A comprehensive exergy-based evaluation on cascade absorption-compression refrigeration system for low temperature applications - exergy, exergoeconomic, and exergoenvironmental assessments

Journal Pre-proof A comprehensive exergy-based evaluation on cascade absorption-compression refrigeration system for low temperature applications - exergy, exergoeconomic, and exergoenvironmental assessments

Seyed Ali Mousavi, Mehdi Mehrpooya PII:

S0959-6526(19)33875-2

DOI:

https://doi.org/10.1016/j.jclepro.2019.119005

Reference:

JCLP 119005

To appear in:

Journal of Cleaner Production

Received Date:

05 August 2019

Accepted Date:

21 October 2019

Please cite this article as: Seyed Ali Mousavi, Mehdi Mehrpooya, A comprehensive exergy-based evaluation on cascade absorption-compression refrigeration system for low temperature applications - exergy, exergoeconomic, and exergoenvironmental assessments, Journal of Cleaner Production (2019), https://doi.org/10.1016/j.jclepro.2019.119005

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A comprehensive exergy-based evaluation on cascade absorption-compression refrigeration system for low temperature applications - exergy, exergoeconomic, and exergoenvironmental assessments Seyed Ali Mousavi, Mehdi Mehrpooya Department of Renewable Energies and Environment, Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran

Abstract The main target of present work is to assess a new cascade absorption-compression refrigeration system from the exergy, exergoeconomic, and exergoenvironmental standpoints. The combined system is simulated by Aspen HYSYS V10, and Matlab software. This hybrid system is able to supply a cooling duty of 60.65 kW with a coefficient of performance of 0.226. Also, the evaporation temperature of this system is calculated to be -54.62 °C. In order to analysis the energy quality and performance of this process, an exergy assessment is conducted. Based on the gained outcomes of exergy evaluation, the total exergy efficiency of process is computed to be 69%. As well as, the overall exergy destruction rate is obtained by 83.4 kW, and the greatest value of irreversibility is found to be in the rectifier (16.05 kW). In continue, to evaluate the process economically, the exergoeconomic evaluation is carried out. It was found that the rectifier has the largest amount of investment cost rate (2.817 $/h). As well as, the highest values of relative cost difference (r) and exergoeconomic factor (f) are related to the compressor and gas heat exchanger, respectively. The environmental impacts of hybrid system are determined by combining life cycle assessment and exergy evaluation (exergoenvironmental method). According to the achieved outcomes, it can be noticed that rectifier and low - pressure pump have the largest and least values of

*Corresponding author. Department of Renewable Energies and Environment, Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran. Tel.: +98 21 61118564; fax: +98 21 88617087. E-mail addresses: [email protected] (M. Mehrpooya).

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environmental impact. At the final stage of this research, to evaluate the interaction between environmental, technical, and economical aspects of process, the 3D parametric assessment is conducted on devices of the auto - cascade refrigeration system. Keywords Cascade

utilization, Low-temperature

applications,

Hybrid

refrigeration,

Exergy

analysis,

Exergoeconomic analysis, Exergoenvironmental analysis. Nomenclature A Area (m2) Environmental impact rate associated with 𝐵 exergy (mPts/h) b Unit environmental impact (mPts/GJ) Exergy cost rate ($/h) 𝐶 c Unit exergy cost ($/GJ) e Specific exergy (kJ/kgmol) Rate of exergy (kW) Ex fb Exergoenvironmental factor (%) fc Exergoeconomic factor (%) G Gibbs free energy (kJ/kgmol) h Specific enthalpy (kJ/kg) Heat transfer rate (kW) 𝑄 ṁ Mass flow rate (KJ/Kg) P Pressure (bar)

Subscripts 0

Dead state

ph

Physical

ch mix k s tot D F P in out ex Abbreviations

Chemical Mixture Component k Isentropic Total Destroyed Fuel Product inlet outlet exergy

PEC

Purchased equipment cost ($)

LMTD

rb

Relative enfvironmental impacts difference (%)

O&M

rc

Relative cost difference (%)

HP

s

Specific entropy (kJ/kg.K)

LP

logarithmic mean temperature difference Operating and Maintenance High pressure Low pressure

S

Entropy (kJ/K)

ABS

Absorber

T

Temperature (K)

ARS

𝑊

Power (kW)

CHEX

absorption refrigeration subsystem cascade heat exchanger

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V

Volume (m3)

COP

x

Mass fraction of ammonia (-)

CON

𝑌

Component-related environmental impacts (mPts/h)

GHEX

yd 𝑍 Greek symbols 𝜏 ∆ Σ

Exergy destruction ratio (-) Capital investment cost flow rate ($/h) Annual operating hours (h) Delta Summation

TUR PUM REC VAL EVA MIX

ε

Exergy efficiency (%)

HRVG

γ

maintenance factor (-)

REB SHEX VHEX

coefficient of performance (–) Condenser gas heat exchanger Turbine Pump Rectifier Valve evaporator Mixer heat recovery vapor generator Reboiler solution heat exchanger vapor heat exchanger

1. Introduction Utilization of carbon dioxide (CO2) as refrigerant in the refrigeration systems, due to its advantages such as no ozone depletion, inexpensive, low global warming, and abundant in nature has been noticed by many researchers (Bingming et al., 2009; Mosaffa et al., 2016). Because of the high pressure difference (ΔP) between condenser and evaporator, applying CO2 gas in single stage refrigeration systems is not economically. By increasing the pressure deference, the coefficient of performance (COP) of the system reduces (Dincer and Kanoglu, 2010). In order to solve this problem, cascade refrigeration systems can be utilized (Kilicarslan et al., 2010). A cascade refrigeration system consists of two refrigeration cycles, which are combined together by an interface heat exchanger (Dakkama et al., 2015). This heat exchanger plays the role of evaporator for high temperature cycle and condenser for low temperature cycle. As well as, in order to achieve the low temperature applications, compression refrigeration cycle and absorption refrigeration cycle (ARC) stand – alone, cannot be used. Namely, according to the previous

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investigations, ARC systems is not able to supply an evaporation temperature lower than -20 °C (Kang et al., 2000). Employing two-stage compression refrigeration systems is the common method for supplying the low temperatures, but in this method a high amount of electricity is consumed, and as a result, the COP of system reduces (Dopazo and Fernández-Seara, 2011). In recent years, to achieve the low temperature applications with high COP, the ARC combined with compression refrigeration cycles have been investigated in several investigations. The optimization is conducted to maximize the COP of CO2/NH3 cascade refrigeration system(Lee et al., 2006). It was found, by increasing the evaporator temperature, COP of the system increases. The performance of a CO2/NH3 cascade cooling system is assessed (Dopazo et al., 2009). The outcomes demonstrate by increasing the evaporator temperature (55 to -30°C) and condenser temperature (25 to 50°C), the COP of system increases by 70% and 45%, respectively. In other research, a CO2/NH3 cascade system for freezing application is proposed and analyzed (Dopazo and Fernández-Seara, 2011). The results show this system can supply a 9 kW cooling duty at -50°C evaporation temperature. Also, it was found that by using an economizer, the COP of system increase by 20%. The energy analysis is carried out for a CO2/NH3 cascade system (FernandezSeara et al., 2006). The COP, heat duty of the absorption generator, and consumed electricity of compressor are calculated by 0.253, 2.933 kW, and 0.384 kW, respectively. A new absorptioncompression cascade for low-temperature applications (-170°C) is introduced and assessed (Xu et al., 2015). The outcomes illustrate this system is not a feasible system, but can be developed in future. In order to apply a comprehensive investigation to performance of the thermodynamic systems, such as power plants, desalination systems, refrigeration cycles, and heating generation systems, the first law of thermodynamic (energy analysis) cannot be a proper method (Kasaeian et al., 2019; Kotas, 2013). So, the second law of thermodynamic (exergy assessment) is employed. As well as, in order to assess the technical, economical, and environmental aspects of a process simultaneously, the combination of exergy evaluation with economic analysis (exergoeconomic analysis) and environmental analysis (exergoenvironmental analysis) are utilized (Boyano et al., 2011). Recently, the exergoeconomic and

