Advanced Exergoeconomic Analysis of C3MR, MFC and DMR ‎Refrigeration Cycles in an Integrated Cryogenic Process

Document Type: Original Article

Authors

1 Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran

2 Amol University of Special Modern Technologies

3 Department of Renewable Energies and Environment, Faculty of New Sciences & Technologies, University of Tehran, Tehran, Iran

Abstract

C3MR, MFC, and DMR processes in an integrated LNG-NGL-NRU structure are investigated using the conventional and advanced exergy and exergoeconomic analyses. The results of advanced exergy analysis reveal that in most of the equipment, the highest amount of irreversibility is occurred because of endogenous exergy destruction. In C3MR process, compressor C5 with 9730 kW; in MFC process, compressor C1 with 6342 kW; and in DMR process, compressor C3 with 10008 kW; have the most amount of avoidable endogenous exergy destruction in comparison with the other equipment. According to the advanced exergoeconomic analysis, the amount of endogenous part of exergy destruction cost and investment cost is higher than the exogenous part for most of the equipment, representing that interactions among the equipment is not considerable. Compressors have the highest amount of avoidable endogenous investment cost in all of the processes. Furthermore, in C3MR process, HX2 heat exchanger with 1121 $/h; in MFC process, compressor C1 with 450 $/h; and in DMR process, HX3 heat exchanger with 3955 $/h; have the most amount of avoidable endogenous exergy destruction cost. Based on total costs defined for the equipment, in C3MR process, HX2 heat exchanger with 1126 $/h should be modified. In MFC process, compressor C1 with 504.7 $/h should be considered. In DMR process, HX3 heat exchanger with 3963 $/h should be improved its performance. Finally, sensitivity analysis as well as validation have been conducted, and three different strategies are used to reduce the cost of avoidable exergy destruction of system equipment.

Keywords

Main Subjects


1. Introduction

Enhancing the energy efficiency of the liquefaction processes can be the most important issue in LNG plants (Mehdizadeh-Fard, Pourfayaz, Mehrpooya, & Kasaeian, 2018). The availability and low cost of natural gas open the possibility of transporting it to places where there is significant demand (Raj, Suman, Ghandehariun, Kumar, & Tiwari, 2016). Natural gas can be transported long distances as liquefied natural gas (LNG) (Raj et al., 2016). 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 CO2 and other pollutants than the combustion of coal and oil (Davarpanah, Mirshekari, Behbahani, & Hemati, 2017) (Mazarei, Davarpanah, Ebadati, & Mirshekari, 2018). Thus, natural gas has emerged as a preferred fuel due to its inherent environmental benignity, greater efficiency, and cost effectiveness (Mehrpooya, Jarrahian, & Pishvaie, 2006). Liquefying the natural gas to reduce its volume by a factor of approximately 600 for transportation has been identified as a practical solution when the distance between natural gas reservoirs to downstream markets is long enough (Mehrpooya, Sharifzadeh, and Rosen, 2015). 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 optimize the process configurations (Ding, Sun, Sun, & Chen, 2017).  The importance of energy saving for high energy demand industries increased in recent years because of economic factors and surging in fuel costs, in order to inspire more and more efficient use of energy (Aslani, Akbari, & Tabasi, 2018). The increasing demand and cost of energy lead to develop more efficient energy consuming methods, especially in complex energy intensive industries (Mehdizadeh Fard, Pourfayaz, Kasaeian, and Mehrpooya, 2017). Several studies have been carried out for obtaining possible improvement of various processes and systems in terms of thermodynamic laws in low temperature applications (Shirmohammadi, Ghorbani, Hamedi, Hamedi, & Romeo, 2015). Exergy analysis has been employed as a tool for the integration of very complex energy systems (Romeo, Usón, Valero, & Escosa, 2010). As an illustration for conventional exergy and exergoeconomic analyses, the comprehensive analyses of exergy and exergoeconomic are applied to an integrated process of LNG, NGL and NRU with reasonable energy consumption and high ethane recovery (Ghorbani, Hamedi, & Amidpour, 2016). Advanced exergy-based methods use the outcomes of the conventional analyses by presenting new calculation steps to disclose equipment interactions and possibility for enhancement (Petrakopoulou, Tsatsaronis, & Morosuk, 2013). Exergy destruction can be divided into endogenous and exogenous parts to increase the interactions among system equipment and offers valuable data for refining an exergy conversion system, chiefly while the concept is united with the concept of avoidable and unavoidable exergy destruction (Kelly, Tsatsaronis, & Morosuk, 2009). A detailed advanced exergetic analysis  of a novel co-generation concept that combines LNG regasification with the generation of electricity is investigated (Tsatsaronis & Morosuk, 2010).   An electricity-generating facility operating with natural gas is examined using advanced exergetic and exergoeconomic analyses (Açıkkalp, Aras, & Hepbasli, 2014). Advanced Exergoeconomic evaluation of single mixed refrigerant natural gas liquefaction processes was carried out (Mehrpooya & Ansarinasab, 2015b). Additionally, advanced exergoeconomic analysis was employed for analyzing multistage mixed refrigerant systems (Mehrpooya & Ansarinasab, 2015a). Advanced exergy analysis has been also employed for evaluating of novel flash based Helium recovery from natural gas processes. Results of endogenous and exogenous destructions demonstrates that portion of endogenous exergy destruction among equipment is higher than the exogenous portion and interactions among the equipment do not affect the inefficiencies significantly (Mehrpooya & Shafaei, 2016).

In this paper, C3MR, MFC, and DMR processes in an integrated LNG-NGL-NRU structure are investigated using the conventional and advanced exergy and exergoeconomic analyses. Suggestions to improve the system economical parameters as well as equipment performance along with sensitivity analysis are also provided.

2. Process Description

Process flow diagram of C3MR, MFC and DMR process in the integrated structure of natural gas liquids, natural gas liquefaction, and nitrogen removal unit are presented in Figures 1, 2 and 3, respectively. NGL recovery section, nitrogen rejection unit and LNG production section for these processes are basically the same; consequently, these cases have just been explained for MFC process in the following sections. Table 1 illustrates properties of feed and product streams and refrigeration system for C3MR, MFC and DMR processes. Tables 2, 3 and 4 represent thermodynamic data like temperature, pressure and flow rate of different streams for C3MR, MFC and DMR processes, respectively.


 

 

Table 1. Properties of feed, product streams and cooling system of process

Stream

N2

CH4

C2H6

C3H8

C4H10+

CO2

C2H4

C3MR process

 

 

 

 

 

 

 

Feed gas

0.0545

0.8251

0.0579

0.036

0.0240

0.002

0

LNG

0.012

0.9822

0.0054

0

0

0

0

NGL

0

0

0.4641

0.314

0.2086

0.0123

0

Nitrogen

0.9966

0.0034

0

0

0

0

0

116

0.0616

0.9324

0.0051

0

0

0.0005

0

200

0

0

0

1

0

0

0

300

0.2566

0.3341

0.2390

0.170

0

0

0

Side1

0

0

0.6407

0.242

0.0912

0.0253

0

Side2

0

0

0.6457

0.181

0.0948

0.0784

0

Side3

0.0001

0.1441

0.4408

0.172

0.0996

0.1425

0

115

0.0081

0.3370

0.1181

0.193

0.3370

0.0030

0

127

0.0175

0.9773

0.0048

0

0

0

0

108

0.0581

0.8623

0.0533

0.024

0

0.0019

0

131

0.0643

0.9355

0.0002

0

0

0

0

MFC process

 

 

 

 

 

 

 

Feed gas

0.0545

0.825

0.0579

0.0365

0.024

0.002

0

LNG

0.0088

0.984

0.0063

0.0005

0

0

0

NGL

0

0

0.4636

0.3197

0.212

0.0039

0

Nitrogen

0.9948

0.0005

0

0

0

0

0

200

0

0.136

0.3547

0.2098

0

0

0.2992

300

0.279

0.471

0.1879

0.0618

0

0

0

400

0

0

0.1787

0.6784

0.142

0

0

Side1

0

0

0.6873

0.2356

0.068

0.0087

0

Side2

0

0

0.7488

0.1421

0.069

0.0399

0

Side3

0

0.003

0.5063

0.1384

0.074

0.27

0

115

0.0614

0.930

0.0059

0.0005

0

0.0021

0

129

0.0122

0.981

0.0062

0.0005

0

0

0

118

0.0238

0.971

0.0049

0.0004

0

0

0

DMR process

 

 

 

 

 

 

 

