00

2032.89

53452.92

119.20

2.90

LR4

-97.03

372.40

53452.92

119.20

2.91

LR5

-43.95

372.40

53452.92

636.71

5.53

LR6

17.96

1000.00

53452.92

721.95

5.59

LR7

69.20

2062.89

53452.92

797.02

5.63

LR8

30.00

2032.89

53452.92

723.24

5.41

SR1

30.00

4088.66

29383.59

-2105.04

7.76

SR2

-40.00

4088.66

29383.59

-2263.45

7.17

SR3

-92.00

4088.66

29383.59

-2632.01

5.33

SR4

-150.00

4088.66

29383.59

-2823.04

4.08

SR5

-153.61

419.00

29383.59

-2823.04

4.13

SR6

-95.43

419.00

29383.59

-2293.55

7.85

SR7

-41.58

1000.00

29383.59

-2207.54

7.92

SR8

71.96

4118.66

29383.59

-2014.74

8.04

SR9

30.00

4088.66

29383.59

-2105.04

7.76

40

20

Temperature (℃)

0

-20

Liquefaction

-40 -60

Pre-cooling

Sub-cooling

-80 -100

Hot composite curve Cold composite curve

-120 -140

-160 0

100

200

300

400

500

Heat flow (MW)

15

600

700

800

40 20

Temperature (℃)

0

-20 Liquefaction -40

-60 Pre-cooling

Sub-cooling

-80 -100 -120

Hot composite curve Cold composite curve

-140 -160 0

100

200

300

400

500

600

700

800

Heat flow (MW)

Fig. 9. Hot and cold composite curves for MFC process before (top) and after (bottom) optimisation

5.2 Configuration optimisation To improve the heat transfer performance in the pre-cooling temperature range and further reduce the temperature difference between the cold and hot composite curves, configuration optimisation is conducted for the pre-cooling cycle. As illustrated in Figure 10, the pre-cooling cycle is changed from a one pressure level operation to one using two, or three, pressure levels. In Figure 10(a), the PR2 is divided into two streams, one is throttled to an intermediate pressure and used as cold side for LNG-101, the remaining one is further throttled and provides cold energy for LNG-104, it then goes through the compressor, a water-cooler, and mixes with PR5. In Figure 10(b), similarly, PR7 is split into two streams, one is expanded for cooling the LNG-104, and another is further expanded to a low pressure and cools the LNG-105. The temperature of PR16 is below 30 °C, so the water-cooler unit is not required downstream of this node. The number of splitters, compressors, LNG heat exchangers, and mixers increases correspondingly, and the process becomes more complicated. The two proposed configurations are optimised by GA with unit power consumption as the objective function. As indicated in Table 8, although the flow rate of pre-cooling refrigerant is increased, the unit power consumption is decreased significantly (to 4.361 kWh/kmol for a PR with two pressure levels, or 4.205kWh/kmol for a PR with three pressure levels). Correspondingly, the specific water-cooler duty is reduced with more throttling time in the PR. Note that the molar fraction of propane in the PR is increased with more throttling time and this accounts for 92.11 % in MFCP3, the molar fraction of ethylene and methane is decreased and is less than 10 %. From the perspective of the pre-cooling refrigerant composition, after configuration optimisation, the pre-cooling cycle of MFC process is closer to that of a C3MR process. As indicated in Figure 11, the temperature difference between the cold and hot composite curves is reduced significantly when two or three pressure levels are used in the pre-cooling cycle. Although propane accounts for a greater molar fraction in the PR, compared with that in a pure propane pre-cooling cycle in C3MR, the cold composite is a closer match to the refrigeration demand with increased throttling times. The heat duties of the entire process is 696.35 MW, or 690.43 MW, for two, or three, pressure levels, which are 3.38 % and 4.20 % less than that of the MFC process, which means that the heat transfer performance is improved within the pre-cooling temperature range by configuration optimisation.

