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
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 nonlinear 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. Precooling 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 NGLLNG 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, (multicomponent 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 NGLLNGNRU 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 multistream 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 multistream 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. Deethanizertop gas is channelled to HX4 through V5 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 HX3 from the bottom. Stream 128 is channeled to D2 flash drum and the gas product of this separator returns to the HX4. Line 123 is branched into two: branch one, (88%), stream 126, enters HX4 multistream 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 supercooled by HX4 supercooling 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, precooling and liquefaction systems are carried out by applying an absorption refrigeration cycle for precooling and two refrigeration cycle (multicomponent refrigerant).
Figure 2. Schematic of block flow diagram of the first stage for typical NGLLNGNRU 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, LópezGonzález, & LópezOchoa, 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 y_{k} 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 yearbyyear basis. Finally, the nonuniform 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, TRR_{j} is the total revenue requirement in j^{th} year of system operation, BL is economic life cycle of the system (yr) and i_{eff} is the average annual rate of effective devaluation. Capital recovery factor (CRF) is calculated as follows:
(4) 
TRR_{j} 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, FC_{0} 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}
C_{w} = unit cost of fuel (0.071 $ kWh^{1})
= power (kW)
Cost of electricity during the j^{th} year is computed as follows:
(7) 
The constant escalation levelization factor (CELF) for the fuel is obtained through:
(8) 
where:
(9) 
r_{FC} is the average annual escalation rate of fuel cost. The levelized annual operating and maintenance costs OMC_{L} are calculated as follows:
(10) 
where,

(11) 
r_{OMC} is the annual escalation rate for the operating and maintenance costs. The levelized carrying charges CC_{L} 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 PEC_{k} are the total annual hours of plant operation and the purchasedequipment cost of the k^{th} 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 (i_{eff}) 
10% 
Average nominal escalation rate for the operating and maintenance cost (r_{OMC}) 
5% 
Average nominal escalation rate for fuel (r_{FC}) 
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 
C_{C}=7.90(HP)^{0.62} C_{C}= Cost of Compressor (k$)

Expander 
C_{Ex} = 0.378(HP)^{0.81} C_{Ex} = Cost of Expander (k$) 
Heat exchanger 
C_{E}=a(V)^{b}+c C_{E}= Cost of Heat exchanger ($) 
Pump 
C_{P}=f_{M}f_{T}C_{b} C_{P}= Cost of Pump ($) C_{b}=1.39exp[8.8330.6019(lnQ(H)^{0.5})+0.0519(lnQ(H)^{0.5})^{2}], Q in gpm, H in ft head f_{M}= Material Factor f_{T}=exp[b_{1}+b_{2}(lnQ(H)^{0.5})+b_{3}(lnQ(H)^{0.5})^{2}] b_{1}= 5.1029, b_{2}= 1.2217, b_{3}= 0.0771 
Air cooler 
C_{AC}=1.218f_{m}f_{P}exp[a+blnQ+c(lnQ)^{2}], Q in KSCFM C_{AC}= Cost of Air cooler (k$) f_{m}=Material Factor f_{P}=Pressure Factor a=0.4692, b=0.1203, c=0.0931 
Drum 
C_{D}=f_{m}C_{b}+C_{a} C_{D}= Cost of Drum ($) C_{b}=1.218exp[9.10.2889(lnW)+0.04576(lnW)^{2}], 5000<W C_{a}=300D^{0.7396 }L^{0.7066}, 6<D<10, 12<L f_{m}= Material Factor

Cooler 
C_{C }=1.218k(1+fd+fp)Q^{0.86 } , 20<QC= Cost of cooler ($) f_{m}=Design Type f_{P}=Design Pressure (psi) a=0.4692, b=0.1203, c=0.0931 
Absorber

C_{b}=1.128exp(6.629+0.1826 (logW)+0.02297*(logW) ^{2}) C_{p1}=300 (D^{0.7395}) (L^{0.7068}) C_{1}=1.218 [(1.7C_{b}+23.9V1+Cp1) ] C_{2}=Cost of installed manholes, trays and nozzles C_{3}= Cost of Cooler C_{4}= Cost of Heater C_{Ab} = C_{1}+C_{2}+C_{3}+C_{4} C_{Ab}= Cost of Drum ($) 
Table 5. Purchased equipment and investment costs for configuration process components
Equipment 
PEC (×10^{3} $) 
Z^{CI} ($/hr) 
Z^{OM} ($/hr) 
Z ($/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 

HX3 

HX4 

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 

HX3 

HX4 

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 k^{th} 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 k^{th} 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 LNGNGLNRU
Figure 4. Breakdown of compressors, expander and pump exergy losses in the integrated structure of LNGNGLNRU
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 LNGNGLNRU
Figure 6. Breakdown of towers’ exergy losses in the integrated structure of LNGNGLNRU
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. HX2 and HX3 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 
c_{w} 
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) 
i_{eff} 
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 (%) 
r_{FC} 
annual escalation rate for the fuel cost 
TCR 
Return on investment 
r_{OM} 
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 k^{th} component including Capital investment and operatingmaintenance cost 

Rate of capital investment of k^{th} component 

Rate of operating and maintenance cost of k^{th} 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 
k^{th} 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 
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