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exergoenvironmental analyses methods have been employed for the high number of systems, which some of them are presented following: The exergoeconomic assessment method is utilized to evaluate a double effect ARC (Farshi et al., 2013). The results indicate the overall cost rate of system is about 627.9 $/year. As well as, the exergoeconomic factor of all of the equipment is more than 61%, which illustrates in this process, the capital investment cost is dominant. The exergy and parametric analyses are conducted for a combined system includes ARC, power generation and desalination system (Ghorbani et al., 2019). According to the obtained outcomes, the overall exergy efficiency of this hybrid system is gained by 88.95%. Amongst the components of the hybrid system, Molten carbonate fuel cell (MCFC) (91062 kW) and one of the flash drums (0.0148) have the biggest and least irreversibility rate, respectively. A solar driven combined storage ARC, which can produce 5 kW of cooling load is assessed by exergoeconomic assessment (Siddiqui et al., 2014). The outcomes display the total exergy destruction rate and exergy destruction cost rate of system are found to be 2.54 kW and 1626 $/year, respectively. Furthermore, the largest and lowest exergoeconomic factor belong to the refrigerant heat exchanger (95.6%) and solution heat exchanger (15.95%), respectively. Asadnia et al. (Aasadnia et al., 2019) performed a exergy based evaluation for a novel combined Claude cycle. The results illustrate the overall exergy efficiency of the system is about 31.6%. As well as, it was found the greatest overall cost rate and overall environmental impact rate are related to the HX-203 (1176.02 $/h) and HX-201 (2142.13 Pts/h) heat exchangers, respectively. Khani et al. (Khani et al., 2016) applied the exergoeconomic evaluation to a hybrid system includes solid oxide fuel cell (SOFC) and ARC. This system can provide a 512.9 kW of electricity and 381.4 of cooling load. The outcomes exhibit the exergoeconomic factor and total cots rate of this system are 27.3% and 10.63 $/h, respectively. As well as, it was observed that the biggest and smallest values of relative cost difference associated with SOFC (97.71%) and rectifier (0.002%), respectively. In (Ansarinasab et al., 2019) the interaction between irreversibility rate, environmental impact rate, and

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cost rate is investigated for a hydrogen liquefaction plant. The outcomes illustrate that compressor and turbine need an optimization in order to get an optimum point for isentropic efficiency and pressure ratio, respectively. Also, the largest and least exergy destruction are found to be in the TE -5 turbine (2835 kW) and P -1 pump (2.5 kW), respectively. An integrated solar hybrid system, which can produce 400 MW of electricity is investigated by exergoeconomic and exergoenvironmental analyses methods (Cavalcanti and Reviews, 2017). The results depict that the highest exergoeconomic factor belongs to the super heater (53.85%). Hence, the non-related exergy cost is dominant in this device. Also. The exergoenvironmental factor is very low (less than 2%) in all of the equipment, which indicates the related – exergy environment impact is dominant for this system In a comprehensive research, the exergoeconomic assessment is carried out for two kinds of CO2/NH3 cascade refrigeration (system 1 & 2) with different flash tanks (Mosaffa et al., 2016) . the obtained results indicate the lowest overall cost rate occurred in evaporation temperatures - 41.5 °C (system 1) and – 40 °C (system 2). Furthermore, the maximum and minimum exergoeconomic factor belong to the ammonia flash tank (100%) and CO2 flash tank (1.73%), respectively.

This paper presents a comprehensive exergy-based evaluation on cascade

absorption-compression refrigeration system for low temperature applications. the exergy based evaluation is carried out component by component. In continue, by considering the control volume around each equipment, the exergy, cost and environmental balances are written. In order to calculate the exergy efficiency and irreversibility rate, the exergy analysis is conducted for each equipment. In continue, in order to investigate the economic and environmental aspects of the hybrid system, the exergoeconomic and exergoenvironmental analyses are performed. Finally, in order to find out the relationship between three important parameters: 𝑍‚ 𝑌‚ 𝑎𝑛𝑑 𝐸𝐷 , the 3D parametric analysis is done. 2. Hybrid system description This novel cascade absorption-compression refrigeration system has been proposed by Y. Chen et al. (Chen et al., 2017) in 2017, and the comprehensive exergy based (3E) evaluation of this system is

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conducted in current investigation. Figure 1 represents the process flow diagram of hybrid system. As well as, the thermodynamic performance and design data of the hybrid system are tabulated in Table1. According to Figure 1, this hybrid system including three subsystems: 1) Rankine power generation Cycle, which is utilized as power source for providing the required electricity of pumps and compressor. The mixture of H2O –NH3 is employed as the working fluid for this subsystem. So, this system does not need an external power source, and can be utilized stand alone. 2) Absorption Refrigeration Cycle (ARC) in high - temperature level, which its working fluid is H2O –NH3 mixture. 3) CO2 compression refrigeration cycle in low – temperature level. Table 2 presents the thermodynamic specifications of hybrid system streams. The flue gas stream (stream 27) at atmospheric pressure, 350 °C and 3600 kg/h enters the heat recovery vapor generator (HRVG). The pressure of stream 1 after passing via the high pressure pump (HP) reaches to the 10000 kPa. In order to generate super-heated vapor, stream 2 at 68.49°C with 302.4 kg/h mass flow rate is sent to the HRVG. The super-heated stream (stream 3) at 335°C is fed to the turbine. 32.27 kW of electricity is produced by turbine, and stream 4 at 156.7 °C and 1049 kPa leaves the turbine. Stream 4 is utilized as required heat duty of rectifier reboiler. Stream 5 at 127.6°C is sent to the vapor heat exchanger (VHEX) for exchanging heat with stream 11 (35.24°C, 1356 kPa, and 34% wt. NH3). The temperature of Stream 12 reaches to 113.8 12 °C, and it goes to gas heat exchanger (GHEX). In GHEX, the H2O –NH3 mixture stream is heated by flue gas stream. The outlet stream of GHEX (stream 29) at 140.1 °C is emitted to atmosphere. Also, Stream 13 at 128.2 °C, 1356 kPa with 608.4 kg/h mass flow rate goes to the REC. the rectifier is used to separate the weak solution and strong solution of ammonia. As well as, stream 10 at 114.2 °C, 1356 kPa with 914.4 kg/h is fed to the REC. the pressure drop of REC is considered to be 10 kPa. This distillation column has 8 trays, and inlet streams are fed to the tray 4. Stream 14 at 52.19°C with 99.8% wt. NH3, as strong solution leaves the top of column, and stream 20 at 138.3°C with 20% wt. NH3, as weak solution leaves the bottom of column. Stream 14 enters the CON condenser, and after exchanging 90.87 kW of eat duty with water stream, its temperature reduces to 35 °C. Stream 15 is introduced to the sub cooler heat exchanger

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(SUBC), and subcooled to 15°C. After passing via the VAL2 valve, the pressure of stream 17 reduces to 217 kPa. The ARC and CO2 compression cycle are hybridized to form the cascade system by cascade heat exchanger (CHEX). Actually, this heat exchanger operates as evaporator for ARC, and condenser for CO2 compression cycle. Stream 24 at 97.4°C and 2471 kPa goes to the CHEX, and after exchanging 90.2 kW heat load with ammonia – water mixture stream, its temperature decreases to -11.8°C. The pressure and temperature of CO2 stream after passing through the VAL3 valve reach to 543 kPa and 54.62 °C, respectively. 60.65 kW of heat duty is absorbed in EVA, and stream 23 at vapor saturated state enters the COMP compressor. The overall coefficient of performance (COP) of this system can be calculated as following:

𝐶𝑂𝑃𝑡𝑜𝑡 =

𝑄𝐶 𝑄𝐻

=

(1)

60·65 = 0·268 226·56

In this relation, 𝑄𝐶 (kW) and 𝑄𝐻 (kW) denote the absorbed heat duty in evaporator and total heat input, respectively. Stream 20 in bottom of the column enters the solution heat exchanger (SHEX), and its temperature decrease to 66.12°C. In continue, stream 19 (strong solution) and stream 22 (weak solution) are mixed together in MIX mixer. Then, stream 6 at 61.48 °C, 217 kPa with 1523 kg/h mass flow rate is sent to the ABS. Then stream 7 at 35°C and 217 kPa goes to the low pressure pump (LP), and its pressue reaches to 1356 kPa (operating pressure of rectifier). Finally, by utilizing a Tee, the stream 8 is divided into two stream 9 (914.4 kg/h) and stream 11 (608.4 kg/h). Streams 9 and 11 are fed to the SHEX and VHEX heat exchangers, respectively. The main specifications of hybrid system devices are presented in Table3. Figure 1. Table 1. Table 2.