16

(a)

(b) Fig. 10 Schematic representation of the pre-cooling cycle (a) with two pressure levels, (b) with three pressure levels

Table 8 MFC pre-cooling cycle configuration optimisation results MFC

MFCP2

MFCP3

C2H4 (%)

7.26

6.35

6.02

C3H8 (%)

77.43

87.75

92.11

n-C4H10 (%)

15.31

5.91

1.87

PR flow rate (kmol/h)

60881

71601

75502

w (kWh/kmol)

4.655

4.361

4.205

Specific water-cooler duty

8.649

8.400

8.245

Wcom (MW)

230.00

215.48

207.77

qLNG (kmol/h)

49410.09

49410.09

49410.09

17

40

20

Temperature (℃)

0

-20

Liquefaction

-40 -60

Subcooling

-80

Pre-cooling

-100 Hot composite curve Cold compposite curve

-120 -140

-160 0

100

200

300

400

500

600

700

800

Heat flow (MW)

(a) 40 20

Temperature (℃)

0 -20 Liquefaction

-40 Subcooling

-60 -80

Pre-cooling

-100

-120

Hot composite curve Cold composite curve

-140 -160 0

100

200

300

400

500

600

700

Heat flow (MW)

(b) Fig. 11. Hot and cold composite curves for MFC process (a) with two pressure levels, (b) with three pressure levels

Due to the lower temperature range in the sub-cooling cycle, the degree of compressor suction superheat cannot be guaranteed with more pressure levels, so the sub-cooling cycle with one throttling time only is recognised as the optimal configuration. The liquefaction refrigerant cycle is used to liquefy the natural gas from the vapour phase at the feed pressure. As indicated in Figure 3, in this liquefaction temperature range, the feed gas requires 45.47 % of the entire cooling duty at 5 MPa, so it is necessary to investigate the configuration of the liquefaction refrigeration cycle. Apart from the base configuration, another two suggested configurations are illustrated in Figure 12. In Figure 12(a), the LR3 is divided into two streams, one is throttled to an intermediate pressure and used as the cold side for LNG-102, the other stream is further throttled and provides cold energy for LNG-105, it then goes through the compressor, and emerges with LR6 to be compressed further. The temperatures of both LR11 and LR13 are below 30 °C, so water-cooler unit is not required in this configuration. Additionally, to make the degree of superheating of LR10 greater than 10 K, the temperature of 103 has to be set to -52 °C, which will result in an unbalanced distribution of cold energy in LNG-102 and LNG-105. In Figure 12 (b), a separator is introduced: LR2 is separated into a vapour stream and a 18

liquid stream in the flash separator, the liquid stream goes through the LNG-102 and is expanded in VLV-104 to reduce its temperature and pressure, the vapour stream is cooled in LNG-102, and then LNG-106, before entering a JT valve. After expansion, it provides cold energy for LNG-106, then mixes with liquid stream LR5 and acts as cold side for LNG-102. After being superheated, it goes through two-stage compression and a one-stage water-cooling process to complete the cycle. To investigate the performance of this configuration, the temperatures of 103 and 104 were set to -85 °C and -100 °C for MFCLS1, and -75 °C and -92 °C for MFCLS2.

(a)

(b) Fig. 12. Schematic representation of the liquefaction cycle (a) with two pressure levels, (b) with a separator

The MFCLP2, MFCLS1, MFCLS2 processes are optimised by genetic algorithm, and the optimised results are listed in Table 9. The base MFC process is still the most efficient from the perspective of unit power consumption and specific water-cooler duties: liquefaction with two pressure levels performs better than that with an added separator. The ethylene molar fraction in MFCLP2 is increased compared with that in the MFC process, which confirms the rule summarised in pre-cooling cycle configuration optimisation by which the amount of main refrigerant will increase as more pressure levels are added. Simulation data for the liquefaction cycle for a globally optimised MFCLP2 are presented in Table 10. The ethylene molar fraction is decreased in MFCLS1 and MFCLS2 processes, because the feed gas has to undergo phase transition in this temperature range: this only occurs in LNG-102 of MFCLS1, and LNG-102 and LNG-106 of the MFCLS2 process. To provide enough cold energy for LNG-106, more vapour stream flow is required, and the vapour stream flow will increase with more lower boiling point refrigerant, such as methane, being discharged into the LR. Furthermore, the flow rate of LR increases significantly in the MFCLS1and MFCLS2 processes due to the unbalanced distribution 19

of LR cold energy. As a consequence, the PR flow rate has to increase to allow completion of the pre-cooling temperature range cooling duties. Table 9 MFC liquefaction cycle configuration optimisation results MFC