Feed gas

0.0545

0.8251

0.0579

0.036

0.024

0.002

0

LNG

0.012

0.9823

0.0052

0.0005

0

0

0

NGL

0

0

0.4636

0.319

0.212

0.003

0

Nitrogen

0.9948

0.0005

0

0

0

0

0

200

0

0

0.2482

0.641

0.1103

0

0

300

0.1284

0.3918

0.2802

0.1996

0

0

0

Side1

0

0.0343

0.3960

0.295

0.259

0.015

0

Side2

0

0.0770

0.3398

0.284

0.286

0.012

0

Side3

0.0004

0.1737

0.3325

0.245

0.235

0.012

0

115

0.0617

0.9322

0.0050

0

0

0.0006

0

133

0.0642

0.9356

0.0002

0

0

0

0

134

0.012

0.9823

0.0052

0.0005

0

0

0

 


 

Stream

T (ºC)

P (kPa)

  Molar flow rate
  (kg mole/h)

Stream

T (ºC)

P (kPa)

Molar flow rate
      (kg mole/h)

Feed gas

37

6309

14000

200

35

1430

25000

101

4

6309

14000

201

1.63

500

25000

102

-17

6309

14000

204

1.63

500

5633

103

-41

6309

14000

206

14.34

500

5633

106

-41

6309

5201

209

-25.4

200

7470

108

-77.1

2600

7802

212

-42.3

100

3516

109

-41

6309

299.1

214

-30.3

100

3194

111

-45.6

2550

697.8

216

-31.4

100

3516

112

-92

6309

5201

217

7.8

250

3516

113

-103

2500

5201

219

15.8

500

13144.8

114

-62

6309

299.1

220

12

500

25000

115

-64.5

2500

299.1

221

63.05

1430

25000

116

-99.8

2500

12390

300

38

3800

37000

117

-114

1379

12390

302

-17

3800

37000

118

-119

1379

12390

304

-28

3800

23799.7

119

-164

1358

10297.8

308

-134

200

13200

120

-164

1358

9680

310

-60.5

200

37000

122

-120

1358

632.4

311

-169

3800

23799.7

126

-170

1358

9680

313

-144

200

23799.7

127

-118

1400

13133.8

314

105

2200

37000

128

-118

1400

13133.8

315

38

2200

37000

130

-118

1400

170.2

Side1

13.98

2500

2700

131

75

1400

170.2

Side2

-6.34

2500

2700

134

-132

1367

1199

Side3

-36.9

2500

2700

135

-118

1400

11764.4

Side1R

35

2500

2700

136

-108

1400

11764.4

Side2R

0

2500

2700

137

-72.9

2500

11764.4

Side3R

-20

2500

2700

138

-126

2500

11764.4

NGL

25.8

2500

1610

139

-165

2500

11764.4

LNG

-164

1000

11764.4

140

-164

1

11764.4

Nitrogen

20

1358

632.4

 Table 2. Thermodynamic properties of streams for C3MR configuration

 

 

 

 

 

Table 3. Streams thermodynamic properties for MFC configuration

Stream

T (ºC)

P(kPa)

Mass flow(kg/s)

Stream

T(ºC)

P (kPa)

Mass flow(kg/s)

Feed gas

37

6309

84.785

203

-85

2790

156.721

101

8

6309

84.785

204

-86.6

600

156.721

103

-27

6309

67.353

206

-27

600

156.721

104

-27

6309

17.431

207

30

1500

156.721

105

-27

6309

33.676

208

35

1500

156.721

106

-27

6309

33.676

209

77.92

2790

156.721

107

-66.3

2600

33.676

300

35

2900

244.120

108

-88

6309

33.676

301

8

2900

244.120

109

-27

6309

5.229

302

-29

2900

244.120

110

-27

6309

12.201

303

-50

2900

244.120

111

-30.4

2550

12.201

304

-173

2900

244.120

112

-50

6309

5.229

305

-177

330

244.120

113

-51.1

2500

5.229

308

35

2500

244.120

114

-102

2500

33.676

309

47.98

2900

244.120

115

-98.9

2500

58.424

400

36

1700

339.077

116

-113

1379

58.424

401

8.8

1700

339.077

117

-119

1379

58.424

402

8.8

1700

169.538

118

-119

1400

68.692

403

-27

1700

169.538

119

-118

1400

68.692

404

-27.8

310

169.538

120

-164

1358

80.341

405

1.83

310

169.538

121

-164

1358

75.521

406

37.38

670

169.538

122

-170

1358

75.521

407

8.8

1700

169.538

123

-118

1400

15.452

408

1.51

700

169.538

124

-118

1400

1.921

409

26.2

700

169.538

125

-75

1400

1.921

410

31

670

339.077

126

-118

1400

13.531

411

78.39

1700

339.077

127

-132

1400

13.531

Side1

14.50

2500

46.338

128

-131

1367

13.531

Side2

6.81

2500

45.455

129

-118

1400

53.416

Side3

-7.4

2500

49.774

130

-99

1400

53.416

Side1R

35

2500

46.338

131

7.20

6300

53.416

Side2R

0

2500

45.455

134

-164

101.3

53.416

Side3R

-20

2500

49.774

200

35

2790

156.721

NGL

27.34

2500

26.381

201

3

2790

156.721

LNG

-164

101.3

52.324

202

-31

2790

156.721

Nitrogen

-30

1358

4.820

 

Table.4. Streams thermodynamic properties for DMR configuration

Stream

T (ºC)

P (kPa)

Molar Flow (kgmole/h)

Stream

T (ºC)

P (kPa)

Molar Flow (kgmole/h)

Feed gas

37

6309

14672.508

139

-165

101.3

11627

101

3

6309

14672.508

200

36.8

1900

30000

102

-33

6309

14672.508

201

0

1900

30000

103

-33

6309

12670.271

202

0

1900

13200

104

-33

6309

2002.236

203

-1.2

800

13200

105

-33

6309

5068.108

204

26.3

800

13200

106

-33

6309

7602.163

205

0

1900

16800

107

-33

6309

600.670

206

-33

1900

16800

108

-33

6309

1401.565

207

-34.5

300

16800

109

-71

2600

7602.163

208

-8.75

300

16800

110

-50

6309

600.671

209

-8

300

16800

111

-37.1

2550

1401.565

210

38.39

800

16800

112

-52.32

2500

600.671

211

33.11

800

30000

113

-88

6309

5068.108

212

78.44

1900

30000

114

-102.7

2500

5068.108

300

35

2100

40500

116

-114.3

1379

12356.271

302

-34

2100

40500

117

-119

1379

12356.271

303

-34

2100

14221

118

-118.7

1400

13862.962

304

-128

2100

14221

119

-158

1358

11699.102

305

-129

150

14221

121

-170

1358

10997.156

309

-183.9

150

26278

122

-158

1358

701.946

310

-144

150

26278

123

-120

1358

701.946

311

-137.7

150

40500

124

-40

1358

701.946

312

-64.37

150

40500

125

-5

1358

701.946

313

-64

150

40500

127

-118

1400

13862.9

314

107.5

2100

40500

128

-118

1400

2214.57

Side1

12.97

2500

2700

129

-118

1400

275.271

Side2

-4.88

2500

2700

130

-188

1400

1939.301

Side3

-42.25

2500

2700.03

131

-75

1400

275.271

Side1R

35

2500

2700

134

-118

1400

11627.846

Side2R

0

2500

2700

135

-109

1400

11627.846

Side3R

0

2500

2700

136

-7.94

6300

11627.846

NGL

32.81

2500

2315

137

-134

6300

11627.846

LNG

-165.5

101.3

11627

138

-168

6300

11627.846

Nitrogen

30

1358

701


 

 

2.1. NGL Recovery Section

Inlet feed stream is entered into the multi-

stream heat exchangers HX1 and HX2 and is cooled up to -27. The outlet gas from the NGL recovery unit follows into the D3 separator. Line 105 is delivered into the HX3 and is cooled. The stream after passing through V6 sends into the highest tray of NGL tower. Line 106 is delivered into an expander and after dropping its pressure enters into the top side of NGL tower. Pressure of the stream is diminished to the operation pressure of the tower. The liquefied product is separated into two parts. A part of that is delivered to heat exchanger HX3 and after passing through V5 enters into the down side of the column. The outlet streams from the heat exchanger are returned to the column. Stream 115 from by passing through HX4 and expansion valve is finally prepared to send to the nitrogen removal unit (Cuellar, Wilkinson, Hudson, & Pierce, 2002).

 

2.2. Nitrogen Rejection Unit

The stream 117 at the temperature of -119 °C and pressure of 13.79 bar is entered to nitrogen rejection column. Stream 118 is exited from the bottom of column and after passing through HX3 is entered into the separator D2 in phases of liquid and gas. Line 123 is separated into the two parts. Line 126 is sent to HX4 multi-stream heat exchanger and its temperature drops and converts to liquid. Then, the cooled liquid by passing through an expansion valve V10 is delivered to the top of the nitrogen rejection tower as washing liquid. Line 124, comprising gaseous phase, is also entered into NRU tower by passing through HX3 and supply required heating load of tower.

