Exergoeconomic Evaluation of an Integrated Nitrogen Rejection Unit with LNG and NGL Co-Production Processes Based on the MFC and Absorbtion Refrigeration Systems

Document Type: Original Article

Authors

1 Mechanical Engineering Faculty, Energy Conversion Group, KNToosi University of Technology, Tehran, Iran

2 Mechanical Engineering Faculty, Energy System Group, KNToosi University of Technology, Tehran, Iran

Abstract

Natural gas is often associated with nitrogen and heavy compounds. The Heavy components in the natural gas not only can feed downstream units, owing to the low temperature process may be formed solid as well. Therefore, heavy components separation can be a necessity and produce useful products. Virtually, all natural gases are containing nitrogen ​​that would lower the heating value of natural gas. Removing nitrogen from natural gas at a concentration of more than 4% can be vital. Integration of the natural gas liquids (NGL), liquefied natural gas (LNG) and nitrogen rejection unit processes is an effective procedure which can reduce the required refrigeration. In the present paper, a novel mixed fluid cascade natural gas liquefaction process is investigated by exergy and exergoeconomic analysis methods. one of the vapor compression cycles is replaced with a water-ammonia absorption refrigeration cycle. The results include cost of exergy destruction, exergoeconomic factor, exergy destruction and exergy efficiency. Results of exergoeconomic analysis indicates that the maximum exergoeconomic factor, which is 89.49%, is related to the HX8 in the water-ammonia absorption refrigeration cycle and the minimum exergoeconomic factor, which is 0.0026%, is related to the HX2 in the liquefaction cycle. In this process, the fourth compressor has the highest exergy destruction cost (5750307 $/hr) and HX8 in the absorption refrigeration cycle has the lowest exergy destruction cost (2.033 $/hr). Due to the high value of fuel cost rate in compressor, their exergy destruction cost is much higher than other devices.

Keywords

Main Subjects


Natural gas contains heavy ingredients and nitrogen. According to negative influence of nitrogen on fuel heating value, it is necessary to remove the nitrogen of more than 4% concentration from natural gas streams. Liquefied natural gas plants are increasing in number because of the growing demand for natural gas (Alabdulkarem, Mortazavi, Hwang, Radermacher, & Rogers, 2011).  Gas is widely recognized as a clean and economical energy source because of its low carbon intensity and relatively low price in comparison with other fossil fuel types (Wang, Khalilpour, & Abbas, 2014). The LNG facilities are equipped with an intermediate pressure distillation column for recovery ethane and heavier components from the processed natural gas stream in a manner where surges operational and capital costs remain unchanged. (Ransbarger, 2006).Value of the SPE changes from 0.2 to 0.6 kW/kg LNG and at large scale liquefaction processes it ranges from 0.4 to 0.25. However increasing this value decreases the operating cost of the plant, while the process configuration and number of the equipment is another important factor which can affect the capital costs of the plant significantly (Ghorbani, Hamedi, & Amidpour, 2016; Ghorbani, Hamedi, Amidpour, & Mehrpooya, 2016). Separation of Methane, Ethane, Propane, and natural gas liquids (NGL) from the natural gas is generally carried out through one of the following alternativ processes: i) external refrigeration (ER), ii) turbo expansion TE), iii) JouleeThompson expansion, and iv) absorption. In many procedures, a combination of these processes is applied to improve the energy efficiency or obtain greater recoveries (Amidpour et al., 2015; Ghorbani, Mafi, Shirmohammadi, Hamedi, & Amidpour, 2014; Ghorbani, Salehi, Ghaemmaleki, Amidpour, & Hamedi, 2012; Shirmohammadi, Ghorbani, Hamedi, Hamedi, & Romeo, 2015).

New methods in energy saving have led to the development of analyses techniques based on the second law of thermodynamics, particularly, the concept of exergy. In exergoeconomic analysis the quality of energy (exergy) in allocating the production costs of a process to its products is considered. A general methodology for this kind of analysis is presented by Electric Power Research Institute (Bejan & Tsatsaronis, 1996; Fazelpour, 2015), known as the Total Revenue Requirement method (Total Revenue Requirement method).

A systematic method based on a combination of mathematical methods and thermodynamic viewpoints are adopted to acquire optimal design configuration through non-linear programming techniques (Ghorbani, Mafi, Amidpour, Nayenian, & Salehi, 2013; Lashkajani, Ghorbani, Amidpour, & Hamedi, 2016; Mafi, Ghorbani, Salehi, Amidpour, & Nayenian). A superstructure optimization is applied for a separation system which includes distillation column units, heat exchangers and heat integration (Lashkajani et al., 2016). LNG production technologies of compression cooling cycles are applied for cooling. Compression cooling cycles are widely applied in various fields, especially in oil and gas industry and there exist many studies regarding how to enhance their return. Where theim proved performance of vapor compression cooling cycles are applied. In this field the operational characteristics like pressure, flow rate cooling and combined cooling are optimized through studies run by (Ghorbani, Hamedi, Shirmohammadi, Mehrpooya, & Hamedi, 2016; Ghorbani, Ziabasharhagh, & Amidpour, 2014; Salehi et al., 2012).

When the design and integration of the processes take place in a simultaneous manner, the number of required equipment and energy consumption decrease (Ghorbani, Mafi, et al., 2013; Ghorbani, Maleki, Salehi, Salehi, & Amidpour, 2013; Ghorbani, Salehi, Amidpour, & Hamedi, 2012; B Ghorbani, GR Salehi, H Ghaemmaleki, et al., 2012; Khan & Lee, 2013; Lashkajani, Ghorbani, Salehi, & Amidpour, 2013a, 2013b). In order to integrate these units, Conoco Phillips, APCI and Ortloff Company have introduced new plants. Some smaller companies have addressed several patented design limitations in this respect. In design plants based on ConocoPhillips cascade cycle], for better separation in the column is used lean liquid ethane in recycle. Pre-cooling cycle runs through by pure propane or a mixture of propane and ethane . The APCI Company has introduced a method for the production of these two products where the kettle type heat exchanger, absorption tower, and separation and external refrigeration cycle are applied (Roberts & Brostow, 2005). Ortloff Company has designed a process based on recovery NGL process liquefied natural gas (GSP). Lee et al designed and patented an integrated process for the production of LNG and NGL. This process used two columns that work in different pressure in the NGL recovery. [After initial cooling gas enter into this section and the liquid recycle, that must be rich from heavy hydrocarbons, produce from condensing of gas exited from second column or liquefaction section. M.S. Khan et al. analyzed a new process of KSMR system for the simultaneous production of natural gas condensate and NGL. Integrated nitrogen rejection unit for producing LNG is considered using dedicated reinjection circuit (Chen, Liu, Krishnamurthy, Ott, & Roberts, 2015a). In addition, the integrated nitrogen rejection process for the production of LNG is carried out through the intermediate feed gas separator (Ott, Krishnamurthy, Chen, Liu, & Roberts, 2015) . Integrated nitrogen removal in LNG production is assessed through the refrigerated heat pump (Ott, Krishnamurthy, Chen, Liu, & Roberts, 2015)..As an alternative approach to improving energy return cycles of absorption cooling units, LNG can be used as the cooling agent. Taking advantage of the energy dissipation properties of absorption cooling cycles from different parts of the unit is possible in this cycles (Ghorbani, Salehi, Esnaashary, & Amidpour, (2012); Mafi, Ghorbani, Amidpour, & Naynian, (2013); Salarian, Ghorbani, Amidpour, & Salehi, (2014)).