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Table 3.

3. Simulation and considered assumptions In order to compute the thermodynamic specifications of each stream and device, the cascade refrigeration system is simulated by Aspen HYSYS V10 software. The exergetic terms of each stream is calculated by coupling MATLAB with Aspen HYSIS. As well as, in order to applied exergoeconomic analysis to the process, the purchased equipment cost (PEC) of each device are needed. The PEC of heat exchangers is a function of area. Hence, Aspen Exchanger Design and Rating (EDR) V10 software, is employed to calculate the area of each heat exchanger. In this simulation, three thermodynamic models are utilized: 1) Peng- Robinson model; for CO2 compression refrigeration cycle. 2) PSRK model; for ammonia-water mixture. 3) Ideal model; for flue gas stream. The mentioned thermodynamic models (fluid packages) include a wide range of thermodynamic properties, and enjoy the fast calculations. The most remarkable assumptions, which are considered for evaluating this hybrid system can be listed as below: 1. This process operates at steady state mode. 2. For applying exergy assessment, the temperature of 298.15 K and pressure of 101 kPa are assumed as standard state. 3. The changes of kinetic and potential exergy for each equipment are assumed to be zero. 4. The pressure drop in heat exchanges are neglected. 5. The heat loss from hybrid system devices is assumed to be zero. 6. The isentropic efficiency of compressor, pumps and turbine are considered to be 55%, 75%, and 85%, respectively (Chen et al., 2017).

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7. The outlet streams of evaporator and condenser is considered to be saturated vapor (at -54.62°C) and saturated liquid (at 35°C), respectively. 8. The flue gas composition is 14.67 % mole H2O, 78.01 % mole N2, and 7.31 % mole CO2. 4. Exergy evaluation In order to assess the energy quality in a process, the second law of thermodynamic is employed. On the other hand, exergy can be defined as the maximum reversible work, which can be achieved in a process(Ghorbani et al., 2017; Mehrpooya et al., 2018b; Niasar et al., 2019). In an exergy assessment, the conditions and specifications of system and environment are considered simultaneously. In fact, by applying exergy evaluation, the quality and quantity of energy are measured (Naseri et al., 2017b). In this investigation, 298.15 K and 1 bar are considered as standard conditions. Hence, in dead state conditions, the exergy of a system is equal to zero. By employing exergy balance for each subsystem of a process, two valuable parameters including: exergy efficiency and exergy destruction are calculated. With the generation of entropy in a system, exergy (useful energy) is destroyed. For each equipment, exergy destruction rate can be computed as following formula (Mehrpooya et al., 2018a): (2)

𝐸𝑥𝐷 = 𝑇0𝑆𝑔𝑒𝑛

The entropy generation rate can be obtained by employing entropy balance around each subsystem as below(Cengel and Boles, 2002):

𝑆𝑔𝑒𝑛 =

∑𝑚

𝑜𝑢𝑡𝑠𝑜𝑢𝑡

―

∑𝑚

𝑖𝑛𝑠𝑖𝑛

―

∑(𝑇𝑄 )

(3)

𝑘

As well as, the irreversibility rate can be obtained as the difference between actual work and reversible work for each device (Mehrpooya et al., 2018a): 𝐸𝑥𝐷 = |𝑊𝑟𝑒𝑣 ― 𝑊𝑎𝑐|

(4)

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In this relation, 𝑊𝑟𝑒𝑣 (kW) and 𝑊𝑎𝑐 (kW) refer to the actual power and reversible power, respectively. The exergy destruction ratio (𝑦𝐷) is an important parameter, which is applied to determine the share of each device of a process to total irreversibility. This parameter can be defined as below:

𝑦𝐷‚𝑘 =

𝐸𝐷‚𝑘

(5)

𝐸𝐷‚𝑡𝑜𝑡

By neglecting the potential and kinetic terms of exergy, the exergy rate of each stream can be gained as following relation (Mohammadi et al., 2018): 𝐸𝑥𝑡𝑜𝑡 = 𝐸𝑥𝑝ℎ + 𝐸𝑥𝑐ℎ

(6)

The physical and chemical exergy streams can be calculated by using equations (7) and (8): 𝐸𝑥𝑝ℎ = 𝑚𝑒𝑥𝑝ℎ = 𝑚 (ℎ ― ℎ0 ― 𝑇0(𝑠 ― 𝑠0))

(7)

𝐸𝑥𝑐ℎ = 𝑚𝑒𝑥𝑐ℎ = 𝑚 (∑𝑥𝑖𝑒0𝑖 +𝐺 ― ∑𝑥𝑖𝐺𝑖)

(8)

In above equations, 𝑚 (kg/s) denotes the mass flow rate, h (kJ/kg) stands for the specific enthalpy, and s (kJ/kg.K) is related to the specific entropy. As well as, xi associated with the mole fraction of component i. G (kJ/kg mole) represents the Gibbs free energy and 𝑒0𝑖 (kJ/kg mole) is related to the standard chemical exergy of component i. After calculating the fuel exergy (𝐸𝑥𝐹) and product exergy (𝐸𝑥𝑃) for each subunit, Exergy efficiency ( 𝜀), which is a useful parameter for investigating the performance of a system, can be formulated as following relation (Naseri et al., 2017a):

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𝜀=

𝐸𝑥𝑃 𝐸𝑥𝐹

=1―

𝐸𝑥𝐷 𝐸𝑥𝐹

𝑂𝑟 𝜀 =

(9)

𝐸𝑥𝑂𝑢𝑡 𝐸𝑥𝐼𝑛

By assuming the steady state conditions for each subunit of hybrid system, the exergy balance can be expressed as following (Cengel and Boles, 2002):

∑𝐸𝑥 ― ∑𝐸𝑥 𝑖𝑛

𝑜𝑢𝑡

(10)

= 𝐸𝑥𝑑𝑒𝑠𝑡

By minimizing the exergy loss of each subsystem, the exergy efficiency is maximized. So, for each equipment of hybrid system, the exergetic improvement potential rate (IP) can be defined as below (Noroozian et al., 2017): (11)

𝐼𝑃 = (1 ― 𝜀)(𝐸𝑥𝑖𝑛 ― 𝐸𝑥𝑜𝑢𝑡)

For computing the exergy stream associated with heat duty, the equation (12) is employed (Jahangir et al., 2019).

𝐸𝑥𝑄 = (1 ―

𝑇0 )𝑄 𝑇𝑗

(13)

Table 4 denotes the summarize of utilized relations for calculating the irreversibility rate and exergy efficiency for each device of the hybrid system. Table 4 5. Exergoeconomic evaluation In order to assess a thermodynamic system technically and economically, exergoeconomic evaluation is utilized. Actually, a proposed process before applying in industry, should be determined is a cost – effective system. we often need to know how much such inefficiencies cost(Ahmadi and Dincer, 2018). Knowledge of these information about the costs is very beneficial for rectifying the cost effectiveness of the process, that is, for decreasing the costs of the final products produced by the system. As a result, exergoeconomic evaluation is a powerful tool for determining the cost – effectiveness of a

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thermodynamic system(Ahmadi and Dincer, 2018). For this purpose, after computing the total exergy of each stream and fuel and product exergy rate of each device, the capital investment cost rate (𝑍𝑘) of each equipment is computed. So, the cost balance around each device can be expressed with equations (14) and (15) (Baghernejad et al., 2011): 𝑐𝑃𝐸𝑥𝑃 = 𝑐𝐹 𝐸𝑥𝐹 + 𝑍𝑘

(14)

𝐶𝑃 = 𝐶𝐹 + 𝑍𝑘

(15)