 

2.3. LNG Production Section

Liquid gas, line 129, from the bottom of D2 is exited and ready to be sent to liquefaction exchanger after separating of ethane and nitrogen gases and reaches to the standard amount. First, it is heated by passing through the heat exchanger HX4 and converts to gaseous phase, and the gas phase enters to the compressor C3 to increase the pressure up to 63 bar. After that, the temperature and pressure by passing through the heat exchanger HX4 and HX3 reach to -164 and 63

 

bar. Finally, for converting to the final product it is passed through throttle valve V8 and its pressure is reduced up to atmosphere pressure and entered into the phase separator of D1. The final product i.e. LNG is exited from the bottom of the separator. Gas stream is also sent out from the top of the separator to the atmosphere.

 

2.4. Refrigeration Cycles

2.4.1. C3MR process

C3MR process has consisted of two refrigeration cycle, i.e. cycle 200 and 300, used for precooling and liquefaction, respectively. As can be seen in Table 1, this cycle only contains pure propane. This cycle provides the required cold utility in HX1, HX2 and HX3 heat exchangers (Ghorbani, Hamedi, & Amidpour, 2016).

 

2.4.2. MFC process

MFC (Mixed Fluid Cascade) cycle is employed to meet the requirements cooling. This system has three continuous cycles with mixed refrigerant. Cycle 400 is the hottest cycle and utilizes ethane, propane, and n-butane (Ghorbani, Hamedi, Amidpour, & Mehrpooya, 2016).

 

2.4.3. DMR process

In DMR process, cycle 200 for precooling and cycle 300 for liquefaction have been employed to meet the requirements cooling.

 

3. Methodology

3.1. Conventional Exergy Analysis

Exergy is a tool to measure distance of a system from reference state (Aghniaey & Mahmoudi, 2014). The reference state is also called the dead state, which is in fact the same as surrounding (Ghorbani, Mafi, Amidpour, Nayenian, & Salehi, 2013). The total exergy of multi component streams is the sum of its two contributions: the exergy change due to chemical exergy, and physical exergy (Khademi, Jafarkazemi, Ahmadifard, & Younesnejad, 2013; Shirmohammadi, Soltanieh, & Romeo, 2018):

   

Physical exergy is calculated as follow (Pattanayak, Sahu, & Mohanty, 2017):

 

(2)

In which the subscript “0”, refers to the ambient temperature and pressure. Irreversibility or exergy destruction can calculated by difference between the fuel exergy rate and product exergy rate and defined as follow (Abbassi & Aliehyaei, 2004):

 

(3)

 

 

 


Figure 1. Process flow diagram of the C3MR configuration

 

 

Figure 2. Process flow diagram of the MFC configuration

 

Figure 3. Process flow diagram of the DMR configuration



Exergetic efficiency of each equipment is also calculated as follow (Shariati Niasar et al., 2017):

 

 

(4)

Exergy destruction ratio is another parameter in exergy analysis can bedefined as below(Mafi, Ghorbani, Salehi, Amidpour, & Mousavi Nayenian, 2014):

 

(5)

3.2. Advanced Exergy Analysis

Exergetic efficiency and exergy destruction, calculating by exergy analysis, and are used to carry out the advanced exergy analysis of the process equipment. The irreversibility of the equipment can be determined by conventional exergy analysis; however, another tool is needed to discrete irreversibility that occurs within the equipment, or the one that depends on the other equipment. Advanced exergetic analysis divides the irreversibility of a device into two points of view i.e. origin of irreversibility and potency to remove or decrease. It also can be separated into two parts Based on the source of the exergy destruction; endogenous exergy destruction and exogenous exergy destruction. The endogenous part occurs even if other equipment operates ideally, whereas the exogenous part is the result of the other parts not working ideally. Using engineering method, we can calculate the endogenous part of the exergy destruction. In this method, for process equipment, the graph  is plotted with respect to  such as Fig 4. The y-intercept of this graph for each equipment represents the endogenous exergy destruction of that equipment.

By calculating the endogenous exergy destruction, exogenous exergy destruction can be defined as below (Mehdizadeh-Fard et al., 2018):

 

(6)

 Based on the potency to remove or decrease, the exergy destruction is separated into two other parts; avoidable exergy destruction and unavoidable exergy destruction. The unavoidable part is limited by technological restriction, while avoidable part can be reduced by improvement of the system. Table 5 presents assumptions for the advanced exergoeconomic analysis for calculating the unavoidable part (Petrakopoulou, Tsatsaronis, & Morosuk, 2014).

The term is used to calculate unavoidable exergy destruction in kth equipment, which directed from the case where only unavoidable exergy destruction occurs. Thus the unavoidable exergy is calculated by (Mehrpooya, Ansarinasab, Sharifzadeh, & Rosen, 2018):

 =

(7)

Where is stand for exergy product of each equipment. Now the avoidable part can be calculated from difference of total exergy destruction and unavoidable exergy destruction as below:

 

(8)

Where  is stand for exergy destruction of each equipment. After splitting the exergy destruction of each equipment into four categories i.e. endogenous, exogenous, avoidable, and unavoidable parts, the task left to be done is to evaluate how different categories of the exergy destruction can be combined and used to provide expressive information. To make applicable results, avoidable and unavoidable exergy will be divided into two more section, endogenous and exogenous parts. Thus total exergy destruction is divided into four parts, namely Avoidable endogenous exergy destruction ( , Avoidable exogenous exergy destruction ( , Unavoidable endogenous exergy destruction ( ), and Unavoidable exogenous exergy destruction ( ) (Açıkkalp et al., 2014).

The unavoidable endogenous exergy destruction  within kth equipment is calculated by:

 =

(9)

 

 

Likewise, the other term can be calculated as below:

 

 

(10)

 

(11)

 

(12)

3.3. Conventional Exergoeconomic Analysis

The exergoeconomic analysis uses the unit cost of exergy and cost rates of all the different streams of material and exergy to calculate exergoeconomic variables for each equipment of the system (Ashouri et al., 2017). Table 6 presents equation of purchased equipment cost of system. Exergetic variables including exergy destruction rate   exergy destruction ratio yD,K and exergetic efficiency εk are previously determined (Ghorbani, Mehrpooya, Hamedi, & Amidpour, 2017).

 

 

 

 

 

Figure.4. Illustration of engineering method (Mehrpooya & Shafaei, 2016)

 

 

 


 

 

Table.5. Presumption of advanced exergoeconomic analysis

Component

 (Operating conditions or %)

Compressor

90%

Multi stream heat exchanger

= 0.5

Air cooler

= 5

 

Definitions of cost rates of fuel  and product  result from definitions of the fuel and product for calculating the exergetic efficiency. Represents the cost rate of exergy, into which the fuel exergy  is supplied for the

Kth equipment of the system, while represents the cost rate related to the product exergy  for the same equipment(Bellos, Tzivanidis, & Antonopoulos, 2016).

Unit average exergy cost of fuel for the Kth equipment of the system represents the average cost at which the unit fuel exergy is supplied for the Kth equipment of the system (Bejan & Tsatsaronis, 1996):

 

(13)

Correspondingly, the unit cost of the product  and the cost rate associated with the exergy destruction are expressed in the following equations:

 

(14)

 

(15)

Exergy cost rate and unit average exergy cost rate as well as physical, chemical and total exergy rate for different streams of C3MR, MFC and DMR process are presented in Tables 7, 8 and 9, respectively.

The relative cost difference rk between the average cost of the unit product exergy and unit fuel exergy is attained by the following relationship:

 

(16)

The exergoeconomic factor represents the ratio of the investment cost to the sum of the investment, exergy destruction, and exergy lost cost.

 

(17)

Exergoeconomic variables like and offer and absolute criterion for the degree of importance of the Kth equipment, while rk and fk offer relative criteria to evaluate the economic performance of an equipment (Ghorbani et al., 2017).

 

3.4. Advanced Exergoeconomic Analysis

Similarly to the exergy destruction rate, the endogenous and exogenous parts of the investment cost and the cost of the exergy destruction rate are related to the internal operating conditions and the equipment interactions, respectively. Furthermore, depending on whether the costs can be avoided, it can be divided into avoidable and unavoidable parts. The endogenous and exogenous along with avoidable and unavoidable cost rates associated with the exergy destruction of the kth equipment are (Petrakopoulou, Tsatsaronis, Morosuk, & Carassai, 2012):

 

(18)

 

(19)

 

(20)

 

(21)

 

The below equations have been concluded by combination of exergy destruction costs of endogenous/exogenous with avoidable/ unavoidable (Moharamian, Soltani, Rosen, & Mahmoudi, 2018):

 

(22)

 

(23)

 

(24)

 

(25)

Investment costs of endogenous/exogenous and avoidable/unavoidable for equipment are calculated by following equations:

 

 

 

 

 

 

 

 

 


 

Table.6. Equation of the cost of the process

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 ($)

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=300D0.7396L0.7066 , 6<D

fm= Material factor

Absorber

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

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

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

C2=Cost of installed manholes, trays and nozzles

C3=Cost of Cooler

C4=Cost of Heater

CAb=C1+C2+C3+C4

CAb= Cost of Absorber ($)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(26)

 

(27)

 

(28)

 

(29)

Similarly to previous section, the following equations are derived by combination of irreversibility.