Ghorbani et al. developed two integrated NGL-LNG with nitrogen rejection by C3MR and MFC refrigeration cycle. This introduced cycle indicates that, integration due to the reduced in equipment and increase the efficiency.

In this paper, exergy and exergoeconomic analyses are applied to recently alternatives integrated processes for cogeneration of LNG, NGL and NRU with reasonable energy consumption and high ethane recovery. Exergy efficiency and exergy destruction of the process components are calculated. Next all of the equipment are sized and cost of them are calculated with a suitable cost function. Mathematical modeling of the process is done in order to finding the exergoeconomic factors. Exergoeconomic variables, exergy destruction cost, relative cost difference, exergoeconomic factor are computed and thermoeconomic analysis of the process is investigated and discussed.

2. Process Description {Vatani, 2013 #16}

2.1. Conceptual Design

The MFC process consists of three pure refrigerants of methane, ethylene, and propane with different boiling temperatures, . First, the natural gas is cooled up to -25 ºC in the propane cycle, next up to -86 ºC in the ethylene cycle; finally, it is liquefied to -160 ºC in the methane cycle. The MFC process is highly efficient due to the low shaft power consumption of the three MRC compressors. A structure of integrated process consisting of recycling natural gas liquids, natural gas liquefaction, and nitrogen removal from an absorption refrigeration cycle for precooling and two refrigeration cycle, (multi-component refrigerant) for cooling and liquefaction are proposed.

The absorption refrigeration cycle replaced by compression refrigeration cycle (cycle 400) in the integrated process of LNG, NGL, and NRU with the objective to reduce energy consumption is shown in Fig. (1). Natural gas feed enters at about 37 ºC and 63.09 bar with a 14000 kg.mol/h flow rate. The Liquid produced through this process is categorized into three: Natural gas liquids (1578.8 kgmole/h), liquefied natural gas (11559.3 kg.mol/h) and Removing nitrogen (620.7 kg.mol/h). A propane refrigeration cycle is applied to supply both the required cooling for NGL recovery and precooling for the LNG process.

 

 

 

Figure 1. Cascade refrigeration (combined refrigerant and absorption refrigeration) integrated in the NGL-LNG-NRU consumption structure.

 


2.2. Basic Design

The relation between different equipment of the integrated process of natural gas liquids, natural gas liquefaction, and denitrification is shown in Fig. (2). How the alternative absorption refrigeration system is replaced by precooling compression cycle (Cycle 400) is clearly shown in this figure. Inlet feed stream at 37  and 63.09 bar enters the multi-stream heat exchangers HX1 and HX2 and is cooled up to 8  and -27 ,respectively. The next outlet stream, 103, is cooled -41 . A part of the required cooling is provided by a three stage propane refrigeration cycle. The outlet gas from the NGL recovery unit, 102, is channeled into the D3 separator. The required heating for the tower is supplied using three side streams; side1, side2 and side3 at approximately 14.5  ,6.8  and -7.4 , respectively. These streams exit the column and enter the multi-stream heat exchangers. Side1 enters the HX1 heat exchanger and exits at 35 . Side1R is named as the backflow and is marked on the PFD. Side2 and side3 are channeled into the HX2 and HX3 respectively and exit the heat exchangers at 0  and -20 , respectively. The outlet streams from the heat exchanger return to the column.  De-ethanizertop gas is channelled to HX4 through V-5 expansion valve where its temperature reaches -119 . Next the stream is ready to enter the nitrogen rejection unit. Stream 118 containing methane and nitrogen with a standard volume of about 1.2% from bottom of the column T200 as the liquid product enters HX-3 from the bottom. Stream 128 is channeled to D2 flash drum and the gas product of this separator returns to the HX-4. Line 123 is branched into two: branch one, (88%), stream 126, enters HX4 multi-stream heat exchanger and its temperature decreases up to -132  and turns to liquid. This cooled liquid passes through an expansion valve where its pressure and the temperature reach up to about 25 bar and -131 . Then it is channeled to the top of the nitrogen removal column as washing liquid. Stream 124, containing 12% of gas output from D2, enters HX3 as well and is cooled up to -75 . Next stream 125 is channeled to column. After eliminating the ethane plus hydrocarbons and nitrogen from the gas stream, it is channeled to the liquefaction section. Stream 129 is compressed up to 63 bar and enters the HX4 heat exchanger. This stream is first heated up to -99  when passing through HX4 and it is then super-cooled by HX4 super-cooling heat exchanger up to 63 bar and at -164  and eventually becomes the final product after passing through V8 where the pressure is reduced to atmospheric pressure, and enters phase D1. The final product is named LNG stream which exits from the separator as gas stream containing a high percentage of nitrogen in which is channeled back into the unit. To meet the cooling requirements, pre-cooling and liquefaction systems are carried out by applying an absorption refrigeration cycle for precooling and two refrigeration cycle (multi-component refrigerant).

 

 

Figure 2. Schematic of block flow diagram of the first stage for typical NGL-LNG-NRU plants

 

 

 

Table 1. Thermodynamic data for configuration process of material streams

Stream

no.

Temperature

( C)

Pressure

(kPa)

Flow

(kg.mol/h)

Physical exergy

(kW)

Chemical exergy

(kW)

Total exergy

(kW)