In above equation, 𝑐𝑃 ($/GJ), 𝑐𝐹 ($/GJ), and 𝑍𝑘 ($/h) are related to the unit product exergy cost, unit fuel exergy cost, and investment cost rate, respectively. Moreover, 𝐶𝑃 ($/h) and 𝐶𝐹 ($/h) stand for the product cost rate and fuel cost rate, respectively, which can be achieved by applying equations (16) and (17). 𝐶𝑃 = 𝑐𝑃𝐸𝑥𝑃

(16)

𝐶𝐹 = 𝑐𝐹𝐸𝑥𝐹

(17)

Table 7 illustrates the cost equations of hybrid system components. The purchased equipment cost (PEC), which are presented in Table 7, must be changed to the reference year (in this study 2019). For example, the PEC of hybrid system equipment have been presented in 2003. So, the cost of devices must be converted to 2019. For this purpose, Chemical Engineering Plant Cost Index (CEPCI), which is an inflation indicator is utilized. The PEC of the reference year is computed as follows (Bejan et al., 1996): 𝐶𝐸𝑃𝐶𝐼 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑃𝐸𝐶 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 𝑃𝐸𝐶 𝑜𝑟𝑖𝑔𝑖𝑛 × ( ) 𝐶𝐸𝑃𝐶𝐼 𝑜𝑟𝑖𝑔𝑖𝑛

(18)

The investment cost rate for each equipment of the hybrid system can be gained by relation (19)(Soltanian et al., 2019):

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𝑍𝑘 =

𝑍0𝑘 × 𝐶𝑅𝐹 × 𝜙

(19)

𝜏 × 3600

In above formula, 𝑍0𝑘 ($), 𝐶𝑅𝐹 (-), 𝜙 (-), and 𝜏 (h) represent the capital cost, capital recovery factor, maintenance factor, overall annual working hours, respectively. As well as, the CRF can be formulated as following relation (Jahangir et al., 2019):

𝐶𝑅𝐹 =

𝑖(1 + 𝑖)𝑛

(20)

(1 + 𝑖)𝑛 ― 1

In the above Formula, i (%) and n (year) refer to the interest rate and life time of the hybrid system, respectively. In this investigation, the interest rate and life time are considered to be 12% and 25 years, respectively. Table 5 represents the utilized assumptions and constants for exergoeconomic assessment. By solving the cost balance of each equipment, the unit cost of each stream ($/GJ) should be obtained. Generally, the number of unknowns is more than number of relations. So, for solving this problem, some auxiliary equations based on the product and fuel exergy rate of each subunit is exploited. Table 6 presents the cost balances and auxiliary equations of each component. Therefore, by applying the cost balances and auxiliary relations, a linear matrix is formed as below: [𝐸𝐾] × [𝑐𝑘] = [𝑍𝐾]

(21)

In above equation, [𝐸𝐾] belongs to the vector of stream exergy rate, [𝑐𝑘] is related to the vector of unit cost, and [𝑍𝐾] associated with the vector of coefficient. Based on the outcomes of exergoeconomic evaluation, three valuable and important indexes are defined, which create a relation between the technical and economic aspects of the process. these indicators are Relative cost deference (r), exergy destruction cost rate (𝐶𝐷), and exergoeconomic factor (f). In continue, each of the mentioned indicators are expressed.

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Relative cost deference (r) represents the relative increase in the average cost per exergy unit between fuel and product of the equipment. This is a valuable parameter for analyzing and optimization of a thermodynamic system devices. Namely, if the fuel cost of a major device varies from one iteration to the next, the target of the cost optimization of the device must be to minimize the relative cost difference instead of minimizing the product cost for this device. This indicator can be expressed as below (Mehrpooya et al., 2018b):

𝑟𝑘 =

𝑐𝑃.𝑘 ― 𝑐𝐹.𝑘

(22)

𝑐𝐹.𝑘

As can be seen in cost balance for each subunit (equation (14)), no parameter is defined for exergy destruction cost rate (𝐶𝐷). Hence, this parameter is known as a hidden cost. By fixing the product exergy rate (𝐸𝑝), the exergy destruction cost rate associated with kth device, can be formulated as following: 𝐶𝐷.𝑘 = 𝑐𝐹.𝑘 𝐸𝐷.𝑘

(23)

Exergoeconomic factor (f) is one of the most valuable indexes in exergoeconomic assessment, which illustrates the relative relationship between the investment and O&M costs (non – exergy related costs) and exergy destruction cost rate (exergy related costs) (Tsatsaronis and Winhold, 1985). The high values of this indicator illustrate that the contribution of O&M and investment costs is more than irreversibility cost rate for this device. Accordingly, in order to decrease the cost of process, the capital investment cost rate associated with corresponding device must be reduced. Moreover, the low values of this index express that the share of exergy destruction cost rate is more than the investment and O&M costs for this equipment. Hence, in order to decrease the irreversibility of system, the configuration and performance of the process should be decreased. The exergoeconomic factor is formulated as following formula (Mehrpooya et al., 2018b):

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𝑓=

𝑍𝑘 𝑍𝑘 + 𝐶𝐷.𝑘

=

(24)

𝑍𝑘 𝐶𝑡𝑜𝑡.𝑘 Table 5 Table 6 Table 7

6. Exergoenvironmental evaluation By enhancing the overall efficiency of energy systems, the environmental impacts, such as greenhouse gases (CO2, NOx . etc.) emissions reduce. By exergoenvironmental evaluation, the impact of environmental variables on performance of the process is specified (Ahmadi et al., 2012). This evaluation including three steps: in the first stage, by applying exergy assessment, the fuel and product exergy, and exergy destruction rate for each component of process are obtained. In the second step, to determine the environmental effects, life cycle assessment (LCA) concept is carried out. Finally, the outcomes of exergy analysis are linked to the LCA calculations in order to conduct the exergoenvironmental analysis. 6.1. Life Cycle Assessment (LCA) LCA is a powerful and appropriate tool in order to evaluate the environmental impact of a process. The environmental impacts of an energy system during the life time of project consist of: generation, operating and maintenance (O&M), and disposal (Ifaei et al., 2016). The significance of LCA for exergoenvironmental assessment of a process is to determine the environmental impact of the product during its lifetime. Up to now, several methods such as ReCiPe Endpoint, TRACI 2, CML 2001, and Eco - indicator 99 have been proposed and developed to evaluate the environmental impact of thermodynamic systems (Siddiqui and Dincer, 2019). In this investigation, LCA is conducted by applying Eco - indicator 99. This index exploits the average European data, and specifies environmental

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impacts based on three damages classes: (a) ecosystem quality; (b) human health; (c) resources (Elbar et al., 2019). The LCA aspect including five phases as following (Ansarinasab et al., 2019): 1. The utilized materials in manufacturing (per kg of material). 2. Treatment and Production processes of fabrication. 3. Transportation of materials, devices, and fuels (per unit ton kilometer). 4. The required energy for productions such as electricity and heat duty. 5. Disposal for materials and waste. The obtained outcomes are weighted, and presented as Eco-indicator points (Pts or mPts). The environmental impact can be defined as “ecopoints” Pts, (1000 mPts=1 Pts), where one point can be considered as 1/1000 of the annual environmental rate (damage) of one average European resident (Paraskevas et al., 2013). As the obtained values be higher, the environmental impact is greater. The millipoint outcomes are more applied for most describing the environmental impacts of most processes. The outcomes of each product concept indicate the share of one person in the environmental impacts of the ovearll that country in one year. As a summary, millipoints demonstrate an overall impact score in one number. The life time of this process is considered to be 25 years. Table 8 depicts the eco- indicator for materials of hybrid system equipment. As well as, the eco- indicator and weight function of each device are listed in Table 9. As well as, the weight of compressor can be gained as following (Cavalcanti and Reviews, 2017): 𝑚 = 𝜌𝑉𝐴

𝑡=

𝑃 ∙ 𝐷 ∙ 𝐹𝑆 2𝜎

(25)

(26)

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In above formulas, 𝜌

( ).𝑉 ( ). 𝑎𝑛𝑑 𝐴 (𝑚 ) refer to the density of the inlet gas, fluid velocity, and inlet 𝑘𝑔