MFCLP2

MFCLS1

MFCLS2

CH4 (%)

10.55

9.14

26.33

27.25

C2H4 (%)

78.29

83.71

68.10

66.84

C3H8 (%)

11.16

7.15

5.57

5.92

PR flow rate (kmol/h)

60881

67223

68422

66559

LR flow rate (kmol/h)

53455

69795

89472

86467

w (kWh/kmol)

4.655

4.874

5.244

5.306

Specific water-cooler duty

8.649

8.914

9.283

9.345

Wcom (MW)

230.00

240.82

259.11

262.17

qLNG (kmol/h)

49410.09

49410.09

49410.09

49410.09

Table 10 Detailed simulation results: liquefaction cycle for overall optimised MFCLP2 Temperature

Pressure

Molar flow

Mass enthalpy

Mass

(°C)

(kPa)

(kmol/h)

(kJ/kg)

entropy(kJ/(kg·K))

LR1

15.06

1810.00

69793.47

1000.41

5.44

LR2

-40.00

1810.00

69793.47

603.51

3.82

LR3

-52.00

1810.00

69793.47

521.17

3.46

LR4

-52.00

1810.00

25235.61

521.17

3.46

LR5

-61.64

1052.00

25235.61

521.17

3.48

LR6

-44.50

1052.00

25235.61

836.85

4.90

LR7

-52.00

1810.00

44557.86

521.17

3.46

LR8

-92.00

1810.00

44557.86

418.62

2.95

LR9

-97.66

331.03

44557.86

418.62

2.97

LR10

-55.07

331.03

44557.86

921.59

5.58

LR11

17.52

1050.00

44557.86

1020.06

5.65

LR12

-22.00

1050.00

69793.47

953.81

5.40

LR13

15.06

1810.00

69793.47

1000.41

5.44

Node

The reason why the thermodynamic performance of the two suggested liquefaction cycle configurations is less efficient than the base MFC process can be explained by their heat transfer curves and T-s diagrams. As indicated in Figure 13(a), the temperature difference in the LNG-102 cold end is too large, which means that the heat transfer driving force is most likely over-set. Due to this over-design, the compressors expend too much unnecessary shaft work. Additionally, because the sum of the ethylene and propane molar fractions increases in MFCLP2, the dew point in the first-stage compressor suction chamber of LR10 increases to approximately -60 °C, the temperature of 103 has then to be set to -52 °C to ensure that the degree of superheating of LR10 exceeds 10 K. So LNG-105 accounts for more cooling duty work than LNG-102, and the composition of LR is more inclined to shift towards the optimal composition for LNG-105 during optimisation. The hot and cold curves were well-matched in LNG-105, however the ethylene molar fraction in LR is excessive for LNG-102, which makes the temperature difference at the 20