Feed

37

6309

14000

37575.23

6750765.02

6788340.25

101

8

6309

14000

37635.72

6750765.02

6788400.75

102

-27

6309

14000

38762.02

6750765.02

6789527.05

103

-27

6309

13211.4

37226.85

5173680.15

5210907.01

104

-27

6309

788.5

1356.56

1577263.47

1578620.03

105

-27

6309

6605.7

18613.42

2586840.07

2605453.50

106

-27

6309

6605.7

18613.42

2586840.07

2605453.50

107

-66.4

2600

6605.7

16204.49

2586840.07

2603044.57

108

-88

6309

6605.7

23688.3

2586840.07

2610528.37

109

-27

6309

236.5

406.96

473179.04

473586.01

110

-27

6309

551.9

949.59

1104084.43

1105034.02

111

-30.43

2550

551.9

798.15

1104084.43

1104882.58

112

-50

6309

236.5

471.42

473179.04

473650.46

113

-51.2

2500

236.5

408.39

473179.04

473587.43

114

-102.3

2500

6605.7

22948.07

2586840.07

2609788.15

115

-98.9

2500

12421.1

32367.89

2716170.75

2748538.64

116

-113.3

1379

12421.1

28589.66

2716170.75

2744760.42

117

-119

1379

12421.1

38532.65

2716170.75

2754703.41

118

-119.7

1400

15079.3

59524.15

3434793.95

3494318.11

119

-118

1400

15079.3

53951.44

3434793.95

3488745.40

120

-164.1

1358

10346.6

29198.37

14303.69

43502.07

121

-164.1

1358

9725.8

27446.47

13445.47

40891.95

122

-170

1358

9725.8

47793.23

13445.47

61238.70

123

-118

1400

3311.4

7746.42

718797.52

726543.94

124

-118

1400

411.6

962.88

89346.53

90309.41

125

-75

1400

411.6

827.83

89346.53

90174.37

126

-118

1400

2899.7

6783.54

629450.99

636234.53

127

-132

1400

2899.7

12115.22

629450.99

641566.21

128

-131.9

1367

2899.7

12113.03

629450.99

641564.02

129

-118

1400

11772.5

46117.20

2717083.49

2763200.69

130

-99

1400

11772.5

25529.79

2717083.49

2742613.28

131

7.2

6300

11772.5

32531.14

2717083.49

2749614.63

132

-85.2

6300

11772.5

41428.45

2717083.49

2758511.94

133

-164

6300

11772.5

58282.65

2717083.49

2775366.14

134

-164.1

101.3

11772.5

56447.91

2717083.49

2773531.41

135

-164.1

101.3

213.2

214.93

39745.98

39960.92

136

-164.1

1358

620.7

1751.90

858.22

2610.12

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(Continuation)

Stream

no.

Temperature

( C)

Pressure

(bar)

Flow

(kg.mol/h)

Physical exergy

(kW)

Chemical exergy

(kW)

Total exergy

(kW)

137

-30

1358

620.7

1137.18

858.22

1995.40

200

35

2790

18500

39355.95

7744424.76

7783780.71

201

3

2790

18500

40714.69

7744424.76

7785139.45

202

-31

2790

18500

45921.58

7744424.76

7790346.34

203

-85

2790

18500

54625.4

7744424.76

7799050.16

204

-86.6

600

18500

53681.77

7744424.76

7798106.53

205

-32.8

600

18500

24984.58

7744424.76

7769409.34

206

-27

600

18500

23502.11

7744424.76

7767926.87

207

30

1500

18500

32866.37

7744424.76

7777291.14

208

35

1500

18500

32903.43

7744424.76

7777328.20

209

77.9

2790

18500

40728.29

7744424.76

7785153.05

300

35

2790

18500

39355.95

7744424.76

7783780.71

301

8

2900

37000

83669.08

8303601.04

8387270.13

302

-29

2900

37000

86445.10

8303601.04

8390046.15

303

-50

2900

37000

93194.73

8303601.04

8396795.78

304

-173

2900

37000

190776.71

8303601.04

8494377.76

305

-177.5

330

37000

187617.77

8303601.04

8491218.82

306

-67.2

330

37000

36880.06

8303601.04

8340481.11

307

85.5

2500

37000

82416.34

8303601.04

8386017.39

308

35

2500

37000

80016.16

8303601.04

8383617.21

309

47.9

2900

37000

83823.71

8303601.04

8387424.75

500

31.9

120

153176.8

270.92

3843117.85

3843388.78

501

32

1300

153176.8

1437.09

3843117.85

3844554.95

502

122.8

1300

153176.8

51936.02

3843117.85

3895053.88

503

45.5

1300

17887.1

30286.07

1693908.89

1724194.96

504

146.2

1300

135278.1

61024.15

2154922.16

2215946.32

505

33.9

1300

17887.1

27219.46

1693908.89

1721128.36

506

33.4

1300

17887.1

27211.95

1693908.89

1721120.85

507

-29.5

120

17884.9

23516.64

1693706.62

1717223.26

508

-29.5

120

17884.9

9741.91

1693706.62

1703448.53

509

27.5

120

17884.9

2066

1693706.62

1695772.62

510

28.9

120

17829.7

2062.47

1688472.60

1690535.08

511

37

1300

135278.1

1697.18

2154922.16

2156619.35

LNG

-164.1

101.3

11559.3

56172.09

2677398.39

2733570.48

NGL

27.4

2500

1578.8

2168.70

1271730.56

1273899.27

Nitrogen

-80

1358

620.7

1234.72

858.22

2092.94

Exside1

14.5

2500

4000

7498.65

2254297.09

2261795.74

Exside2

6.7

2500

4000

7917.59

2137273.77

2145191.36

Exside1R

35

2500

4000

7377.91

2254297.09

2261675

Exside2R

0

2500

4000

7980.68

2137273.77

2145254.45

 


 

 

3. Exergy Analysis

Exergy is the maximum available work when some forms of energy are transferred in a reverse manner to a reference system, which is in thermodynamic equilibrium with the surroundings, and is disable. Exergy is a measure of distance of a system from global equilibrium; with respect to the state variables of temperature, pressure, and composition of the system approaching surroundings]. therefore, the reference state is named the dead state. The total exergy of multicomponent streams is the sum of its three contributions: change due to mixing, chemical exergy, and physical exergy. The exergy of mixing results from the isothermal and isobaric mixing of streams at the actual process conditions. The chemical exergy is the difference between the process and reference components in their environmental concentration, temperature, and pressure in chemical potentials. The physical exergy is the maximum obtainable amount of shaft work (electrical energy) when a stream is brought from process conditions (T, P) to an equilibrium at ambient temperature by a reversible heat exchange. In general practice the exergy analysis is based on the overall thermodynamic efficiency, the ratio of the lost work to the ideal work required for separation. The overall exergy efficiency for distillation is the product of external and internal exergy efficiencies. (B Ghorbani, GR Salehi, M Amidpour, et al., 2012; B Ghorbani, GR Salehi, H Ghaemmaleki, et al., 2012; Meratizaman, Amidpour, Jazayeri, & Naghizadeh, 2010; Morosuk & Tsatsaronis, 2008; Romero Gómez, Romero Gómez, López-González, & López-Ochoa, 2016; Sheikhi, Ghorbani, Shirmohammadi, & Hamedi, 2014, 2015). The exergy of the process material streams is tabulated in Table (2). In this study , and , are defined as the fuel exergy rate, the product exergy and the exergy destruction rate, respectively.

The exergy balance over the kth component is

 

                    (1)

where, , and  are the exergy rates of fuel, product and destruction, respectively. and  yk is defined as the exergy destruction ratio:

 

                  (2)

The streams operating conditions and exergy analysis of refrigeration cascade structure are tabulated in Table2.  The definitions applied for calculation of exergy efficiency of the process components and the exergy efficiency of the process components are tabulated in this table.