𝑚3

𝑚 𝑠

2

cross section, respectively. As well as, FS and 𝜎 belong to the factor of safety and rupture stress, respectively. the values of these parameters have been presented in (McGuire and Granovetter, 1993). Table 8. Table 9. 6.2. Exergoenvironmental variables For each subunit of the hybrid system, the environmental impact balance can be written as below(CasasLedón et al., 2017): 𝐵𝑘‚𝑃 = 𝐵𝑘‚𝐹 + 𝑌𝑘

(27)

In this balance, 𝐵𝑘‚𝑃 (mPts/h), 𝐵𝑘‚𝐹 (mPts/h) and 𝑌𝑘 (mPts/h) denote the product environmental impacts rate, fuel environmental impacts rate, and environmental impacts rate of kth equipment, respectively. The environmental impact associated with kth device includes three parts: construction level (𝑌𝐶𝑜 𝑘 ), 𝐷𝐼 operating and maintenance (O&M) level (𝑌𝑂𝑀 𝑘 ) and disposal level (𝑌𝑘 ). the environmental impact for

each equipment is computed by sum of these parameters as below (Cavalcanti and Reviews, 2017):

𝑂𝑀 𝐷𝐼 𝑌𝑇𝑂𝑇 = 𝑌𝐶𝑜 𝑘 𝑘 + 𝑌𝑘 + 𝑌𝑘

(28)

The environmental impact rate of each device can be measured as below (Dincer et al., 2018):

𝑌𝐾 =

𝑌𝑇𝑂𝑇 𝑘

(29)

𝑛×𝜏

Also, the unit fuel environmental impact (𝑏𝑘‚𝐹) and unit product environmental impact (𝑏𝑘‚𝑃) can be measured as bellows:

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𝑏𝑘‚𝐹 =

𝑏𝑘‚𝑃 =

𝐵𝑘‚𝐹

(30)

𝐸𝑥𝑘‚𝐹

𝐵𝑘‚𝑃

(31)

𝐸𝑥𝑘‚𝑃

Similar to the exergoeconomic analysis, the number of unknowns is more than number of relations. So, for solving this problem, some auxiliary equations based on the product and fuel exergy rate of each device is utilized. after employing the environmental balances and auxiliary equations, the following linear matrix is formed: [𝐸𝐾] × [𝑏𝑘] = [𝑌𝐾]

(32)

Where, [𝑏𝑘] and [𝑌𝐾] represent the vector of unit environmental impact and the vector of environmental impact of kth component, respectively. Table 10 presents the environmental impact balance equations of the hybrid system equipment. The exergy destruction environmental impact rate (𝐵𝑘‚𝐷) is known as a hidden impact in equation (25). By fixing the product exergy rate (𝐸𝑝), the exergy destruction environmental impact rate associated with kth equipment, is gained by using equation (33):

𝐵𝑘‚𝐷 = 𝑏𝑘‚𝐹 𝐸𝑥𝑘‚𝐷

The overall environmental impact rate of each subunit is obtained by equation (34):

(33)

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(34)

By applying this indicator, the potential for reduction of environmental impacts of each component can be defined. The relative difference of the environmental impacts can be defined as bellows (Aghbashlo et al., 2019):

𝑟𝑘‚𝑏 =

𝑏𝑘‚𝑃 ― 𝑏𝑘‚𝐹

(35)

𝑏𝑘‚𝐹

The exergoenvironmental factor (fb) expresses the ratio of non-exergy related environmental impact ( 𝑇𝑂𝑇 𝑌𝑇𝑂𝑇 𝑘 ) to overall environmental impact of each a subunit (𝐵𝑇𝑂𝑇 = 𝐵𝐷 + 𝑌𝑘 ). By using this indicator, it

is determined, which types of the environmental impact (𝐵𝐷 𝑜𝑟 𝑌𝑇𝑂𝑇 𝑘 ) is dominant for each device. This valuable index can be expressed as follows(Aasadnia et al., 2019):

𝑓𝑘‚𝑏 =

𝑌𝑇𝑂𝑇 𝑘

(36)

𝑌𝑇𝑂𝑇 + 𝐵𝑘‚𝐷 𝑘

Table 10. 7. Interaction of Zk, Yk, and ED,k: 3D parametric evaluation The most valuable and important outcomes of exergy, exergoeconomic, and exergoevironmental analyses for each equipment are exergy destruction rate, capital investment cost rate, and environmental impact rate, respectively. These parameters can influence on each other. So, by increasing one of them, the rest of parameters can increase or reduce. One of the main targets of the process engineering researchers is to find out some solutions to reduce the 𝐸𝐷. 𝑌𝑘. 𝑎𝑛𝑑 𝑍𝑘 associated with a process. Accordingly, determining the effective factors on these parameters is essential. For example, in rotary

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machines (turbine, pump, and compressor), isentropic efficiency and pressure ratio are effective parameters, or in the heat exchangers, minimum temperature approach (ΔTmin) and inlet pressure are the 𝐸𝑑

𝑌

𝑝

𝑝

𝑍

main factors. For this purpose, the variations of three parameters (𝐸 ), (𝐸 ), and (𝐸 ) according to the 𝑝

changes of isentropic efficiency, pressure ratio, ΔTmin , and inlet pressure are investigated. So, by applying 3D parametric evaluation, it is found, which devices in a process should be optimized. For 𝐸𝑑

example, by increasing the isentropic efficiency of the compressor, the irreversibility (𝐸 ) reduces. On 𝑝

the other hand, a higher effective compressor, has a higher investment cost and more complex 𝑌

𝑍

construction. So, with the increase of isentropic efficiency, (𝐸 ) and (𝐸 ) increase. Therefore, determining 𝑝

𝑝

an optimum isentropic efficiency is necessary. Figure 2 demonstrates the relationship between 𝑍‚ 𝑌‚ 𝑎𝑛𝑑 𝐸𝑑

𝑌

𝑝

𝑝

𝑍

𝐸𝐷. As can be seen, the size effect of devices is described by combining (𝐸 ), (𝐸 ), and (𝐸 ) for operating 𝑝

conditions of process. According to this figure, each line depicts a wide zone, presenting that for each 𝐸𝑑

𝑌

𝑝

𝑝

𝑍

value of (𝐸 ), the other values of (𝐸 ), and (𝐸 ) are able to vary in a considerable range. As a whole, 𝑝

the following possibilities are found for quarters (Ⅰ, Ⅱ, and Ⅲ):  

𝐸𝑑

𝑌

𝑝

𝑝

𝑍

The irreversibility (𝐸 ) can be reduced by reducing 𝐸 (line 3) or with the increase of 𝐸 (line 1). 𝑍 𝐸𝑝

(line 2) has a direct relationship with

𝑝

𝐸𝑑

𝑌

𝐸𝑝

𝐸𝑝

. Moreover,

(line 4) is in the reverse relationship

𝐸𝑑

with 𝐸 . 𝑝

𝑌

𝑍



The quantities of 𝐸 (lines 2-4 and 1-3) are proportional to the quantities of 𝐸 .



By decreasing the 𝐸 . the quantities of 𝐸 (lines 2-3 and 1-4) increase.

𝑝

𝑝

𝑍

𝑝

𝑌

𝑝

The more description about 3D parametric analysis can be found in (Lara et al., 2017). Figure 2.

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8. Results and discussion In this section, the outcomes of 3E evaluation and 3D parametric analysis are presented and discussed. 8.1.