LNG-102 cold end excessively large which prevents the LR from being a closer match to the refrigeration demand in LNG-102. As illustrated in Figure 14, the evaporation temperature of MFCLP2 is lower than that in the MFC process: it is well known that, the lower the evaporation temperature, the more work the refrigeration system has to do. Although, the condensing temperature and condensing pressure (1810 kPa) in MFCLP2 are lower those in the base MFC process, the lower evaporation temperature of MFCLP2 plays the dominant role and makes this suggested configuration less efficient compared with that of the base MFC process. Generally, the mixed refrigerant is separated into vapour and liquid streams in a flash separator, the vapour stream sub-cools the feed gas, and then mixes with the liquid stream to complete the liquefaction duty cycle. It is demonstrated as efficient in the C3MR temperature range (-30 to -160 °C), while this configuration is less efficient in the liquefaction temperature range (-40 to -92 °C) in the MFC process. Compared with the base configuration, the unit power consumption and specific water-cooler duty increase synchronously. Combining the heat transfer curves and the T-s graph, the mechanism for this phenomenon is explained as follows: as indicated in Figure 13(b), the temperature difference at the LNG-106 cold end is excessive, which means that the heat-transfer driving force is mostly over-set; because of this unreasonable design, the compressor system might expend too much work. As illustrated in Figure 13(c), the temperature difference is too large, not only at the cold end of LNG-106, but also along the whole heat transfer temperature range of the liquefaction cycle, which causes the entire process to consume more power. A comparison of MFC and MFCLS1 is mapped on the T-s diagram, as indicated in Figure 15: the liquefaction cycle condensing temperature of MFCLS1process is almost as same as that of the base MFC process, while the liquefaction cycle evaporation temperature of MFCLS1 is much lower than that of the base MFC process, and the condensing pressure of MFCLS1 is 2485 kPa higher than the 2033 kPa of the MFC process, so this configuration is less efficient than the base configuration. The molar composition of the vapour stream is 45.06 % methane, 53.98 % ethylene, and 0.95 % propane, while it is 10.55 % methane, 78.29 % ethylene, and 11.16 % propane for the LR in the MFC process. In the liquefaction temperature range, ethylene should be the primary refrigerant, while the vapour stream in MFCLS1 contains too much methane, which results in the large temperature difference at the cold end of LNG-106. Additionally, due to the unreasonable composition of the vapour stream, it does not provide a good match with the refrigeration demand, and the flow rate of the vapour stream has to increase to keep the minimum approach in LNG-106 greater than 3 K, but the molar fraction of methane in the LR of the MFCLS1 process has to increase to make the flash separator produce a larger vapour stream, which further increases the temperature difference at the cold end of LNG-106 and makes the compressor system expend too much shaft work. To demonstrate further that the configuration with a separator is not optimal in the liquefaction range, an MFCLS2 process is established in which the temperatures of 103 and 104 are set to -75 °C and -92 °C for MFCLS2. Compared with the liquefaction cycle configuration in the base MFC process, it is divided into two liquefaction temperature ranges, as indicated in Figure 16: the liquefaction cycle condensing temperatures of MFCLS1 (solid line) and MFCLS2 (dashed line) are similar, the condensing pressures for MFCLS1 and MFCLS2 are 2485 kPa and 2486 kPa, respectively, the evaporation temperatures of the vapour streams of MFCLS2 are slightly lower than that of MFCLS1, and the evaporation temperatures of the mixed vapour and liquid streams are practically equal in the two processes, so the MFCLS1 process performs better 21

from a thermodynamic perspective. In terms of cold energy distribution, the feed gas has not been liquefied completely at -75 °C, and the vapour fraction is 39.75 %. The vapour stream that contains a 45.67 % methane molar fraction is less efficient in the temperature range of -75 °C to -92 °C, as it has to liquefy and sub-cool the feed gas in LNG-106. When the temperature of 103 is changed to -85 °C, the feed gas has been liquefied completely, the vapour stream has only to sub-cool the feed gas over the temperature range from -85 °C to -100 °C, which can exploit the advantage bestowed by the methane of being more efficient in the sub-cooling temperature range. To summarise the aforementioned discussion, the liquefaction cycle with two pressure levels, or a separator, is inefficient in the liquefaction temperature range, thus the base configuration of the MFC liquefaction cycle is adopted as the optimal configuration, and the configuration of the MFCP3 process is identified as the most efficient and is thence deemed optimal. 40 20

Temperature (℃)

0

-20 Liquefaction -40

-60 Sub-cooling

-80

Pre-cooling

-100 Hot composite curve Cold composite curve

-120 -140 -160 0

100

200

300

400

500

600

700

800

Heat flow (MW)

(a) 40 20

Temperature (℃)

0

-20 Liquefaction

-40

-60

Subcooling

-80

Pre-cooling

-100 -120

Hot composite curve Cold composite curve

-140 -160

0

100

200

300

400

500

Heat flow (MW)

(b)

22

600

700

800

900

40 20

Temperature (℃)

0 -20 Liquefaction

-40 Subcooling

-60 -80

Pre-cooling

-100

-120 Hot composite curve Cold composite curve

-140

-160

0

100

200

300

400 500 600 Heat flow (MW)

700

800

900

(c) Fig. 13. Hot and cold composite curves (a) for MFCLP2, (b) for MFCLS1, (c) for MFCLS2