 

 


 

 

 

 

 

 

 

Table2.  Definitions for exergy efficiencies of the process components

 

Exergy efficiency (%)

 

Component identifier

Exergy efficiency (%)

Component identifier

Components and exergy efficiency expression

 

 

 

 

Heat Exchanger

 

 

Cooler

 

 

97.35

97.81

98.24

96.38

HX5

HX6

HX7

HX8

 

87.78

91.35

94.03

86.35

 

HX1

HX2

HX3

Hx4

-

-

67.33

96.87

C6

C7

Ex

Pump

78.24

76.68

72.61

74.97

78.54

C1

C2

C3

C4

C5

 

Compressor and Pump

 

 

16.73

6.2

34.64

63.17

22.91

51.63

V7

V8

V9

V10

V11

V12

 

13.3

34.8

80.8

17.08

43.01

63.82

 

V1

V2

V3

V4

V5

V6

Expansion valve

 

99.19

-

AC4

AC5

99.12

98.27

98.26

AC1

AC2

AC3

Air cooler

 

57.39

T300

 

79.37

49.88

 

T100

T200

Column[38,39]

 

 

 

s

irr

 

 

 

Cycle/process

 

57.96

 

 



4. Exergoeconomic Analysis

All the costs associated with a project, including a minimum required return on investment is calculated through this method. Based on the estimated total capital investment and assumptions made in economical, financial, operating, and market input parameters, the total revenue requirement is calculated on a year-by-year basis. Finally, the non-uniform annual monetary values associated with the investment, operating (excluding fuel), maintenance, and the fuel costs of the system subject to analysis are levelizedو that is, they are converted into an equivalent series of constant payments (Fazelpour & Morosuk, 2014; B Ghorbani, GR Salehi, M Amidpour, et al., 2012).

4.1. Economic Model

Total Revenue Requirement method is applied in this study for economic analysis. The detailed descriptions on the economic model and its terms are presented in Table 3. Economic constants and assumptions are tabulated in Table 3.

The levelized annual total revenue requirement  is calculated as follows through the Capital Recovery Factor:

 

 (3)

where, TRRj is the total revenue requirement in jth year of system operation, BL is economic life cycle of the system (yr) and ieff is the average annual rate of effective devaluation. Capital recovery factor (CRF) is calculated as follows:

 

           (4)

TRRj is the sum of four annual terms: minimum return on investment (ROI), total capital recovery (TCR), operation and maintenance costs (OMC) and fuel costs (FC)(Fazelpour & Morosuk, 2014; Wang et al., 2014; Yang, Wei, & Chengzhi, 2009).  More explanation about the economic terms and analysis are found in:

 

(5)

where, FC0 is the fuel cost at the beginning  point, the  year and calculated as follows:

  

(6)

 

where:

= total annual time (in hours) that is 7300 h year-1

Cw = unit cost of fuel (0.071 $ kWh-1)

= power (kW)

Cost of electricity during the jth year is computed as follows:

 

(7)

The constant escalation levelization factor (CELF) for the fuel is obtained through:

 

 

(8)

where:

   

    (9)

rFC is the average annual escalation rate of fuel cost. The levelized annual operating and maintenance costs OMCL are calculated as follows:

 

(10)

 

where,

 

 

(11) 

rOMC is the annual escalation rate for the operating and maintenance costs. The levelized carrying charges CCL is calculated as follows:

 

(12)

 

Capital investment  and operating and maintenance costs  of the total plant are gained based on the process components purchased cost.

 

  (13)

 

(14)

where,  and PECk are the total annual hours of plant operation and the purchased-equipment cost of the kth component, respectively. Symbol  is the cost rate associated with the capital investment and operating and maintenance costs:

 

(15)

Rate of levelized costs is calculated as follows:

 

(16)

The cost functions used for calculation of the process equipment cost and the purchased equipment and investment costs are tabulated, respectively in Tables 4 and 5.

 

 

 

 

Table 3. Economic constants and assumptions.

Economic parameters

Value

Average annual rate of the cost of money (ieff)

10%

Average nominal escalation rate for the operating and maintenance cost (rOMC)

5%

Average nominal escalation rate for fuel (rFC)

5%

Plant economic life (book life)

25 years

Total annual operating hours of the system, at full load

7300

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 4. Equations regarding the cost of the process components

Component

Purchased equipment cost functions

Compressor

CC=7.90(HP)0.62

CC= Cost of Compressor (k$)

 

Expander

CEx = 0.378(HP)0.81

CEx = Cost of Expander (k$)

Heat exchanger

CE=a(V)b+c

CE= Cost of Heat exchanger ($)

Pump

CP=fMfTCb

CP= Cost of Pump ($)

Cb=1.39exp[8.833-0.6019(lnQ(H)0.5)+0.0519(lnQ(H)0.5)2], Q in gpm, H in ft head

fM= Material Factor

fT=exp[b1+b2(lnQ(H)0.5)+b3(lnQ(H)0.5)2]

b1= 5.1029, b2= -1.2217, b3= 0.0771

Air cooler

CAC=1.218fmfPexp[a+blnQ+c(lnQ)2],  Q in KSCFM

CAC= Cost of Air cooler (k$)

fm=Material Factor

fP=Pressure Factor

a=0.4692, b=0.1203, c=0.0931

Drum

CD=fmCb+Ca

CD= Cost of Drum ($)

Cb=1.218exp[9.1-0.2889(lnW)+0.04576(lnW)2], 5000<W

Ca=300D0.7396 L0.7066, 6<D<10, 12<L

fm= Material Factor

 

Cooler

CC =1.218k(1+fd+fp)Q0.86  , 20<QC= Cost of cooler ($)

fm=Design Type

fP=Design Pressure (psi)

a=0.4692, b=0.1203, c=0.0931

Absorber

 

Cb=1.128exp(6.629+0.1826 (logW)+0.02297*(logW) 2)

Cp1=300 (D0.7395) (L0.7068)

C1=1.218 [(1.7Cb+23.9V1+Cp1) ]

C2=Cost of installed manholes, trays and nozzles

C3= Cost of Cooler

C4= Cost of Heater

CAb = C1+C2+C3+C4

CAb= Cost of Drum ($)

 

Table 5. Purchased equipment and investment costs for configuration process components

Equipment

PEC (×103 $)

ZCI ($/hr)

ZOM ($/hr)

Z ($/hr)