Exergy evaluation

The physical, chemical, and total exergy rate of each hybrid systems are tabulated in Table 11. It can be seen that, the chemical exergy rate of each stream, after passing via rotary machines (compressor, turbine, and pumps), heat exchangers, and valves be remind constant. Actually, when the chemical exergy changes, that the component percentage of stream changes (such as: column and reactor). The highest and least total exergy rate belongs to the stream 6 (2986.57 kW) and stream 23 (134.56 kW), respectively. Table 12 presents the exergetic values of each equipment of process includes: fuel exergy rate, product exergy rate, exergy destruction rate, exergy efficiency, and improvement potential. It can be deduced that, REC (16.05 kW), HRVG (11.55 kW), and COMP (11.53 kW) have the largest values of exergy destruction rate in contrast to other devices. Accordingly, in order to reduce the process exergy wasting, it must be suggested some solutions to reduce irreversibility in these components. The greatest improvement potential is related to the REC, due to its high exergy destruction rate. It is shown, there is a high potential to rectify its performance from the exergetic viewpoint. Among the rotary machines, it was calculated that, COMP destroys 11.53 kW of exergy (Rank 1). As well as, the lowest and biggest improvement potential are found to be in the COMP (4.5 kW) and LP (0.06 kW), respectively. Figure 3 illustrates the share of heat exchangers in exergy destruction rate. Based on this figure, amongst the heat exchangers, the highest contribution of irreversibility associated with HRVG (26%). Also, the second and third ranks are related to the CHEX (15%) and SHEX (13%), respectively. The least share of exergy destruction rate belongs to the SUBC with the value of 1%. Figure 4 demonstrates the share of hybrid system devices in exergy destruction rate. As can be noticed, the main exergy wasting component is found to be REC by 19.25% of the total exergy destruction rate. HRVG (13.85%) and COMP (13.83%) Stand for the next ranks of irreversibility contribution. Figure 5 displays the share of each subsystem in

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overall exergy destruction rate. As can be noted, amongst the three subsystems of hybrid system, ARC has the biggest contribution of overall exergy destruction rate (43%). This outcome is expected because the main exergy wasting equipment such as REC and CHEX belong to this subsystem. Figure 6 demonstrates the Sankey diagram of the destroyed exergy rate of the process devices. As can be seen, the input and output exergy of the hybrid system are 268.23 kW and 184.84 kW, respectively. As a result, the overall exergy efficiency of the hybrid system is computed by 69%. Heat exchangers destroy the 17% of the input exergy (45.18 kW). So, the operating parameters of heat exchangers must be optimized. Figure 7 depicts the exergy efficiency of hybrid system components. As can be seen, the expansion valves have the lowest amount of exergetic efficiency in contrast to other equipment of process. Whereas, the heat exchangers have the best performance from the exergetic viewpoint. Namely, the first and second ranks of exergy efficiency in process devices are computed to be in CHEX (99.38%), and SUBC (99.11%), respectively. Amongst the rotary machines, the fewest value of exergy efficiency is calculated to be in the COMP (61%). Table 11 Table 12 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 8.2.

Exergoeconomic evaluation

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Table 13 represents the outcomes of exergoeconomic and exergoenvironmental analyses for hybrid system streams. According to this table, stream 6 (2558.84 $/h) and stream 8 (2548.04 $/h) have the greatest values of cost rate. Table 14 exhibits the results of exergoeconomic analysis parameters for each subunits of hybrid system. As can be seen, the largest value of exergoeconomic factor (f) is related to the VHEX by 10.32%. the non- exergy related cost in this device is higher than other equipment. Hence, in order to decrease the cost associated with this heat exchanger, it is vital to replace it with a cheaper one. Actually, in order to decrease the overall cost of the hybrid system, the capital and operating and maintenance costs associated with VHEX must be minimized. Moreover, the smallest amount of exergoeconomic factor belongs to the EVA and SHEX heat exchangers with the values of 9.17% and 10.25%, respectively. As a result, the related exergy cost of these components is high incomparison to other devices. Therefore, to reduce the overall cost of the hybrid system, the thermodynamic design of these subunits should be rectified. On the other hands, the heat exchangers with higher efficiency and better performance must be utilized. Figure 8 indicates the share of two types of the cost in overall cost for each subunit. As can be seen, the contribution of exergy - related cost (𝐶𝐷) is more than 48% for rotary machines of the process. as well as, amongst the heat exchangers, the highest conurbation of exergy - related cost stands for EVA and SHEX. In 73% of the hybrid system devices, the share of exergy - related cost is more than 55%. So, it is concluded that the irreversibility related cost of system is dominant. The relative cost deference (r) has a noticeable role for analyzing and optimization of each thermodynamic system. It can be deduced from Table12, the greatest and smallest relative cost deference stand for the GHEX and EVA, respectively. The values of product and fuel exergy cost specify the cost of exergy for each equipment. The maximum product and fuel unit costs stand for the REC (414.5 $/GJ) and ABS (238 $/GJ), respectively. The highest values of fuel unit cost are related to the heat exchangers, as a result, heat exchangers have the maximum exergy destruction cost rate. SHEX (5.08 $/h) and EVA (3.62 $/h) have the maximum quantities of exergy destruction cost rate. As well as, amongst the rotary

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machines, the biggest exergy destruction cost rate stands for the COMP by 1.04 $/h. The largest quantity of total cost rate belongs to the SHEX (5.66 $/h), followed by ABS (4.36 $/h) and REC (4.14 $/h). Accordingly, these subunits need to be rectified first to improve the effectiveness and performance of the hybrid system. Table 13 Table 14 Figure 8

8.3.

Exergoevironmental evaluation

Based on Table 13, the largest quantities of environmental impact rate are related to stream stream 6 (382.16 Pts/h) and stream 8 (380.56 Pts/h). The outcomes of exergoevironmental analysis parameters for each equipment are summarized in Table 15. It can be seen that the exergoenvironmental factor for all of the hybrid system subunits is less than 11%. So, the related- exergy environmental impact is high and the dominant source of the environmental impact of the hybrid system. The greatest values of exergoenvironmental factor associated with VHEX (10.32%) and GHEX (9.35%). It means that, in order to minimize the environmental impacts associated with these subunits, the environmental impacts of installation, fabricating, disposal and O&M associated with these heat exchangers must be reduced. As well as, COMP and REC have the lowest values of exergoenvironmental factor. So, the effectiveness and performance of mentioned devices must be improved. Furthermore, the maximum and minimum quantities of the environmental impact of irreversibility occurred in the REC and LP pump, respectively. These outcomes are expected, due to the mentioned devices have the highest and least values of irreversibility. Figure 9 illustrates the comparison between the two kinds of environmental impact (exergy destruction and the component itself) for hybrid system devices. Based on this figure, in all of

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the devices, the share of exergy – related environmental impact is more than 89%. As well as, the largest contribution of exergy – related environmental impact for rotary machines and heat exchangers associated with COMP and CHEX, respectively. The highest relative environmental impacts difference (rb) belongs to the REC. As a result, this device has a significant potential to decrease the environmental impact. Also, the lowest relative environmental impacts difference is found to be in the EVA (4.31%) and TUR (12.3%). REC with the value of 6455.96 mPts/h, has the first rank of overall environmental impact rate. Moreover, the second and third ranks are related to the CHEX (932.39 mPts/h) and SHEX (767.84 mPts/h), respectively. The mentioned components have a remarkable role in environmental impacts of this refrigeration system. Accordingly, in order to make this process more suitable environmental aspect, it is essential to reduce the environmental impacts associated with the mentioned equipment. By applying exergoeconomic and exergoenvironmental analyses, it was found that the exergy – related cost and environment impact are dominant. Therefore, the configuration of this hybrid system should be rectified, and the equipment should be replaced with more efficient one. Table 13 Figure 9 Table 15. 8.4.

3D parametric evaluation

Figure 10 (a) indicates the effect of compressor isentropic efficiency on interaction between 𝑍‚ 𝑌‚ 𝑎𝑛𝑑 𝐸𝐷 . The isentropic efficiency changes from 50 to 70%. It was found that by improving the effectiveness of 𝐸𝑑

compressor (increasing isentropic efficiency), (𝐸 ) reduces, but environmental impact and capital cost 𝑝

associated with compressor increase. Accordingly, in order to find an optimum point for isentropic

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efficiency, the multi - objective optimization should be performed for compressor. Figure 10 (b) denotes 𝐸𝑑

𝑌

𝑝

𝑝

𝑍

the variations of (𝐸 ), (𝐸 ), and (𝐸 ) versus the changes of pressure ratio of compressor. It can be noticed 𝑝

that for reducing the exergy destruction, environmental impact and capital cost simultaneously, the pressure ratio of compressor must be maximized. Figure 11 (a) depicts the influence of isentropic efficiency of turbine on interaction between 𝑍‚ 𝑌‚ 𝑎𝑛𝑑 𝐸𝐷. The isentropic efficiency is considered to be variable, from 70 to 90%. It can be concluded, with the increase of isentropic efficiency, the 𝑍

𝑌

irreversibility of turbine reduces. As well as, by enhancing the isentropic efficiency, (𝐸 ) and (𝐸 ) 𝑝