 

(30)

 

(31)

 

(32)

 

(33)

In advanced exergoeconomic analysis like the conventional exergoeconomic analysis can introduce and define parameters for comparing performance of equipment. These parameters can be calculated based on cost of the exergy destruction and avoidable endogenous of the investment cost.

 

(34)

 

(35)

 

(36)

 

4. Results and Discussion

4.1.  Results of Conventional Exergy and Exergoeconomic Analyses

In Table 10, the results of the exergy and exergoeconomic analyses are presented for the equipment of the C3MR, MFC and DMR processes, respectively. The maximum and minimum amount of the irreversibility in C3MR process is related to compressor C5 with 15024 kW and compressor C1 with 663 kW, respectively. In MFC process, compressor C1 with 12661 kW has the highest amount of irreversibility and AC1 air cooler has the smallest one. In DMR process, HX3 heat exchanger with 20251 kW and HX1 heat exchanger with 1802 kW have the highest and smallest amount of irreversibility, respectively. In C3MR, MFC and DMR processes, AC3 air cooler with 98%, AC1 air cooler with 99.6% and HX2 heat exchanger with 87% have the most amount of exergy efficiency, respectively. Results of exergoeconomic analysis show that the highest amount of exergy destruction cost is related to heat exchangers, so that in C3MR process HX5 heat exchanger with 3733 $/h; in MFC process, HX3 heat exchanger with 2943 $/h; and in DMR process, HX3 heat exchanger with 9824 $/h have the highest amount of exergy destruction cost. In addition, in C3MR process, compressor C1 with 47 $/h; in MFC process, AC1 air cooler with 20 $/h; and in DMR process, compressor C2 with 225 $/h; have the smallest amount of exergy destruction cost in comparison with other equipment. Exergoeconomic factor is considered as an important parameter in process analysis. When this parameter for a component is high, for decreasing the process cost, investment cost should be decreased. On the other hand, if exergoeconomic factor for a component is small, for decreasing the process cost, equipment efficiency should be increased.

In C3MR process, the highest value of exergoeconomic factor is related to compressor C1 with 63.7% and the smallest one is related to HX5 heat exchanger with 0.4%. In MFC process, AC1 air cooler with 90% and HX3 heat exchanger with 0.4% have the highest and smallest amount of exergoeconomic factor, respectively. In DMR process, the highest value of this factor is related to compressor C2 with 55.5% and the smallest one is related to HX3 heat exchanger with 0.2%. Generally it can be concluded that compressors and air coolers have the greatest value of exergoeconomic factor among the equipment. Therefore, investment cost should be decreased for decreasing the process cost.

 

4.2. Results of advanced exergy and exergoeconomic analyses

Table 11 illustrates the advanced exergy destruction analysis of the C3MR, MFC and DMR processes. Generally in compressors the amount of avoidable exergy destruction is greater than unavoidable part, while in air coolers and heat exchangers the amount of unavoidable exergy destruction is higher than the avoidable one. Except for compressor C4 and AC2 air cooler in C3MR process and compressor C6 and AC1 air cooler in MFC process, in the rest of the equipment the endogenous exergy destruction is greater than the exogenous part. This issue indicates that the most source of the irreversibility belongs to the equipment by them, not the interaction between the equipment. According to the avoidable endogenous exergy destruction part, in C3MR process, Compressor C5 with 9730 kW, in MFC process, compressor C1 with 6342 kW and in DMR process, compressor C3 with 10008 kW have the highest amount of avoidable endogenous exergy destruction in comparison with other equipment. Consequently, improving the efficiency of these equipment can reduce the irreversibility significantly.

Table 12 shows the analysis of the advanced exergy destruction cost rates. In all three processes, the amount of avoidable exergy destruction cost is higher than unavoidable one for compressors, while in air coolers and heat exchangers the unavoidable part of exergy destruction cost has greater amount. Except for compressor C4 and AC2 air cooler in C3MR process, and compressor C6 and AC1 air cooler in MFC process, in the rest of the equipment the endogenous exergy destruction cost is greater than the exogenous part. Based on results of avoidable endogenous exergy destruction cost rates, in C3MR process, HX2 heat exchanger with 1121 $/h, in MFC process, compressor C1 with 450 $/h and in DMR process, HX3 heat exchanger with 3955 $/h have the highest cost of avoidable endogenous exergy destruction. Therefore, improving performance of these equipment has great impact on decreasing the irreversibility costs. Also, the charts related to four categories of exergy destruction cost i.e. unavoidable endogenous, unavoidable exogenous, avoidable endogenous and avoidable exogenous, for C3MR, MFC and DMR process has been shown in Figures 5, 6 and 7, respectively.

Table 13 shows the analysis of the advanced investment cost for each component of these three processes. In all the equipment the unavoidable investment cost is greater than the avoidable part. In addition, except for compressor C4 and AC2 air cooler in C3MR process, in the rest of the equipment the endogenous investment cost is greater than the exogenous part. The results of avoidable endogenous investment cost show that in C3MR process, compressor C5 with 71$/h, in MFC process, compressor C6 with 57 $/h and in DMR process, compressor C3 with 56.7 $/h have the greatest amount of avoidable endogenous investment cost among the other equipment.

 

 

Figure 5. Dividing of exergy destruction equipment cost into avoidable/unavoidable endogenous/exogenous: C3MR process

 

 

Figure 6. Dividing of exergy destruction equipment cost into avoidable/unavoidable endogenous/exogenous: MFC process

 

 

Figure 7. Dividing of exergy destruction equipment cost into avoidable/unavoidable endogenous/exogenous: DMR process

 

 

 


 

In Table 14, the comparison between some of the parameters for the conventional and advanced exergy and exergoeconomic analyses is performed. In all of three processes, modified exergy efficiency for all equipment is higher than exergy efficiency. Due to the total cost of exergy destruction, in C3MR process, the performance of the HX2 and HX5 heat exchangers should be considered and amended, respectively, since they have the highest amount of total costs by 1126 $/h and 1062 $/h, respectively. In MFC process, the performance of the compressor C1 and HX2 heat exchanger should be modified, respectively. Because these equipment with 504.7 $/h and 435.7 $/h have the greatest amount of total costs, respectively. In DMR process, the performance of the HX3 heat exchanger and compressor C3 should be modified, respectively. Since, they have the highest amount of total costs by 3963 $/h and 767 $/h, respectively. In advanced analysis, compressor C4 and AC2 air cooler have the highest and lowest amount of exergoeconomic factor, respectively for C3MR process. In MFC process, compressor C6 and HX2 heatexchanger have the maximum and minimum amount of exergoeconomic factor, respectively. In DMR process, compressor C2 and HX3 heat exchanger have the highest and lowest amount of exergoeconomic factor, respectively.

Three strategies are available to reduce the cost of avoidable exergy destruction as shown in Table 15. When the cost of avoidable exergy destruction for equipment in the system is high, there is a good potential for improvement in the system performance. It can be improved by either improving its performance or replacing it with a high-performed component. In this way, system performance has been improved and the rate of irreversibility is reduced. This method is a strategy considered here for all equipment of these processes, except for compressor C4 and AC2 air cooler in C3MR process and compressor C6 in MFC process. In strategy B, the irreversibility of the desired component can be reduced by increasing the efficiency of the other equipment. This strategy is used when the rate of avoidable exogenous exergy destruction cost is significant compared to the endogenous portion. For example, in C3MR process, compressors C2 and C4 as well as the AC2 and AC3 air coolers; in MFC process, compressors C1 and C6, AC1 air cooler and HX1 and HX3 heat exchangers; in DMR process, compressor C3 and HX1, HX2 and HX3 heat exchangers have this feature and this strategy can be used for these components. Finally, strategy C is used when the cost of avoidable exogenous exergy destruction is significant and at least is about half of the total cost of avoidable exergy destruction. In this strategy, the system's structural optimization should reduce the irreversibility of the system. As it can be seen, strategy C can be used for the compressors C2 and C4 in C3MR process; compressors C1 and C6 as well as HX1 and HX3 heat exchangers in MFC process; and HX2 and HX3 heat exchangers in DMR process.

 

5. Sensitivity analysis

A sensitivity analysis of the system key parameters, including compressors compression ratio and pressure drop in expansion valves, has been carried out for determining the influence of thermodynamic parameters on the system performance.