HX1

1969

109.3

2.2986

111.6

HX2

2564

142.3

2.9923

145.3

HX3

1004

55.7

1.1721

56.9

HX4

1349

74.9

1.5750

76.5

HX5

306

17

0.3568

17.3

HX6

306

17

0.3568

17.3

HX7

306

17

0.3568

17.3

HX8

306

17

0.3568

17.3

C1

49835

2766.4

58.1660

2824.6

C2

15580

864.8

18.1843

883

C3

23511

1305.1

27.4417

1332.6

C4

27603

1532.2

32.2169

1564.5

C5

23993

1331.9

28.0039

1359.9

Ex

7786

432.2

9.0880

441.3

Pump1

2790

154.9

3.2559

158.1

AC1

18597

1032.3

21.7061

1054.1

AC2

18597

1032.3

21.7061

1054.1

AC3

6159

341.9

7.1883

349.1

AC4

9079

504

10.5964

514.6

D1

4294

238.4

5.0122

243.4

D2

5603

311

6.5399

317.6

D3

4294

238.4

5.0122

243.4

T100

4554

252.8

5.3151

258.1

T200

3160

175.4

3.6887

179.1

T300

2403

133.4

2.8051

136.2

 


4.2. Cost Balance Equations

The exergy cost of the streams is gained by writing the cost balance over each component. The cost balance terms are: outlet streams cost, inlet streams cost, primary investment cost, , and the operation and maintenance  costs.

 

(17)

For the components which have more than one output, some auxiliary equations are written ; therefore, based on the cost balances and auxiliary equations for all components a set of linear equations is yield as follows:

 

(18)

where, , and  are exergy rate matrix, costs per unit of exergy vector and coefficient vector for , respectively. The cost balance and auxiliary equations for the process components are tabulated in table 6.

 

Table 6. Main equations and auxiliary equations for the process components

Equip.

Equation Main

HX1

 

HX2

 

HX-3

 

HX-4

 

HX5

 

HX6

 

HX7

 

HX8

 

C1

 

C2

 

C3

 

C4

 

C4

 

Ex

 

AC1

 

AC2

 

AC3

 

AC4

 

D1

 

D2

 

D3

 

Pump

 

T100

 

T200

 

T300

 

V3

 

V4

 

V5

 

V6

 

V7

 

V8

 

V9

 

V10

 

V11

 

V12

 

TEE1

 

TEE2

 

TEE3

 

TEE4

 

MIX1

 

.Equip.

Auxiliary Equations

HX1

 

HX2

 

HX-3

 

HX-4

 

HX5

,

HX6

 

HX7

,

HX8

 

D1

 

D2

 

D3

 

T100

, ,

T200

 

TEE1

 

TEE2

 

TEE3

 

TEE4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4.3. Exergoeconomic variables

Based on the fuel/product concept for a component,  and are the fuel and product exergy rates, respectively. Accordingly  and are defined as fuel cost and product cost rates, respectively. For the kth component of a system ( ) is the average cost per unit of exergy of fuel:

 

(19)

 is the product average cost per unit of exergy:

 

(20)

 is the cost of exergy destruction for the kth component.

 

(21)

Relative cost difference is defined as follows:

 

(22)

Exergoeconomic factor is the ratio of investments’ cost to the total investment plus exergy destruction costs, calculated as follows:

 

(23)

Table7 show the exergy unit cost for each stream is obtained of the processes.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 7. Unit exergy cost of configuration process streams

Stream

no.

   

Stream

no.

   

Feed

59618

2.439

137

8500

131.15

101

10720

2.438

200

5770400

205.92

102

59490

2.433

201

5529700

197.30

103

45470

2.423

202

5854300

208.743

104

13780

2.423

203

5897700

210.059

105

22740

2.423

204

5897700

210.084

106

22740

2.423

205

5774500

206.452

107

22310

2.381

206

22300

0.797

108

48090

5.116

207

5772800

206.182

109

9640

5.655

208

5772400

206.169

110

22500

5.655

209

5770900

205.909

111

22500

5.656

300

5770400

205.927

112

4450

2.612

301

6474400

214.426

113

4450

2.612

302

6301400

208.626

114

48090

5.118

303

6267700

207.342

115

184960

18.692

304

5797300

189.578

116

184960

18.718

305

5797300

189.649

117

137030

13.817

306

6439000

214.447

118

38110

3.029

307

6442400

213.397

119

61910

4.929

308

6443500

213.493

120

185810

1186.453

309

6444400

213.427

121

174660

1186.453

500

6900

0.497

122

272740

1237.140

501

7100

0.509

123

12960

4.953

502

7100

0.509

124

1610

4.953

503

5700

0.917

125

2190

6.737

504

1300

0.167

126

11350

4.953

505

5700

0.917

127

14360

6.215

506

5700

0.917

128

14360

6.215

507

5700

0.919

129

49270

4.953

508

5600

0.919

130

137210

13.896

509

5600

0.919

131

138650

14.006

510

5600

0.919

132

94200

9.485

511

1300

0.167

133

139350

13.947

LNG

137500

13.971

134

139350

13.956

NGL

221500

48.292

135

2010

13.971

Nitrogen

8500

186.45

136

11150

186.453

Exside1

63500

7.793

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5. Results and Discussion

5.1. Exergy analysis

The highest rates for exergy destruction occurs in the Modified MFC, in AC3 by 16.9%, in V11 by amount of 16.52% and in AC2 by of 13.23%, respectively, Table 8. The least amount of exergy destruction in the Modified MFC structure occurs  at 0.00001% in V10, 0.00002% in HX7, and 0.00031% in V5 rates, respectively. 

the Modified MFC structure exergetic efficiency of expansion valves are less than in comparison with the other equipment, while their irreversibilities are low, Fig. (2). This fact indicates that the equipment performance in energy consumption must be analyzed in terms of irreversibility and exergy efficiency. The structure of Modified MFC exchanger HX7 with efficiency of 98.24% has the most exergetic efficiency and HX4 with efficiency of 86.35% has the lowest exergetic efficiency. The contribution of each heat exchanger in the total exergy losses is shown in a pie chart Fig. (3), wherethe most exergy loss occurs in the heat exchangers HX4 and HX5 which are responsible for more than 39.23% of the total exergy loss among the heat exchangers.Among the heat exchangers HX4 by 21784.68 kW has the highest Exergy loss and HX7 with 4.6 kW has the least amount of exergy loss.