𝑝

parameters decrease. Figure 11 (b), shows the effect of pressure ratio on interaction between 𝑍‚ 𝑌‚ 𝑎𝑛𝑑 𝐸𝐷. The pressure ratio varies from 0.065 to 0.145 bar. It can be noticed, by increasing the pressure ratio, 𝑍

𝑌

the exergy destruction rate decreases. Whereas, the cost rate (𝐸 ) and environmental impact rate (𝐸 ) 𝑝

𝑝

increase. Accordingly, in order to obtain an optimum pressure ratio, the optimization should be applied to the turbine. Figure 12 (a) demonstrates the interaction between 𝑍‚ 𝑌‚ 𝑎𝑛𝑑 𝐸𝐷 according to the changes of ΔTmin for HRVG heat exchanger. the minimum temperature approach changes from 7 to 15 °C. As can be seen, by decreasing ΔTmin, and consequently improvement of the heat exchanger performance, 𝐸𝑑

𝑌

𝑝

𝑝

𝑍

irreversibility rate (𝐸 ), environmental impact rate (𝐸 ), and cost rate (𝐸 ) reduce. Therefore, to rectify 𝑝

the environmental, technical, and economical aspects associated with this heat exchanger, ΔTmin must 𝐸𝑑

𝑌

𝑝

𝑝

𝑍

be decreased as much as feasible. Figure 12 (b) illustrates the changes of (𝐸 ), (𝐸 ), and (𝐸 ) according 𝑝

to the variations of inlet pressure. The inlet pressure is considered to be variable from 80 to 120 bar. It 𝐸𝑑

𝑌

𝑝

𝑝

𝑍

was found, in order to minimize the (𝐸 ), (𝐸 ), and (𝐸 ), the inlet pressure must be increased as much 𝑝

as feasible. Table 16 presents the comparison between the economic and exergetic parameters of some devices of this investigation and Reference (Mosaffa et al., 2016). The exergoeconomic factor and exergy efficiency of the compressor, condenser, cascade heat exchanger, and evaporator are compared

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to the reference. As can be seen, the exergoeconomic factor of the reference devices is higher than paper devices (except cascade heat exchanger). Therefore, the capital investment cost is dominant for reference paper. As well as, the exergy efficiency of the paper devices is higher than reference considerably, which it indicates the better performance of paper devices. Table 17 indicates the comparison of this combined process with hybrid systems consists of ARC, from the technical standpoint. The overall exergy efficiency, exergy destruction rate, and column exergy efficiency are presented as technical parameters. Clearly, the performance of this auto cascade system is better than previous proposed systems. As well as, the overall irreversibility rate is lower than references considerably, which indicates by applying auto cascade remigration system, the wasting exergy can be reduced.

Figure 10 (a) Figure 10 (b) Figure 11 (a) Figure 11 (b) Figure 12 (a) Figure 12 (b) Table 16. Table 17.

9. Conclusions In this article, a comprehensive exergy based assessment is applied to a new cascade refrigeration at low temperature conditions. The required power of compressor and pumps are supplied by a Rankine cycle, which is hybridized with this system. In order to calculate the exergy efficiency and irreversibility rate, the exergy analysis is conducted for each equipment. In continue, in order to investigate the economic

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and environmental aspects of this process, the exergoeconomic and exergoenvironmental analyses are carried out. At the end of this work, to find out the relationship between three important parameters: 𝑍‚ 𝑌 ‚ 𝑎𝑛𝑑 𝐸𝐷 , the 3D parametric analysis is conducted. Actually, by applying this sensitivity analysis, it was found, which devices require the optimization. The most noticeable results of this work, can be drawn as following list: 1. According to the exergy assessment, the overall exergy efficiency and irreversibility rate of the hybrid system are computed to be 69% and 83.4 kW, respectively. 2. The largest value of exergy destruction rate belongs to the REC rectifier (16.05 kW), which is 19.25% of the total destroyed exergy rate. Hence, in order to rectify the thermodynamic performance and reduce the wasting exergy of hybrid system, the exergy destruction rate in this device must be decreased. 3. Among the heat exchangers of hybrid system, the lowest amount of exergy efficiency is related to the ABS absorber (65%). As well as, the highest exergy destruction rate occurred in heat recovery vapor generator (11.55 kW), which has the second rank in the hybrid system devices. 4. Amongst the hybrid system components, cascade heat exchanger and rectifier have the greatest and fewest values of exergy efficiency, by 99.38% and 51%, respectively. 5. Based on the results of exergoeconomic evaluation, the largest value of exergoeconomic factor (f) is related to the GHEX (79.95%). Accordingly, the non-exergy related cost of this equipment is high, and in order to decrease the overall cost of process, the investment cost associated with this component must be reduced. 6.

The EVA evaporator has the lowest exergoeconomic factor (f), with the value of 9.17%. Hence, the exergy related cost associated with this device is low, and in order to reduce the total cost of this equipment, the hybrid system configuration must be rectified.

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7.

Based on the outcomes of exergoenvironmental analysis, the exergoenvironmental factor (fb) of all of the hybrid system devices is low. Therefore, the thermodynamic configuration must be modified to reduce the environmental impact associated with the process.

8. The biggest value of exergoenvironmental factor (fb) is found to be in the VHEX (10.32%). Accordingly, to improve the hybrid system from the environmental impacts aspect, the life cycle environmental impact associated with this device must be minimized. 9. The largest values of overall cost rate and environmental impact rate are related to the SHEX (5.66 $/h) and REC (6455.96 mPts/h), respectively. So, in order to decrease the cost and environmental impact of hybrid system, the operating conditions in these devices, must be optimized. 10. Based on the 3D sensitivity assessment, it can be deduced, with the increase of turbine isentropic efficiency, the capital investment cost and environmental impact rate of turbine reduce simultaneously. As well as, by increasing the pressure ratio, the capital investment cost and environmental impact rate increase simultaneously. 11. By minimizing the minimum temperature approach and maximizing the input pressure, the environmental impacts and exergy cost of devices reach to their minimum value. 12. With the growth of isentropic efficiency of compressor, the irreversibility rate reduces, but environmental impact and cost rate increase. Accordingly, an optimum point must be determined for isentropic efficiency. For first time, by applying exergoenvironmental and exergoeconomic analyses, the environmental, economical, and technical aspects of cascade absorption-compression refrigeration systems are investigated simultaneously. Furthermore, in order to determine the origin of irreversibility related – cost

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rate and environmental impact in cascade absorption-compression refrigeration systems, the advanced exergoeconmic and advanced exergoenvironmental assessments are suggested for future investigations. As well as, by utilizing 3D parametric analysis, it was determined, which parameters should be optimized. Accordingly, applying the optimization is recommended.

Tables Table 1. The summarize of thermodynamic performance and design data of the hybrid system. Standard conditions

25°C, 101.3 kPa

Flue gas temperature (°C)

350

Thermal energy of flue gas, Qf (kW)

335.52

Cooling water temperature (°C)

30

Pressure drop in the REC (bar)

0.1

CHEX heat duty (kW)

90.2

Cooling energy output, QC (kW)

60.65

Total heat input, QH (kW)

226.56

COP of the total system, COPtot (–)

0.268

Evaporation temperature (°C)

-54.62

NH3 mass concentration of the refrigerant (-)

0.998

Table 2. The thermodynamic characteristics of the hybrid system streams. Stream No.

T (°C)

P (kPa)

𝑚 (kg/h)

x (-)

Stream No.