Inasmuch as advanced exergoeconomic analysis has not been carried out in the integrated structure of LNG / NGL / NRU, the presented integrated structure should be validated with the similar structures. As shown in Fig. 8, the amount of specific power for the integrated processes developed in this article is less than the previous research, which indicates the high degree of process design in this paper. For example, the amount of specific power in the MFC process in this article has decreased by about 19% compared to the reference (Ghorbani, Shirmohammadi, Mehrpooya, & Mafi, 2018). Furthermore, the amount of specific power in the DMR process in this paper is about 16% lower than the reference (Vatani, Mehrpooya, & Tirandazi, 2013), which indicates the acceptable accuracy in designing and integrating the proposed structures. Moreover, according to Fig. 9, the LNG and NGL prices in the structures presented in this paper is higher than other previous studies, because in the structures presented in this paper a certain amount cost is spent for nitrogen separation. While in the same LNG / NGL structures, the inlet gas does not contain nitrogen. Following references are employed for comparison and validation presented in figures 8 and 9: (Ansarinasab & Mehrpooya, 2017a, 2017b; Ghorbani, Shirmohammadi, Mehrpooya, & Mafi, 2018; Khan, Chaniago, Getu, & Lee, 2014; Mak & Graham, 2007; Mehrpooya & Ansarinasab, 2015a, 2015b; Mehrpooya, Hossieni, & Vatani, 2014; Peters, Timmerhaus, West, Timmerhaus, & West, 1968; Qualls et al.,

 

 

 

Figure 8. Specific power value in the developed integrated structures and its comparison with other references

 

 

Figure 9. LNG price in the developed integrated structures and its comparison with other references

 

 

2006; Ransbarger, 2006; Roberts & Rowles, 2003; Vatani, Mehrpooya, & Tirandazi, 2013)

Fig 10 represents the variation of LNG price and NGL price with respect to pressure ratio of compressor C4 in C3MR process. It can be seen that the surging in pressure ratio of compressor C4 decreases the LNG price and increases the NGL price. Variation of LNG price and NGL price with respect to pressure ratio of compressor C3 and pressure drop of expansion valve V1 in the MFC process are shown in Figures 11 and 12, respectively. The LNG price decreases by surging in the both pressure ratio of compressor C3 and pressure drop of expansion valve V1, whereas NGL price increases. The same is true for the C3MR process. Figures 13 and 14 show variation of LNG price and NGL price with respect to pressure ratio of compressor C4 and pressure drop of expansion valve V2 in the DMR process, respectively. Unlike the two previous processes, higher pressure ratio in compressor and higher pressure drop in expansion valve, leads to obtaining higher LNG price and lower NGL price.

Results obtained from sensitivity analysis of the integrated structures developed in this paper which are shown in Figures 10 through 14, are function of the design of integrated process structures and all in line with previous research which presented in references (Mehrpooya & Ansarinasab, 2015a, 2015b; Ansarinasab & Mehrpooya, 2017a, 2017b).

 

 

Figure 10. Variation of LNG price and NGL price with respect to pressure ratio of compressor C4 in C3MR process

 

 

Figure 11. Variation of LNG price and NGL price with respect to pressure ratio of compressor C3 in MFC process

 

 

Figure 12. Variation of LNG price and NGL price with respect to pressure drop of expansion valve V1 in MFC process

 

 

Figure 13. Variation of LNG price and NGL price with respect to pressure ratio of compressor C4 in DMR process

 

 

 

Figure 14. Variation of LNG price and NGL price with respect to pressure drop of expansion valve V2 in DMR process

 

6. Conclusion

Comprehensive exergy and exergoeconomic analyses as well as advanced exergy and exergoeconomic analyses for the first time have been employed for malfunction diagnosis of C3MR, MFC, and DMR processes in an integrated cryogenic structure. Additionally sensitivity analysis is also conducted for the cryogenic system. Following results have been obtained from the conventional, advanced and sensitivity analyses:

  • According to the results of exergy analysis, in C3MR process, AC3 air cooler with 98%; in MFC process, AC1 air cooler with 99.6%; in DMR process, HX2 heat exchanger with 87%; have the most amount of exergetic efficiency among the other equipment.
  • According to advanced exergy analysis, just in compressors the avoidable part of exergy destruction is higher than the unavoidable part. In addition, in all of three processes, compressors have the highest amount of avoidable endogenous exergy destruction.
  • Based on the results of advanced exergoeconomic analysis, in C3MR process, HX2 heat exchanger with 1121 $/h; in MFC process, compressor C1 with 450 $/h; and in DMR process, HX3 heat exchanger with 3955 $/h; have the greatest amount of avoidable endogenous exergy destruction cost. Furthermore, in all of three processes, compressors have the highest amount of avoidable endogenous investment cost. Thus, improving the performance of these equipments will have a significant impact on cost reduction.
  • According to the total costs for the equipment, in C3MR process, HX2 heat exchanger with 1126 $/h should be considered in the first priority and modified. In MFC process, compressor C1 with 504.7 $/h should be considered and modified. In DMR process, the performance of HX3 heat exchanger with 3963 $/h should be improved.
  • Comparison the results of this research with previous studies shows that the amount of specific power in the integrated processes developed in this article has been less than previous studies which indicates the acceptable accuracy in designing and integrating of the proposed structures.
  • Results obtained from sensitivity analysis are in line with previous researches.



Table 7. Results of exergy and unit exergy cost of C3MR process

Stream

 

(kW)

 

(kW)

 

(kW)

 

($/h)

 

($/GJ)

Stream

 

(kW)

 

(kW)

 

(kW)

 

($/h)

 

($/GJ)

Feed gas

37575.23

6750765.03

6788340.26

12321.00

0.50

200

36536.71

15022156.95

15058693.65

11756783.58

216.87

101

37696.40

6750765.03

6788461.43

12597.21

0.52

201

34193.23

15022156.95

15056350.17

11756783.58

216.90

102

38282.79

6750765.03

6789047.82

13403.32

0.55

204

8254.94

3385078.62

3393333.56

2649725.54

216.91

103

39753.65

6750765.03

6790518.68

14851.16

0.61

206

6274.71

3385078.62

3391353.33

2648170.94

216.91

106

14974.12

1919650.29

1934624.41

4233.92

0.61

209

11765.43

4488906.28

4500671.71

3514784.99

216.93

108

19936.54

2879475.43

2899411.97

6532.96

0.63

212

5451.09

2112426.48

2117877.58

1654015.15

216.94

109

617.16

585570.14

586187.30

1282.87

0.61

214

185.12

1919442.75

1919627.86

1499215.09

216.94

111

1262.14

1366330.33

1367592.47

2993.36

0.61

216

228.27

2112426.48

2112654.76

1649973.55

216.94

112

18944.47

1919650.29

1938594.76

5489.22

0.79

217

2130.10

2112426.48

2114556.59

1650238.40

216.78

113

18413.98

1919650.29

1938064.27

5489.22

0.79

219

13843.96

7898516.78

7912360.74

6173835.87

216.74

114

698.64

585570.14

586268.78

1308.63

0.62

220

26502.46

15022156.95

15048659.40

11746514.62

216.82

115

626.91

585570.14

586197.05

1308.63

0.62

221

42747.42

15022156.95

15064904.36

11748307.50

216.62

116

32403.37

2711668.94

2744072.31

11634.57

1.18

300

88466.90

10320782.62

10409249.52

3076630.59

82.10

117

28658.93

2712193.19

2740852.12

11634.57

1.18

302

92830.20

10320782.62

10413612.83

3083139.44

82.24

118

37772.26

2712193.19

2749965.44

14515.93

1.47

304

62542.78

4907075.22

4969618.00

1472270.95

82.29

119

29299.26

38750.49

68049.75

608.38

2.48

308

40702.30

5418668.50

5459370.80

1618162.65

82.33

120

27541.30

36425.46

63966.76

571.87

2.48

310

22428.85

10320782.62

10343211.48

3068730.13

82.41

122

1406.10

2325.03

3731.13

33.36

2.48

311

127056.80

4907075.22

5034132.01

1493664.09

82.42

126

48286.27

36425.46

84711.73

7988.74

26.20

313

49628.01

4907075.22

4956703.22

1472052.84

82.50

127

60723.85

3498430.85

3559154.70

31819.35

2.48

314

82339.71

10320782.62

10403122.33

3074720.47

82.10

128

54623.28

3498430.85

3553054.13

31764.85

2.48

315

76271.57

10320782.62

10397054.19

3074871.75

82.15

130

1054.73

97974.12

99028.84

881.82

2.47

Side1

4889.27

1601590.50

1606479.77

6811.30

1.18

131

906.77

97974.12

98880.88

880.50

2.47

Side2

5108.06

1526907.32

1532015.38

6495.58

1.18

134

13267.79

690232.76

703500.55

8300.26

3.28

Side3

6129.49

1398715.56

1404845.05

5956.40

1.18

135

46351.61

2729202.67

2775554.29

24715.40

2.47

Side1R

4816.62

1601590.50

1606407.12

6811.00

1.18

136

26568.33

2729202.67

2755771.00

18460.53

1.86

Side2R

5149.82

1526907.32

1532057.14

6495.76

1.18

137

28450.64

2729202.67

2757653.32

18765.97

1.89

Side3R

5620.61

1398715.56

1404336.17

5954.24

1.18

138

48383.56

2729202.67

2777586.23

25068.14

2.51

NGL

2243.99

1278778.30

1281022.29

5431.40

19.18

139

58217.76

2729202.67

2787420.44

28584.12

2.85

LNG

57770.03

2729202.67

2786972.70

28223.86

20.81

140

57770.03

2729202.67

2786972.70

28584.12

2.85

Nitrogen

1117.42

2325.03

3442.45

30.78

2.48

 