 

 

Table 8. Results of exergy and exergoeconomic analysis of the process

Component

               

HX1

6223.92

17813.13

12066.5

520652.1

3.07

4.1

0.021

520763.7

HX2

5870.51

18272.64

12282.7

5530426

2.89

31.03

 0.0188

5530571

HX3

5012.40

12590.52

18159.22

113427.4

2.47

0.6

0.0538

113484.3

HX4

21784.68

8.439625

12945.43

354910.9

10.75

2.9

0.0165

354987.4

HX5

8828.03

5.695625

8.383281

56.34397

4.35

5.2

23.51

73.64397

HX6

2227.6

11.29995

5.685495

10.13009

1.09

9.02

63.1

27.43009

HX7

4.6

6.88119

11.28258

17.36552

0.002

15.3

49.94

34.66552

HX8

5579.3

6442.407

6.879156

2.033333

2.755

8.02

89.49

19.33333

C1

12661.34

6444.398

6439.582

2824.555

6.25

0.1

50.91

5649.155

C2

1157.33

138.6452

6443.515

883.0313

0.57

9.4

49.99

1766.031

C3

2640.49

5772.753

137.3126

1332.575

1.3

8.6

50.19

2665.175

C4

3124.97

5770.937

22.44673

5750307

1.54

99.6

0.1586

5751872

C5

2137.56

22.73564

5772.512

1575.062

1.05

54.7

46.33

2934.962

Ex

786.9

7.050264

22.32937

406.2791

0.38

17.5

52.066

847.5791

Pump1

38

6447.223

6.892157

158.1064

0.018

22.4

50.21

316.2064

AC1

283.72

6443.461

6444.398

2824.555

0.14

40.42

27.17

3878.655

AC2

26797.68

5772.754

6442.407

1054.054

13.23

29.5

49.99

2108.154

AC3

34241.78

5770.422

5772.404

349.5285

16.9

43.5

49.96

698.6285

AC4

1438.15

488.0531

5770.937

515.181

0.71

27.3

49.97

1029.781

T100

37.63

426.3132

400.0469

88006.22

1.733

17.01

0.292

88264.32

T200

3511.14

17813.13

223.9185

202394.7

4.629

49.92

0.088

202573.8

T300

9374.73

18272.64

12066.5

520652.1

1.823

49.03

0.067

520788.3

 

 

 

 

 

Figure3. Exergy destruction of hrat exchangers in the integrated structure of LNG-NGL-NRU

 

 

Figure 4.  Breakdown of compressors, expander and pump exergy losses in the integrated structure of LNG-NGL-NRU

 

The contribution of the expander, compressors and pump in the total exergy loss are shown in a pie chart in Fig. (4). Among compressors, structure of Modified MFC, the C5 by the efficiency of 78.54% has the highest and C3 by efficiency of 72.61% has the lowest efficiency. Among compressors C1 and C2 have the highest and lowest amount of Exergy destruction equal to 12661.34 kW and 1157.33 kW, respectively. Among the throttle valves in Modified MFC, V3 with efficiency of 80.8% and throttle valve V8 with an output efficiency of 6.2% have the highest and lowest efficiencies, respectively. Among the throttle valves V11 and V10 with exergy loss of 33475.23 kW and 2.184406kW have the maximum and minimum amount of exergy loss, respectively.

The contribution of air coolers in the total exergy loss are shown in Fig. (5). Among the air coolers in the Modified MFC, AC4 with efficiency of 98.9% and AC2 with the efficiency of 97.12% have the highest and lowest efficiency, respectively. Among air coolers AC3 with 34241.78 kW and AC1 with 283.72 kW have the highest and lowest amounts of exergy loss, respectively. Fig.6 demonstrates the contribution of the towers in the total exergy loss.

 

 

 

 

 

 

Figure 5.  Breakdown of air coolers exergy losses in the integrated structure of LNG-NGL-NRU

 

                                                                                                                                          

 

Figure 6.   Breakdown of towers’ exergy losses in the integrated structure of LNG-NGL-NRU

 

 

5.2. Exergoeconomic analysis

In TRR method, the capital cost of the system is estimated first. Next, some economical techniques are applied to calculate the revenue requirement of the system in $/h and then, the cost balance equations are written to calculate the unit cost of exergy for each stream. The exergoeconomic factor is defined and comments are made on the balance between the capital investment and operating costs of the system inflicted by the exergy loss which have to be compensated by more fuel consumption (Ghorbani et al (2016))

There exists a distinct algorithm able to obtain the abovementioned results, where:

1- All the components are put in descending order based on their importance, known from the magnitude of the sum  ,hence, the manner in modeling components based on their importance. C4 column with 5751872  has the greatest value. Accordingly, to improve performance , the components with high value of cost should be considered.

2- The exergoeconomic factor is applied in finding the prominent factor of the cost infliction as follows:

a) if the value of f is large, we should check whether it is economically justified to decrease the capital cost of the equipments, because it is assumed that the capital cost is so high that it has lost its economical justification. The exergoeconomic factor(s) of the process components are illustrated, where, HX8 has the greatest value of 89.49%.

b) if f is small, attempt should be made to increase the efficiency even if it yields higher capital cost, since it is assumed that low efficiency of the system inflicts a high expenditure on the system.

 

 

 

 

 

 

 

 

Table 9. Components, based on their f values

Component

f%

HX8

89.49

HX6

63.1

Ex

52.066

C1

50.91

Pump1

50.21

C3

50.19

AC2

49.99

AC4

49.97

AC3

49.96

 

 

T100

0.292

T200

0.088

T300

0.067

HX3

0.050

HX4

0.021

HX1

0.021

HX2

0.0026

 

 

 

6. Sensitivity Analyses

In order to choose the appropriate decision variables of the system it is necessary to capture determine the behavior of the objective function with respect to decision variables. Since much of the electrical energy consumption of the plant the compressors, optimizing and reducing their exergy loss will lead to a more economical approach of the entire system.

The cost of exergy loss and exergoeconomic factor of C4, HX2, HX3 and HX3 versus pressure ratio of compressor C4, respectively are shown in Figs. (7 and 10). Cost of exergy destruction of of C4, HX2, HX3 and HX3 is subject to pressure ratio; while, the decrease in C4, HX2, HX3 and HX3 exergoeconomic factors is subject pressure ratio. The C4 exergy destruction rate increases with a higher rate compared to the other components because with an increase in the C4 pressure ratio its power increases directly and the cost of exergy destruction increases at a higher rate. The cost of exergy loss and exergoeconomic factor of C1, AC2 and HX4versus pressure ratio of compressor C1, are shown in Figs. (11 and 12), respectively. The cost of exergy destruction of  C1 decreases and cost of exergy destruction of AC2 and HX4 increases as pressure drops. The exergoeconomic factor of AC2 and HX4 decrease while the exergoeconomic factor of C1 increases with pressure ratio.

 

 

 

Figure 7. Variation of exergy loss and exergoeconomic factor of C4 with respect to compression ratio in C4 compressor

 

Figure 8.Variation of exergy destruction and exergoeconomic factor of HX2 with respect to compression ratio in C4 compressor

 

 

 

 

Figure 9. Variation of exergy loss and exergoeconomic factor of HX3 with respect to compression ratio in C4 compressor

 

Figure 10.Variation of exergy destruction and exergoeconomic factor of HX4 with respect to compression ratio in C4 compressor

 

 

 

Figure11.Variation of exergy loss and exergoeconomic factor of C1 with respect to compression ratio in C1 compressor

 

Figure 12.Variation of exergy destruction and exergoeconomic factor of AC2 with respect to compression ratio in C1 compressor.