70

LR7

Base liquefaction cycle Liquefaction cycle with two pressure levels

50

Temperature (℃)

30 10

High pressure LR Low pressure LR

LR1

Base LR bubble point curve

LR6 LR11'

LR1'

Base LR dew point curve Two pressure levels bubble point curve

-10

Two pressure levels dew point curve

LR12'

-30 LR2 LR6'

LR10'

LR5'

-70 -90

LR5

LR2'

LR4' LR7' LR3'

-50

LR3 LR4

-110 2.50

LR8'

LR9'

3.00

3.50

4.00

4.50

5.00

5.50

6.00

Specific entropy (kJ/(kg·K))

Fig. 14. Comparison of the T-s diagram for MFC and MFCLP2 liquefaction cycles

80 60

Temperature (℃)

40 20 0

Base liquefaction cycle LLR+VLR LLR VLR Base LR bubble point curve Base LR dew point curve MFCLS1 LR buddle point curve MFCLS1 LR dew point curve

LR7 LR14' LR1

LR1'

LR6 LR13'

-20 LR2'

LR2

-40

LR3'

LR5

LR6' LR12'

-60 -80 -100

LR3

LR4' LR5'

LR4

-120 -140 2.50

LR11'

LR10'

LR7'

LR8' LR9'

3.00

3.50

4.00

4.50

5.00

5.50

Specific entropy (kJ/(kg·K)) 23

6.00

6.50

7.00

Fig.15. Comparison of the T-s diagram for MFC and MFCLS1 liquefaction cycles

60

LLR+VLR

LR14 LR1

VLR

20

Temperature (℃)

LR14'

LLR

40

LR1'

LLR'+VLR' LLR'

0

VLR'

-20

Buddle point curve

-40

Dew point curve LR3 LR3'

LR2 LR2'

LR13

LR13'

LR12

LR6

LR12'

LR6'

-60 -80

LR4' LR5' LR4

LR5

LR11 LR8

-100 -120 3.00

3.50

LR7'

LR7

LR10'

LR11' LR8'

LR9

LR9'

4.00

4.50

LR10

5.00

5.50

6.00

6.50

Specific entropy (kJ/(kg·K)) Fig. 16. Comparison of the T-s diagram for MFCLS1 and MFCLS2 liquefaction cycles

6 Conclusions 1. The effects of feed gas pressure, LNG storage pressure, water-cooler outlet temperature, different pre-cooing, liquefaction, and sub-cooling refrigerant composition on mixed fluid cascade process performance are investigated: the unit power consumption decreases along with higher feed gas pressure and higher LNG storage pressure, and increases with higher water-cooler outlet temperature. Three factors, derivative pressure ratio (mainly condensing pressure), mass flow rate in the PR, and compressor suction temperature directly influence the process with the variation of water-cooler outlet temperature, the condensing pressure exerts a significant influence on the unit power consumption, while the effect of compressor suction temperature is the weakest. 2. The characteristically excellent numerical calculation ability and user-friendly interface of MATLAB™ and the powerful physical package, Aspen HYSYS, are combined: constraints for the MFC process are folded into a penalty function, which is optimised, instead of the objective function, with a genetic algorithm used as the optimisation tool. After optimisation the unit power consumption can be reduced to 4.655 kWh/kmol or 4.366 kWh/kmol at compressor adiabatic efficiencies of 80 % or 85 %: the specific water-cooler loads are 8.649 kWh/kmol and 8.405 kWh/kmol, respectively. 3. Configuration optimisation is conducted for the MFC process, configurations such that the pre-cooling or liquefaction cycles have more pressure levels and liquefaction cycles with a separator are established. By analysing the heat transfer and thermodynamic performances, the configuration with a pre-cooling cycle with three pressure levels, liquefaction, and sub-cooling with one pressure level is identified as the most efficient and optimal: its unit power consumption is 4.205 kWh/kmol, and its specific water-cooler load is 8.245 kWh/kmol. Additionally, the mechanism responsible for the weak performance of the suggested liquefaction cycle configuration lies in unbalanced distribution of cold energy in the liquefaction temperature range. Maintaining the extent of superheating in the compressor suction stage at above 10 K leads to an unbalanced cold energy distribution in that liquefaction cycle with two pressure levels. The vapour 24