Table 8. Results of exergy and unit exergy cost of MFC process

Stream

 

(kW)

 

(kW)

 

(kW)

 

($/h)

 

($/GJ)

Stream

 

(kW)

 

(kW)

 

(kW)

 

($/h)

 

($/GJ)

Feed gas

37575.23

6750765

6788340

634723

25.97

200

39355.95

7744425

7783781

4554003

162.52

101

37635.72

6750765

6788401

634864.5

25.98

203

54625.40

7744425

7799050

4570469

162.79

103

37226.86

5173680

5210907

488464.6

26.04

204

53681.77

7744425

7798107

4570469

162.81

104

1356.56

1577263

1578620

147977.9

26.04

206

23502.12

7744425

7767927

4551614

162.76

105

18613.43

2586840

2605454

244232.3

26.04

207

32866.38

7744425

7777291

4552776

162.61

106

18613.43

2586840

2605454

244232.3

26.04

208

32903.44

7744425

7777328

4552964

162.62

107

16204.49

2586840

2603045

244363.5

26.08

209

40728.29

7744425

7785153

4553911

162.49

108

23688.30

2586840

2610528

247842.2

26.37

300

83515.58

8303601

8387117

3361008

111.32

109

406.97

473179

473586

44393.36

26.04

301

83669.08

8303601

8387270

3361367

111.33

110

949.59

1104084

1105034

103584.5

26.04

302

86445.11

8303601

8390046

3365150

111.41

111

798.15

1104084

1104883

103584.5

26.04

304

190776.72

8303601

8494378

3415838

111.70

112

471.42

473179

473650.5

44439.21

26.06

305

187617.77

8303601

8491219

3415838

111.74

113

408.39

473179

473587.4

44439.21

26.07

308

80016.17

8303601

8383617

3360186

111.33

114

22948.08

2586840

2609788

247842.2

26.38

309

83823.71

8303601

8387425

3360820

111.30

115

32367.92

2716187

2748555

438130.9

44.28

400

41953.18

16621896

16663849

22713317

378.62

116

28589.56

2716187

2744777

438130.9

44.34

402

21088.32

8310948

8332036

11356920

378.62

117

38536.48

2716187

2754723

442808.2

44.65

404

22580.15

8310948

8333528

11362678

378.75

118

59526.51

3434830

3494357

573965.4

45.63

406

17363.11

8310948

8328311

11347352

378.47

119

53945.68

3434830

3488776

569995.7

45.38

407

21088.32

8310948

8332036

11356920

378.62

120

29197.43

14283.14

43480.57

7141.9

45.63

409

17663.58

8310948

8328612

11352758

378.64

121

27445.59

13426.15

40871.73

6713.385

45.63

411

51868.73

16621896

16673765

22702059

378.21

122

47791.42

13426.15

61217.57

16280.73

73.87

Side1

7498.65

2254312

2261811

360542

44.28

123

7746.42

718797.5

726543.9

118681.2

45.38

Side2

7917.92

2137319

2145237

341959.9

44.28

124

962.88

89346.53

90309.41

14752.15

45.38

Side3

8490.64

1770925

1779416

283646.6

44.28

125

827.84

89346.53

90174.37

14656.09

45.15

Side1R

7377.92

2254312

2261690

360523.2

44.28

126

6783.54

629451

636234.5

103929.1

45.38

Side2R

7981.04

2137319

2145300

341970.2

44.28

127

12115.22

629451

641566.2

106436.2

46.08

Side3R

8704.94

1770925

1779630

283680.4

44.28

128

12113.03

629451

641564

106436.2

46.08

NGL

2168.34

1271611

1273780

203046

19.89

129

46117.21

2717083

2763201

451370.3

45.38

LNG

56172.09

2677398

2733570

450322.5

20.04

130

25529.80

2717083

2742613

441689.4

44.74

Nitrogen

1137.14

856.9882

1994.13

115.9424

2.15

Table 9. Results of exergy and unit exergy cost of DMR process

 

Stream

 

(kW)

 

(kW)

 

(kW)

 

($/h)

 

($/GJ)

Stream

 

(kW)

 

(kW)

 

(kW)

 

($/h)

 

($/GJ)

Feed gas

36487.95

4771470

4807958

339076

19.59

139

56942.16

2682143

2739085

208188

21.11

101

36652.92

4771470

4808123

339501.9

19.61

200

47684.55

17248673

17296357

19269377

309.46

102

38306.43

4771470

4809777

341486.5

19.72

201

48451.94

17248673

17297125

19271358

309.48

103

34340.71

2866506

2900847

205978.1

19.72

202

21318.86

7589416

7610735

8479427

309.48

104

3537.02

1905393

1908930

135545.8

19.72

203

20978.21

7589416

7610394

8479427

309.50

105

13736.28

1146602

1160339

82391.25

19.72

204

17774.41

7589416

7607190

8475815

309.50

106

20604.43

1719904

1740508

123586.8

19.72

205

27133.09

9659257

9686390

10791931

309.48

107

1061.10

571617.8

572678.9

40663.74

19.72

206

29761.12

9659257

9689018

10795085

309.49

108

2475.91

1333775

1336251

94882.04

19.72

207

29104.97

9659257

9688362

10795085

309.51

109

18069.74

1719904

1737973

123794.4

19.79

208

12931.34

9659257

9672188

10777126

309.51

110

1177.01

571617.8

572794.8

40735.43

19.75

210

22729.22

9659257

9681986

10778119

309.23

111

2118.56

1333775

1335893

94882.04

19.73

211

40460.20

17248673

17289133

19253934

309.35

112

1028.40

571617.8

572646.2

40735.43

19.76

212

57419.75

17248673

17306092

19255733

309.07

113

17333.64

1146602

1163936

84616.35

20.19

300

81662.69

13252249

13333911

6445903

134.28

114

16783.08

1146602

1163386

84616.35

20.20

302

93442.79

13252249

13345691

6460833

134.48

116

28546.78

2703464

2732010

187308.6

19.04

304

48429.87

6784329

6832759

3310182

134.57

117

37610.08

2703464

2741074

192293

19.49

305

47492.88

6784329

6831822

3310182

134.59

118

54607.13

3168351

3222959

241845.7

20.84

309

138424.43

6473866

6612291

3211394

134.91

119

31175.82

307912.3

339088.1

25444.61

20.84

311

112719.95

13252249

13364969

6483761

134.76

121

54651.30

289437.6

344088.9

37857.01

30.56

313

18983.26

13252249

13271232

6438006

134.75

122

1870.55

18474.74

20345.29

1526.679

20.84

314

87616.42

13252249

13339865

6445041

134.21

123

1581.39

18474.74

20056.13

1367.656

18.94

Side1

3571.97

2325335

2328907

159453.1

19.02

124

1300.77

18474.74

19775.51

1194.082

16.77

Side2

3681.83

2415270

2418952

165618.3

19.02

125

1260.65

18474.74

19735.39

1145.927

16.13

Side3

5126.60

2132947

2138074

146387.2

19.02

127

50886.10

3168351

3219238

239799.3

20.69

Side1R

3561.12

2325335

2328896

159452.4

19.02

128

5180.94

481248.9

486429.9

36300.67

20.73

Side2R

3613.48

2415270

2418884

165613.5

19.02

129

643.99

59819.24

60463.23

4512.165

20.73

Side3R

4140.30

2132947

2137088

146319.7

19.02

130

4536.95

421429.7

425966.6

31788.5

20.73

NGL

2468.46

2298897

2301365

157567.3

19.02

131

553.65

59819.24

60372.89

4456.285

20.50

LNG

56941.67

2682143

2739085

204859.8

20.78

134

45548.85

2682143

2727692

203558.4

20.73

Nitrogen

1251.21

18474.74

19725.95

1121.566

2.79

                         

Table.10. Exergy and exergoeconomic analyses results for integrated structure

Component

 (kW)

 (kW)

 (kW)

 ($/Gj)

 ($/Gj)

 ($/h)

 ($/h)

 (%)

yD (%)

r (%)

f (%)

C3MR process

 

 

 

 

 

 

 

 

 

 

 