 

 

Figure 13. Variation of exergy loss and exergoeconomic factor of HX4 with respect to compression ratio in C1 compressor

 

The cost of exergy loss and exergoeconomic factor of C4, HX2, HX3 and HX3 versus pressure ratio of compressor C4, respectively are shown in Figs. (7 and 10). Cost of exergy destruction of of C4, HX2, HX3 and HX3 is subject to pressure ratio; while, the decrease in C4, HX2, HX3 and HX3 exergoeconomic factors is subject pressure ratio. The C4 exergy destruction rate increases with a higher rate compared to the other components because with an increase in the C4 pressure ratio its power increases directly and the cost of exergy destruction increases at a higher rate. The cost of exergy loss and exergoeconomic factor of C1, AC2 and HX4versus pressure ratio of compressor C1, are shown in Figs. (11 and 12), respectively. The cost of exergy destruction of  C1 decreases and cost of exergy destruction of AC2 and HX4 increases as pressure drops. The exergoeconomic factor of AC2 and HX4 decrease while the exergoeconomic factor of C1 increases with pressure ratio.

7. Conclusions

In this study the exergoeconomic analysis of an integrated NGL recovery, nitrogen rejection and LNG process is assessed. Results obtained from exergoeconomicanalysis are presented in form of exergy destruction cost and exergoeconomicfactor, as follows:

1. Most important elements in exergy loss cost are related to the air coolers due to their high fuel consumption.

2. Exergoeconomic factor in the heat exchangers, expanders and compressors is higherthan other elements, thus, in order to reduce the total system cost,their cost must be minimized.

3. Based on the exergoeconomic diagnosis the cost of HX8 and HX6 is high, thus it is better to replace them with loss expensive ones. while C4 and HX2 have a high destruction cost. Here, their efficiency improvement is a major concern. . HX2 is in similar situation, that is, it has small exergoeconomic factor. It is deduced that the efficiency column should be increased even it increases the initial investment cost. HX-2 and HX-3 are at the second order of magnitude for improvement.

Nomenclature

BL

book life

c

unit exergy cost ($/kJ)

 

exergy cost rate ($/h)

CC

Carrying charge

CRF

capital recovery factor

cw

Unit cost of the generated electricity ($/kW)

e

Specific flow exergy (kJ/kgmole)

Ė

Exergy rate (kW)

Ex

Exergy (kW)

F

exergoeconomic factor (%)

FC

Fuel cost ($/s)

I

Irreversibility (kW)

ieff

average annual discount rate (cost of money)

j

jth year of operation

m

Number of cold streams

 

Flow rate (kgmole/s)

n

Number of hot streams

OMC

Operating and maintenance cost

PEC

Purchase equipment cost ($)

Q

Heat duty (kW)

r

relative cost difference (%)

rFC

annual escalation rate for the fuel cost

TCR

Return on investment

rOM

Annual escalation rate for the operating and maintenance cost

TCR

Total capital recovery

TRR

Total revenue requirement

 W

Work transfer rate (kW)

 

Power (kW)

  y

Exergy destruction ratio

 

Total cost rate of kth component including Capital investment and operating-maintenance cost

 

Rate of capital investment of kth component

 

Rate of operating and maintenance cost of kth component

Greek Letters

 

annual operating hours (h)

ɛ

Exergy efficiency

Gradient

Subscripts

0

index for first year of operation

a

Air

c

Cold

D

Destruction

F

Fuel

h

Hot

i

Inlet

k

kth component

L

levelized

o

Outlet

P

Production

Tot

Total

Superscripts

CI

Capital investment

OM

Operating and maintenance

∆P

Pressure component

∆T

Thermal component

Abbreviations

AC

Air cooler

APCI

Air Products and Chemicals, Inc

C

Compressor

D

Flash drum

E

Multi stream heat exchanger

LNG

Liquefied Natural Gas

AB

Absorption

MIX

Mixer

MR

Mixed Refrigerant

V

Expansion valve

MFC

Mixed Fluid Cascade

NGL

Natural Gas Liquids

NRU

Nitrogen Rejection Unit

Alabdulkarem, A., Mortazavi, A., Hwang, Y., Radermacher, R., & Rogers, P. (2011). Optimization of propane pre-cooled mixed refrigerant LNG plant. Applied Thermal Engineering, 31(6), 1091-1098.

Amidpour, M., Hamedi, M., Mafi, M., Ghorbani, B., Shirmohammadi, R., & Salimi, M. (2015). Sensitivity analysis, economic optimization, and configuration design of mixed refrigerant cycles by NLP techniques. Journal of Natural Gas Science and Engineering, 24, 144-155.

Bejan, A., & Tsatsaronis, G. (1996). Thermal design and optimization: John Wiley & Sons.

Chen, F., Liu, Y., Krishnamurthy, G., Ott, C. M., & Roberts, M. J. (2015a). Integrated Nitrogen Removal in the Production of Liquefied Natural Gas Using Dedicated Reinjection Circuit: US Patent 20,150,308,736.

Chen, F., Liu, Y., Krishnamurthy, G., Ott, C. M., & Roberts, M. J. (2015b). Integrated Nitrogen Removal in the Production of Liquefied Natural Gas Using Intermediate Feed Gas Separation: US Patent 20,150,308,737.

Fazelpour, F. (2015). Energetic and exergetic analyses of carbon dioxide transcritical refrigeration systems for hot climates. Thermal Science, 19(3), 905-914.

Fazelpour, F., & Morosuk, T. (2014). Exergoeconomic analysis of carbon dioxide transcritical refrigeration machines. International Journal of Refrigeration, 38, 128-139.

Ghorbani, B., Hamedi, M.-H., & Amidpour, M. (2016). Development and optimization of an integrated process configuration for natural gas liquefaction (LNG) and natural gas liquids (NGL) recovery with a nitrogen rejection unit (NRU). Journal of Natural Gas Science and Engineering, 34, 590-603.

Ghorbani, B., Hamedi, M.-H., Amidpour, M., & Mehrpooya, M. (2016). Cascade refrigeration systems in integrated cryogenic natural gas process (natural gas liquids (NGL), liquefied natural gas (LNG) and nitrogen rejection unit (NRU)). Energy, 115, 88-106.

Ghorbani, B., Hamedi, M.-H., Shirmohammadi, R., Hamedi, M., & Mehrpooya, M. (2016). Exergoeconomic analysis and multi-objective Pareto optimization of the C3MR liquefaction process. Sustainable Energy Technologies and Assessments, 17, 56-67. doi:http://dx.doi.org/10.1016/j.seta.2016.09.001

Ghorbani, B., Hamedi, M., Shirmohammadi, R., Mehrpooya, M., & Hamedi, M.-H. (2016). A novel multi-hybrid model for estimating optimal viscosity correlations of iranian crude oil. Journal of Petroleum Science and Engineering.

