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

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

 Table 2. Thermodynamic properties of streams for C3MR configuration

Table 3. Streams thermodynamic properties for MFC configuration

Table.4. Streams thermodynamic properties for DMR configuration

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):

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):

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):

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

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):

 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):

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:

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:

Likewise, the other term can be calculated as below:

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)

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):

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

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 r_k between the average cost of the unit product exergy and unit fuel exergy is attained by the following relationship:

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

Exergoeconomic variables like and offer and absolute criterion for the degree of importance of the Kth equipment, while r_k and f_k 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):

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

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

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

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.

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 13. Advanced investment costs rates of process