C-1

2565.13

1901.83

663.30

19.72

38.68

47.09

82.75

74.14

0.129

96.17

63.73

C-2

9571.04

7173.02

2398.02

19.72

33.56

170.24

187.20

74.94

0.467

70.19

52.37

C-4

3022.15

1882.31

1139.83

19.72

45.18

80.92

91.60

62.28

0.222

129.10

53.10

C-5

74935.39

59910.85

15024.53

19.72

27.77

1066.62

670.52

79.95

2.93

40.84

38.60

AC-2

82375.42

78806.79

3568.63

19.72

21.14

253.34

148.75

95.67

0.695

7.19

36.99

AC-3

90995.70

89297.25

1698.45

19.72

20.56

120.58

148.75

98.13

0.331

4.25

55.23

HX-2

7677.48

4385.36

3292.12

217.69

381.86

2579.98

11.79

57.12

0.641

75.41

0.46

HX-5

73128.99

60497.00

12631.99

82.10

99.31

3733.58

14.87

82.73

2.46

20.96

0.40

MFC process

 

 

 

 

 

 

 

 

 

 

 

C-1

58197.62

45536.27

12661.34

19.72

29.20

898.85

654.78

78.24

5.31

48.06

42.14

C-3

9641.83

7001.34

2640.49

19.72

36.46

187.45

234.60

72.61

1.11

84.91

55.58

C-4

12489.24

9364.26

3124.98

19.72

34.47

221.85

275.42

74.98

1.31

74.80

55.39

C-6

8759.61

6629.59

2130.02

19.72

35.32

151.21

221.05

75.68

0.894

79.10

59.38

C-7

21953.31

17245.50

4707.81

19.72

31.40

334.22

390.73

78.56

1.97

59.21

53.90

AC-1

83859.42

83575.71

283.71

19.72

20.40

20.14

185.57

99.66

0.112

3.47

90.21

HX-1

3156.48

1796.19

1360.29

367.90

649.56

1801.63

19.65

56.90

0.571

76.56

1.08

HX-2

11569.22

9593.59

1975.63

387.16

467.63

2753.62

25.58

82.92

0.829

20.78

0.920

HX-3

28695.11

23676.67

5018.44

162.94

197.59

2943.66

10.02

82.51

2.11

21.27

0.339

DMR process

 

 

 

 

 

 

 

 

 

 

 

C-1

21586.9

16959.54

4627.36

19.72

29.47

328.51

266.72

78.56

1.48

49.44

44.81

C-2

13048.16

9881.116

3167.05

19.72

33.93

224.84

280.73

75.73

1.01

72.07

55.53

C-3

86340.62

68633.15

17707.47

19.72

28.47

1257.09

905.96

79.49

5.66

44.39

41.88

HX-1

3214.644

1412.231

1802.41

312.20

717.15

2025.76

33.04

43.93

0.576

129.71

1.60

HX-2

17228.28

15052.24

2176.04

290.73

333.40

2277.47

34.85

87.37

0.696

14.68

1.51

HX-3

93339.94

73088.99

20250.95

134.75

172.17

9823.81

20.64

78.30

6.48

27.77

0.210

 

 

 

 

Table 11.Values of advanced exergy destruction for integrated structure

Component

 (kW)

 (kW)

 (kW)

 (kW)

 (kW)

 (kW)

 (kW)

 (kW)

 (kW)

 

C3MR process

 

 

 

 

 

 

 

 

 

 

C-1

663.31

223.47

439.84

630.06

33.25

214.33

9.14

415.73

24.11

 

C-2

2398.02

806.88

1591.14

1334.30

1063.72

512.33

294.55

821.97

769.17

 

C-4

1139.83

383.26

756.56

306.15

833.68

142.85

240.42

163.30

593.26

 

C-5

15024.53

5165.91

9858.63

14879.00

145.53

5149.09

16.82

9729.91

128.72

 

AC-2

3568.63

3055.64

512.99

215.73

3352.90

175.74

2879.90

39.99

473.00

 

AC-3

1698.448

1387.27

311.18

1120.20

578.25

917.44

469.83

202.76

108.41

 

HX-2

3292.121

1859.71

1432.41

3289.90

2.22

1858.60

1.12

1431.30

1.10

 

HX-5

12631.99

9046.42

3585.56

12618.00

13.99

9036.37

10.05

3581.63

3.93

 

MFC process

 

 

 

 

 

 

 

 

 

 

C-1

12661.34

4490.98

8170.36

9679.80

2981.54

3337.84

1153.14

6341.96

1828.40

 

C-3

2640.49

860.38

1780.11

2592.90

47.59

846.89

13.49

1746.01

34.10

 

C-4

3124.98

1054.50

2070.47

2494.30

630.68

846.28

208.23

1648.02

422.45

 

C-6

2130.02

701.89

1428.14

677.07

1452.95

283.29

418.59

393.78

1034.36

 

C-7

4707.81

1616.67

3091.15

3995.70

712.11

1381.88

234.78

2613.82

477.33

 

AC-1

283.71

123.43

160.28

120.86

162.85

51.67

71.53

69.19

91.32

 

HX-1

1360.29

1111.38

248.91

728.80

631.49

595.09

516.29

133.71

115.20

 

HX-2

1975.63

1629.76

345.87

1882.50

93.13

1570.48

59.27

312.02

33.86

 

HX-3

5018.44

4620.73

397.72

3233.60

1784.84

3016.11

1604.61

217.49

180.23

 

DMR process

 

 

 

 

 

 

 

 

 

 

C-1

4627.36

1602.11

3025.26

4361.50

265.86

1528.78

73.32

2832.72

192.54

 

C-2

3167.05

1073.88

2093.17

2767.30

399.75

971.14

102.74

1796.16

297.00

 

C-3

17707.47

6345.26

11362.21

15740.00

1967.47

5731.55

613.70

10008.45

1353.76

 

HX-1

1802.41

1523.83

278.58

1139.30

663.11

917.55

606.28

221.75

56.84

 

HX-2

2176.04

1642.34

533.70

1276.40

899.64

982.73

659.61

293.67

240.03

 

HX-3

20250.95

11260.82

8990.13

17627.00

2623.95

9474.27

1786.55

8152.73

837.40

 

 


 

Table 12.Values of advanced exergy destruction cost for integrated structure

Component

 ($/h)

 ($/h)

 ($/h)

 ($/h)

 ($/h)

 ($/h)

 ($/h)

 ($/h)

 ($/h)

C3MR process

 

 

 

 

 

 

 

 

 

C-1

47.09

15.86

31.23

44.73

2.36

15.22

0.65

29.51

1.71

C-2

170.24

57.28

112.96

94.72

75.52

36.37

20.91

58.35

54.60

C-4

80.92

27.21

53.71

21.73

59.18

10.14

17.07

11.59

42.12

C-5

1066.62

366.74

699.88

1056.29

10.33

365.54

1.19

690.75

9.14

AC-2

253.34

216.93

36.42

15.32

238.03

12.48

204.45

2.84

33.58

AC-3

120.58

98.49

22.09

79.53

41.05

65.13

33.35

14.39

7.70

HX-2

2579.98

1457.42

1122.55

2578.24

1.74

1456.55

0.87

1121.69

0.87

HX-5

3733.58

2673.81

1059.77

3729.44

4.13

2670.84

2.97

1058.61

1.16

MFC process

 

 

 

 

 

 

 

 

 

C-1

898.85

318.82

580.03

687.19

211.67

236.96

81.86

450.23

129.80

C-3

187.45

61.08

126.37

184.08

3.38

60.12

0.958

123.95

2.42

C-4

221.85

74.86

146.99

177.07

44.77

60.08

14.78

117.00

29.99

C-6

151.21

49.83

101.39

48.07

103.15

20.11

29.72

27.96

73.43

C-7

334.22

114.77

219.45

283.66

50.55

98.10

16.67

185.56

33.89

AC-1

20.14

8.76

11.38

8.58

11.56

3.67

5.08

4.91

6.48

HX-1

1801.63

1471.97

329.67

965.26

836.37

788.17

683.80

177.09

152.58

HX-2

2753.62

2271.54

482.08

2623.81

129.80

2188.93

82.61

434.88

47.19

HX-3

2943.66

2710.37

233.29

1896.73

1046.93

1769.16

941.21

127.57

105.72

DMR process

 

 

 

 

 

 

 

 

 

C-1

328.51

113.74

214.77

309.63

18.87

108.53

5.21

201.10

13.67

C-2

224.84

76.24

148.60

196.46

28.38

68.94

7.29

127.51

21.08

C-3

1257.09

450.46

806.63

1117.41

139.67

406.89

43.57

710.52

96.11

HX-1

2025.76

1712.66

313.10

1280.48

745.28

1031.25

681.40

249.22

63.88

HX-2

2277.47

1718.89

558.58

1335.89

941.58

1028.54

690.35

307.36

251.22

HX-3

9823.81

5462.66

4361.15

8550.92

1272.89

4596.00

866.66

3954.92

406.23

 


 