stream produced by the added separator has an advantage in the sub-cooling temperature range, however it will generate a large temperature difference at the cold end of the liquefaction cycle exchanger and generates an unbalanced distribution of cold energy. Acknowledgement The authors are grateful for funding from The National Natural Science Foundation of China (Grant no. 51004111: research on the mechanism and regulation of the liquefaction process of natural gas in a supersonic swirling separator) and support from The Science Foundation of China, University of Petroleum, Beijing (Grant no. 2462012KYJJ0407: research on the cryogenic power cycle to recover LNG cold energy and waste heat optimisation study). References [1] Lim W, Choi K, Moon I. Current status and perspectives of liquefied natural gas (LNG) plant design. Industrial & Engineering Chemistry Research. 2013;52(9):3065-88. [2] Kumar S, Kwon H-T, Choi K-H, Lim W, Cho JH, Tak K, et al. LNG: An eco-friendly cryogenic fuel for sustainable development. Applied Energy. 2011;88(12):4264-73. [3] BP.BP statistical review of World Energy 2015. London:BP p.l.c.2015. [4] Castillo L, Dahouk MM, Di Scipio S, Dorao C. Conceptual analysis of the precooling stage for LNG processes. Energy conversion and management. 2013;6641-7. [5] Khan MS, Lee S, Rangaiah G, Lee M. Knowledge based decision making method for the selection of mixed refrigerant systems for energy efficient LNG processes. Applied Energy.2013;111:1018-31. [6] Wang M, Zhang J, Xu Q, Li K. Thermodynamic-analysis-based energy consumption minimization for natural gas liquefaction. Industrial & Engineering Chemistry Research. 2011;50(22):12630-40. [7] Khan MS, Lee M. Design optimization of single mixed refrigerant natural gas liquefaction process using the particle swarm paradigm with nonlinear constraints. Energy. 2013;49:146-55. [8] Xu X, Liu J, Jiang C, Cao L. The correlation between mixed refrigerant composition and ambient conditions in the PRICO LNG process.Applied Energy. 2013;102:1127-36. [9] Alabdulkarem A, Mortazavi A, Hwang Y, Radermacher R, Rogers P. Optimization of propane pre-cooled mixed refrigerant LNG plant. Applied Thermal Engineering. 2011;31(6):1091-8. [10] He T, Ju Y. A novel conceptual design of parallel nitrogen expansion liquefaction process for small-scale LNG (liquefied natural gas) plant in skid-mount packages.Energy. 2014;75:349-59. [11] Wang M, Khalilpour R, Abbas A. Thermodynamic and economic optimization of LNG mixed refrigerant processes. Energy Conversion and Management. 2014;88:947-61. [12] Hatcher P, Khalilpour R, Abbas A. Optimisation of LNG mixed-refrigerant processes considering operation and design objectives. Computers & Chemical Engineering. 2012;41:123-33. [13] Lim W, Lee I, Tak K, Cho JH, Ko D, Moon I. Efficient configuration of a natural gas liquefaction process for energy recovery. Industrial & Engineering Chemistry Research. 2014;53(5):1973-85. [14] Mortazavi A, Somers C, Hwang Y, Radermacher R, Rodgers P, Al-Hashimi S. Performance enhancement of propane pre-cooled mixed refrigerant LNG plant. Applied Energy. 2012;93:125-31. [15] Rodgers P, Mortazavi A, Eveloy V, Al-Hashimi S, Hwang Y, Radermacher R. Enhancement of LNG plant propane cycle through waste heat powered absorption cooling. Applied Thermal Engineering. 2012;48:41-53. [16] Jensen JB, Skogestad S. Steady-state operational degrees of freedom with application to refrigeration cycles. Industrial & Engineering Chemistry Research. 2009;48(14):6652-9. [17] Jensen JB, Skogestad S. Optimal operation of a mixed fluid cascade LNG plant. Computer Aided Chemical