Ghorbani, B., Mafi, M., Amidpour, M., Nayenian, M., & Salehi, G. R. (2013). Mathematical Method and Thermodynamic Approaches to Design Multi-Component Refrigeration Used in Cryogenic Process Part I: Optimal Operating Conditions. Gas Processing Journal, 1(2), 13-21.

Ghorbani, B., Mafi, M., Shirmohammadi, R., Hamedi, M.-H., & Amidpour, M. (2014). Optimization of operation parameters of refrigeration cycle using particle swarm and NLP techniques. Journal of Natural Gas Science and Engineering, 21, 779-790.

Ghorbani, B., Maleki, M., Salehi, A., Salehi, G. R., & Amidpour, M. (2013). Optimization of Distillation Column Operation by Simulated Annealing. Gas Processing Journal, 1(2), 49-63.

Ghorbani, B., Salehi, G., Amidpour, M., & Hamedi, M. (2012). Exergy and exergoeconomic evaluation of gas separation process. Journal of Natural Gas Science and Engineering, 9, 86-93.

Ghorbani, B., Salehi, G., Ghaemmaleki, H., Amidpour, M., & Hamedi, M. (2012). Simulation and optimization of refrigeration cycle in NGL recovery plants with exergy-pinch analysis. Journal of Natural Gas Science and Engineering, 7, 35-43.

Ghorbani, B., Salehi, G. R., Esnaashary, P., & Amidpour, M. (2012). Design and Optimization of Heat Integrated Distillation. Energy Science and Technology, 3(2), 29-37.

Ghorbani, B., Ziabasharhagh, M., & Amidpour, M. (2014). A hybrid artificial neural network and genetic algorithm for predicting viscosity of Iranian crude oils. Journal of Natural Gas Science and Engineering, 18, 312-323.

Khan, M. S., & Lee, M. (2013). Design optimization of single mixed refrigerant natural gas liquefaction process using the particle swarm paradigm with nonlinear constraints. Energy, 49, 146-155.

Lashkajani, K. H., Ghorbani, B., Amidpour, M., & Hamedi, M.-H. (2016). Superstructure optimization of the olefin separation system by harmony search and genetic algorithms. Energy, 99, 288-303.

Lashkajani, K. H., Ghorbani, B., Salehi, G. R., & Amidpour, M. (2013a). The Design and Optimization of Distillation Column with Heat and Power Integrated Systems.

Lashkajani, K. H., Ghorbani, B., Salehi, G. R., & Amidpour, M. (2013b). The Design of the Best Heat Integrated Separation Systems Using Harmony Search Algorithm.

Mafi, M., Ghorbani, B., Amidpour, M., & Naynian, S. M. (2013). Design of mixed refrigerant cycle for low temperature processes using a thermodynamic approach. Scientia Iranica. Transaction B, Mechanical Engineering, 20(4), 1254.

Mafi, M., Ghorbani, B., Salehi, G., Amidpour, M., & Nayenian, S. M. The Mathematical Method and Thermodynamic Approaches to Design Multi-Component Refrigeration used in Cryogenic Process Part II: Optimal Arrangement.

Meratizaman, M., Amidpour, M., Jazayeri, S. A., & Naghizadeh, K. (2010). Energy and exergy analyses of urban waste incineration cycle coupled with a cycle of changing LNG to pipeline gas. Journal of Natural Gas Science and Engineering, 2(5), 217-221.

Morosuk, T., & Tsatsaronis, G. (2008). A new approach to the exergy analysis of absorption refrigeration machines. Energy, 33(6), 890-907.

Ott, C. M., Krishnamurthy, G., Chen, F., Liu, Y., & Roberts, M. J. (2015). Integrated Nitrogen Removal in the Production of Liquefied Natural Gas Using Refrigerated Heat Pump: US Patent 20,150,308,738.

Ransbarger, W. L. (2006). Intermediate pressure LNG refluxed NGL recovery process: Google Patents.

Roberts, M., & Brostow, A. (2005). Integrated NGL recovery and liquefied natural gas production: Google Patents.

Romero Gómez, M., Romero Gómez, J., López-González, L. M., & López-Ochoa, L. M. (2016). Thermodynamic analysis of a novel power plant with LNG (liquefied natural gas) cold exergy exploitation and CO2 capture. Energy, 105, 32-44. doi:http://dx.doi.org/10.1016/j.energy.2015.09.011

Salarian, H., Ghorbani, B., Amidpour, M., & Salehi, G. (2014). Performance study on the dehumidifier of a packed bed liquid desiccant system. Scientia Iranica. Transaction B, Mechanical Engineering, 21(1), 222.

Salehi, G., Salehi, A., Ghorbani, B., Amidpour, M., Maleki, M., & Kimiaghalam, F. (2012). A Pareto Front Approach to Bi-objective of Distillation Column Operation Using Genetic Algorithm. Energy Science and Technology, 3(2), 63-73.

Sheikhi, S., Ghorbani, B., Shirmohammadi, R., & Hamedi, M.-H. (2014). Thermodynamic and Economic Optimization of a Refrigeration Cycle for Separation Units in the Petrochemical Plants Using Pinch Technology and Exergy Syntheses Analysis. Gas Processing Journal, 2(2), 39-52.  Retrieved from http://uijs.ui.ac.ir/gpj/browse.php?a_code=A-10-350-1&slc_lang=en&sid=1

Sheikhi, S., Ghorbani, B., Shirmohammadi, R., & Hamedi, M.-H. (2015). Advanced Exergy Evaluation of an Integrated Separation Process with Optimized Refrigeration System. Gas Processing Journal, 3(1), 1-10.  Retrieved from http://uijs.ui.ac.ir/gpj/browse.php?a_code=A-10-350-2&slc_lang=en&sid=1

Shirmohammadi, R., Ghorbani, B., Hamedi, M., Hamedi, M.-H., & Romeo, L. M. (2015). Optimization of mixed refrigerant systems in low temperature applications by means of group method of data handling (GMDH). Journal of Natural Gas Science and Engineering, 26, 303-312.

Wang, M., Khalilpour, R., & Abbas, A. (2014). Thermodynamic and economic optimization of LNG mixed refrigerant processes. Energy Conversion and Management, 88, 947-961.

Yang, H., Wei, Z., & Chengzhi, L. (2009). Optimal design and techno-economic analysis of a hybrid solar–wind power generation system. Applied Energy, 86(2), 163-169. doi:http://dx.doi.org/10.1016/j.apenergy.2008.03.008

Ghorbani, B., Hamedi, M., Shirmohammadi, R., Mehrpooya, M., & Hamedi, M. H. (2016). A novel multi-hybrid model for estimating optimal viscosity correlations of Iranian crude oil. Journal of Petroleum Science and Engineering, 142, 68-76