Table 13. Advanced investment costs rates of process

 

Component

 ($/h)

 ($/h)

 ($/h)

 ($/h)

 ($/h)

 ($/h)

 ($/h)

 ($/h)

 ($/h)

C3MR process

 

 

 

 

 

 

 

 

 

C-1

82.75

74.13

8.62

79.37

3.38

71.10

3.03

8.27

0.35

C-2

187.20

167.19

20.01

118.86

68.34

106.16

61.03

12.70

7.30

C-4

91.60

81.80

9.80

34.14

57.46

30.49

51.31

3.65

6.15

C-5

670.52

599.01

71.52

668.34

2.18

597.06

1.95

71.28

0.23

AC-2

148.75

148.74

0.0076

8.55

140.20

8.55

140.19

0.00044

0.0072

AC-3

148.75

148.746

0.0048

98.37

50.38

98.37

50.38

0.003188

0.0016

HX-2

11.79

7.17

4.62

11.79

0.0071

7.17

0.0043

4.62

0.0028

HX-5

14.87

11.01

3.86

14.85

0.016

11.00

0.012

3.85

0.0043

MFC process

 

 

 

 

 

 

 

 

 

C-1

715.14

659.10

56.04

695.58

19.56

641.07

18.03

54.51

1.53

C-3

234.60

194.12

40.47

230.40

4.20

190.65

3.48

39.75

0.725

C-4

275.42

246.25

29.18

244.86

30.56

218.92

27.32

25.94

3.24

C-6

221.05

160.44

60.61

207.95

13.09

150.93

9.50

57.02

3.59

C-7

390.73

339.11

51.62

364.11

26.63

316.01

23.11

48.10

3.52

AC-1

185.57

185.21

0.355

139.10

46.47

138.83

46.38

0.266

0.0889

HX-1

19.65

18.48

1.17

10.45

9.21

9.82

8.66

0.623

0.549

HX-2

25.58

24.67

0.914

24.43

1.15

23.56

1.11

0.873

0.0412

HX-3

10.02

8.12

1.90

6.24

3.78

5.05

3.07

1.19

0.719

DMR process

 

 

 

 

 

 

 

 

 

C-1

266.72

245.79

20.93

254.51

12.21

234.54

11.25

19.97

0.958

C-2

280.73

252.61

28.13

253.87

26.86

228.44

24.17

25.44

2.69

C-3

905.96

843.17

62.78

818.33

87.62

761.62

81.55

56.71

6.07

HX-1

33.04

26.48

6.56

19.90

13.15

15.95

10.54

3.95

2.61

HX-2

34.85

27.33

7.52

20.85

14.00

16.35

10.98

4.50

3.02

HX-3

20.64

11.21

9.42

17.36

3.27

9.44

1.78

7.93

1.49

 


 

Table 14.Results Comparison for conventional and advanced exergy and exergoeconomic analyses

Component

Conventional

 

Advanced

 (%)

f (%)

 ($/h)

 

 (%)

 (%)

 ($/h)

C3MR process

 

 

 

 

 

 

 

C-1

74.14

63.73

129.84

 

82.06

21.88

37.78

C-2

74.94

52.37

357.44

 

89.72

17.88

71.06

C-4

62.28

53.10

172.52

 

92.02

23.95

15.25

C-5

79.95

38.60

1737.15

 

86.03

9.35

762.03

AC-2

95.67

36.99

402.09

 

99.95

0.0155

2.84

AC-3

98.13

55.23

269.33

 

99.77

0.0221

14.40

HX-2

57.12

0.46

2591.77

 

75.39

0.410

1126.31

HX-5

82.73

0.40

3748.45

 

94.41

0.362

1062.46

MFC process

 

 

 

 

 

 

 

C-1

78.24

44.31

1613.99

 

87.78

10.80

504.73

C-3

72.61

55.59

422.05

 

80.04

24.28

163.70

C-4

74.98

55.39

497.27

 

85.03

18.15

142.94

C-6

75.68

59.38

372.26

 

94.39

67.10

84.98

C-7

78.56

53.90

724.95

 

86.84

20.59

233.66

AC-1

99.66

90.21

205.71

 

99.92

5.14

5.18

HX-1

56.90

1.08

1821.28

 

93.07

0.351

177.71

HX-2

82.92

0.920

2779.20

 

96.85

0.200

435.76

HX-3

82.51

0.339

2953.68

 

99.09

0.920

128.76

DMR process

 

 

 

 

 

 

 

C-1

78.56

44.81

595.22

 

85.69

9.03

221.07

C-2

75.73

55.53

505.57

 

84.62

16.63

152.95

C-3

79.49

41.88

2163.04

 

87.27

7.39

767.23

HX-1

43.93

1.60

2058.80

 

86.43

1.56

253.17

HX-2

87.37

1.51

2312.32

 

98.09

1.44

311.86

HX-3

78.30

0.210

9844.45

 

89.96

0.200

3962.85


 

Table.15. Diverse strategies for dropping exergy destruction avoidable cost

Component

Cost of exergy destruction categories ($/h)

The part should be focused

Possible strategies to reduce cost of exergy destruction

       

Strategy Aa

Strategy Bb

Strategy Cc

C3MR process

 

 

 

 

 

 

 

 

C-1

47.09

31.23

29.51

1.71

EN.

*

 

 

C-2

170.24

112.96

58.35

54.60

EN./EX.

*

*

*

C-4

80.92

53.71

11.59

42.12

EN./EX.

 

*

*

C-5

1066.62

699.88

690.75

9.14

EN.

*

 

 

AC-2

253.34

36.42

2.84

33.58

EN./EX.

 

*

*

AC-3

120.58

22.09

14.39

7.70

EN./EX.

*

*

 

HX-2

2579.98

1122.55

1121.69

0.87

EN.

*

 

 

HX-5

3733.58

1059.77

1058.61

1.16

EN.

*

 

 

MFC process

 

 

 

 

 

 

 

 

C-1

898.85

687.19

450.23

129.80

EN./EX.

*

*

*

C-3

187.45

184.08

123.95

2.42

EN.

*

 

 

C-4

221.85

177.07

117.00

29.99

EN.

*

 

 

C-6

151.21

48.07

27.96

73.43

EN./EX.

 

*

*

C-7

334.22

283.66

185.56

33.89

EN.

*

 

 

AC-1

20.14

11.38

4.91

6.48

EN./EX.

*

*

 

HX-1

1801.63

329.67

177.09

152.58

EN./EX.

*

*

*

HX-2

2753.62

482.08

434.88

47.19

EN.

*

 

 

HX-3

2943.66

233.29

127.57

105.72

EN./EX.

*

*

*

DMR process

 

 

 

 

 

 

 

 

C-1

328.51

214.77

201.10

13.67

EN.

*

 

 

C-2

224.84

148.60

127.51

21.08

EN.

*

 

 

C-3

1257.09

806.63

710.52

96.11

EN./EX.

*

*

 

HX-1

2025.76

313.10

249.22

63.88

EN./EX.

*

*

 

HX-2

2277.47

558.58

307.36

251.22

EN./EX.

*

*

*

HX-3

9823.81

4361.15

3954.92

406.23

EN./EX.

*

*

*

a Strategy A: Improving the efficiency of the kth equipment or replacing the equipment with efficient devices.

b Strategy B: Improving the efficiency of the remaining equipment.

c Strategy C: Structural optimization of the overall system


 

 

Nomenclature

e           Specific flow exergy (kJ/kg mole)

Ex        Exergy (kW)

          Exergy rate (kW)

ṁ         Mass flow rate (kg mole/s)

h          Enthalpy (kJ/ kg mole)

P          Pressure (kPa)

T          Temperature (°C)

W         Work (kW)

s           Entropy (kJ/ kg mole.°C)

ε           Efficiency (%)

C ̇         Cost rate ($/h)

c           Unit average exergy cost ($/Gj)

r           Relative cost difference (%)

f           Exergoeconomic factor (%)

Z ̇         Investment cost ($)

Subscripts

C          Cold

H         Hot

Tot        Total

D          Destruction

p          Product

F          Fuel

k          kth equipment

Superscript

ph        Physical

ch         Chemical

AV        Avoidable

UN       Unavoidable

EN       Endogenous

EX        Exogenous

Abbreviations

APCI    Air Products and Chemicals, Inc.

C3MR   Propane precooling

DMR    Dual mixed refrigerant

LNG     Liquefied natural gas

MFC     Mixed fluid cascade

NGL     Natural gas liquids

NG       Natural gas

NRU    Nitrogen Rejection Unit

NLP     Non-Linear Programming

PSO     Particle Swarm Optimization

SMR    Single Mixed Refrigerant

Names Used for Blocks in Plants

Ci         Compressor

Exi       Turbo expander

Ti         Tower

HXi      Multi stream heat exchanger

Di         Flash drum

Vi         Valve

ACi       Air cooler

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