25

Engineering. 2006;21(06):1569-74. [18] Mehrpooya M, Omidi M, Vatani A. Novel mixed fluid cascade natural gas liquefaction process configuration using absorption refrigeration system. Applied Thermal Engineering. 2016;98591-604. [19] Mehrpooya M, Ansarinasab H. Advanced exergoeconomic analysis of the multistage mixed refrigerant systems. Energy Conversion & Management. 2015;103705-16. [20] Mehrpooya M, Hossieni M, Vatani A. Novel LNG-Based Integrated Process Configuration Alternatives for Coproduction of LNG and NGL. Industrial & Engineering Chemistry Research. 2014;53(45):17705-21. [21] Castillo L, Dorao C. On the conceptual design of pre-cooling stage of LNG plants using propane or an ethane/propane mixture. Energy Conversion and Management. 2013;65:140-6.

Figure captions Fig. 1. Schematic representation of a mixed fluid cascade process Fig. 2. Effect of feed gas pressure on the process performance Fig. 3. Natural gas cooling curves Fig. 4. Effect of LNG storage pressure on the process performance Fig. 5. Effect of water-cooler outlet temperature on the process performance Fig. 6. Effect of different sub-cooling refrigerant composition on process performance Fig. 7. Effect of different liquefaction refrigerant composition on process performance Fig. 8. Effect of different sub-cooling refrigerant composition on process performance Fig. 9. The hot and cold composite curves for the MFC process before (top) and after (bottom) optimisation Fig. 10. Schematic representation of the pre-cooling cycle (a) with two pressure levels, (b) with three pressure levels Fig. 11.The hot and cold composite curves for MFC process (a) with two pressure levels, (b) with three pressure levels Fig. 12. Schematic representation of the liquefaction cycle (a) with two pressure levels, (b) with a separator Fig. 13.The hot and cold composite curves (a) for MFCLP2, (b) for MFCLS1, (c) for MFCLS2 Fig. 14. Comparison of the T-s diagram for MFC and MFCLP2 liquefaction cycles Fig. 15. Comparison of the T-s diagram for MFC and MFCLS1 liquefaction cycles Fig. 16. Comparison of the T-s diagram for MFCLS1 and MFCLS2 liquefaction cycles Nomenclature f objective function g inequality constraints function k isentropic exponent MW molecular weight m mass flow rate (kg/s) h penalty factor P pressure (kPa) p penalty function T temperature (K) r compression ratio s entropy (kJ/kg K) 26

w W x X z

unit power consumption (kWh/kmol) power (kW) molar fraction key design variable matrix compressibility factor

Subscripts 1 suction 2 discharge COM compressor d derivative in inlet state of compressor out outlet state of compressor Abbreviations BP British Petroleum C3MR propane pre-cooled mixed refrigerant CO2 carbon dioxide DMR dual mixed refrigerant GA genetic algorithm LNG liquefied natural gas LR liquefaction refrigerant LRC liquefaction refrigerant cycle MR mixed refrigerant MFC mixed fluid cascade MFCLP2 liquefaction refrigerant cycle with two pressure levels in the mixed fluid cascade process MFCLS1 first sort of configuration of the liquefaction refrigerant cycle with a separator in mixed fluid cascade process MFCLS2 second sort of configuration of the liquefaction refrigerant cycle with a separator in mixed fluid cascade process MFCP2 pre-cooling refrigerant cycle with two pressure levels in a mixed fluid cascade process MFCP3 pre-cooling refrigerant cycle with three pressure levels in a mixed fluid cascade process MPTA million tonnes per annum PRpre-cooling refrigerant PRC pre-cooling refrigerant cycle SMR single mixed refrigerant SQP sequential quadratic programming SR sub-cooling refrigerant SRC sub-cooling refrigerant cycle UA overall heat transfer coefficient and area of main cryogenic heat exchanger

27

Highlights 1. Effect of key parameters on MFC process performance are investigated and presented. 2. Unit power consumption of MFC process is 4.655kWh/kmol after genetic algorithm optimization. 3. Configuration optimization is conducted for MFC process, unit power consumption of optimal configuration can be reduced to 4.205kWh/kmol and mechanism for poor performance of proposed configurations is revealed.

28