T (°C)

P (kPa)

𝑚 (kg/h)

x (-)

1

66.1

1049

302.4

0.45

18

-7.8

217

270.8

0.998

2

68.49

10000

302.4

0.45

19

29.97

217

270.8

0.998

3

335

10000

302.4

0.45

20

138.3

1356

1252

0.2

4

156.7

1049

302.4

0.45

21

66.12

1356

1252

0.2

5

127.6

1049

302.4

0.45

22

65.68

217

1252

0.2

6

61.48

217

1523

0.34

23

-54.62

543

860.4

-

7

35

217

1523

0.34

24

97.4

2471

860.4

-

8

35.24

1356

1523

0.34

25

-11.8

2471

860.4

-

9

35.24

1356

914.4

0.34

26

-54.62

543

860.4

-

10

114.2

1356

914.4

0.34

27

350

100

3600

-

11

35.24

1356

608.4

0.34

28

173.9

100

3600

-

12

113.8

1356

608.4

0.34

29

140.1

100

3600

-

13

128.2

1356

608.4

0.34

W1

30

100

7200

-

14

52.19

1346

270.8

0.998

W2

50

100

7200

-

15

35

1346

270.8

0.998

W3

30

100

3600

-

16

15

1346

270.8

0.998

W4

51.05

100

3600

-

17

-16.97

217

270.8

0.998

Journal Pre-proof

Table 3. The specifications and operating conditions of the hybrid system components.

HP LP COMP TUR

Rotary machines Power (kW) 1.634 0.969 29.547 32.275 Heat Exchangers Min. Approach (ºC) LMTD (ºC)

Isentropic Eff (%). 75 75 55.18 85

ABS CHEX CON GHEX HRVG SHEX SUBC VHEX

5 5.177 1.139 26.277 15 24.057 5.032 13.763 Duty (kW) 91.138 60.651

REB EVA

REC

7.751 33.380 2.611 35.078 46.405 27.327 21.175 19.18 ΔT (°C) -29.06 0 Column

Number of stages

Feed stage

8

4

ΔP (kPa) 8951 1139 1928 8951 Duty (kW) 173.636 90.199 90.873 37.808 201.986 121.919 80.207 5681 Volume (m3) 0.1 0.1

Tray/Packed Space (m) 0.55

P ratio (-) 9.533 6.249 4.550 0.105 Cold Pinch Temp. (ºC) 30 -16.974 51.052 113.846 334.998 114.2 113.846 28.97 Length (m) 1.78 1.78 Tray/Packed Volume (m3) 0.9719

Table 4. The utilized mathematical equations for calculation of the exergy parameters of the hybrid system equipment. Device

Exergy destruction

Heat exchanger (Ghorbani et al., 2016; Ghorbani et al., 2019)

ExD =

∑(𝑚𝑒)

𝑖𝑛

―

∑(𝑚𝑒)

ε=1―

𝑜𝑢𝑡

Exergy efficiency ∑𝑛(𝑚∆𝑒) ∑𝑚(𝑚∆𝑒) 1 1 ― 𝑚 𝑛 ∑ (𝑚∆ℎ) ∑ (𝑚∆ℎ) 1 1

[{ } { } ] ℎ

Turbine(Jokar et al., 2017)

ExD =

∑(me)

Pump and compressor (Ahmadi et al., 2016)

ExD =

∑(me)

in

in

―W―

∑(me)

+W―

∑(me)

out

𝜀=

out

𝜀=

∑(𝑚𝑒)𝑖𝑛 ― ∑(𝑚𝑒)𝑜𝑢𝑡 ∑(𝑚𝑒)𝑜𝑢𝑡 ― ∑(𝑚𝑒)𝑖𝑛 𝑊𝑖𝑛 𝑇0

Expansion valve (Couper et al., 2009)

ExD =

∑(𝑚𝑒)

𝑖𝑛

―

∑(𝑚𝑒)

𝑐

𝑊𝑜𝑢𝑡

𝑒

∆𝑇

=

∫ 𝑇

𝑜𝑢𝑡

𝑇 ― 𝑇0 𝑑ℎ 𝑇 ∆𝑇 𝑒∆𝑇 𝑜 ― 𝑒𝑖

𝑒𝑃ℎ = 𝑒∆𝑇 + 𝑒∆𝑝, 𝜀 = 𝑒∆𝑝 ― 𝑒∆𝑝 𝑖

Mixer

ExD =

Tee Distillation column (Mohammadi et al., 2017) Cycle (Mehrpooya et al., 2018b)

∑(𝑚𝑒)

𝑖𝑛

ExD = (𝑚𝑒)𝑖𝑛 ―

ExD =

∑(𝑚𝑒) n

𝑖𝑛

―

𝜀=

― (𝑚𝑒)𝑜𝑢𝑡

∑(𝑚𝑒)

∑(𝑚𝑒)

𝑜𝑢𝑡

―

𝜀=

𝑜𝑢𝑡

∑𝑄

𝐾

(1 ―

𝑇0 𝑇𝐾

ExD tot = ∑k = 1ExD k n = number of components

𝜀= )

𝑜

(𝑚𝑒)𝑜𝑢𝑡

∑(𝑚𝑒)𝑖𝑛 ∑(𝑚𝑒)𝑜𝑢𝑡

(𝑚𝑒)𝑖𝑛 ∑(𝑚𝑒)𝑜𝑢𝑡 ― ∑(𝑚𝑒)𝑖𝑛 ∑𝑄𝐾 (1 ―

𝑇0

) 𝑇𝐾 𝑇𝑜𝑡𝑎𝑙 𝑖𝑟𝑟𝑒𝑣𝑒𝑟𝑠𝑖𝑏𝑖𝑙𝑖𝑡𝑦 𝑖𝑛 𝑐𝑦𝑐𝑙𝑒 𝜀=1― 𝑇𝑜𝑡𝑎𝑙 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑑 𝑝𝑜𝑤𝑒𝑟 𝑖𝑛 𝑐𝑦𝑐𝑙𝑒

Journal Pre-proof

Table 5. Assumptions and economic constants of the hybrid system. Parameter

Unit

Value

Plant life time

Year

25

Total annual operating hours of the system operation at full load

Hour

7300

Interest rate

%

12

Maintenance factor

-

1.06

Cost per exergy unit of electricity

($/GJ)

25

Cost per exergy unit of heat load (Mehrpooya et al., 2018b)

($/GJ)

2.056

Device HP LP HRVG GHEX REB EVA CHEX CON SUBC ABS SHEX VHEX REC COMP VAL1 VAL2 VAL3 TUR MIX TEE

Table 6. Exergoeconomic cost balance equations of the hybrid system equipment. Main equations Auxiliary equations 𝑐𝐻𝑃 = 25 $/𝐺𝐽 𝐶1 + 𝐶𝑊 ― 𝐻𝑃 + 𝑍𝐻𝑃 = 𝐶2 𝑐𝐿𝑃 = 25 $/𝐺𝐽 𝐶7 + 𝐶𝑊 ― 𝐿𝑃 + 𝑍𝐿𝑃 = 𝐶8 𝑐27 = 𝑐28 𝐶27 + 𝐶2 + 𝑍𝐻𝑅𝑉𝐺 = 𝐶3 + 𝐶28 𝑐 𝐶28 + 𝐶12 + 𝑍𝐺𝐻𝐸𝑋 = 𝐶29 + 𝐶13 29 = 𝑏28 𝑐4 = 𝑐5 𝐶4 + 𝑍𝑅𝐸𝐵 = 𝐶5 + 𝐶𝑅𝑄 𝐶26 + 𝐶𝑄 ― 𝐸𝑉𝐴 + 𝑍𝐸𝑉𝐴 = 𝐶23 None 𝑐24 = 𝑐25 𝐶24 + 𝐶17 + 𝑍𝐶𝐻𝐸𝑋 = 𝐶18 + 𝐶25 𝐶14 + 𝐶𝑊3 + 𝑍𝐶𝑂𝑁 = 𝐶15 + 𝐶𝑊4 𝑐14 = 𝑐15, 𝑐𝑊3 = 0 𝑐16 = 𝑐15 𝐶15 + 𝐶18 + 𝑍𝑆𝑈𝐵𝐶 = 𝐶16 + 𝐶19 𝐶7 + 𝐶𝑊1 + 𝑍𝐴𝐵𝑆 = 𝐶8 + 𝐶𝑊2 𝑐7 = 𝑐7𝑎, 𝑐𝑊1 = 0 𝑐20 = 𝑐21 𝐶9 + 𝐶20 + 𝑍𝑆𝐻𝐸𝑋 = 𝐶10 + 𝐶21 𝑐5 = 𝑐1 𝐶5 + 𝐶11 + 𝑍𝑉𝐻𝐸𝑋 = 𝐶12 + 𝐶1 𝑐14 = 𝑐20 𝐶5 + 𝐶11 + 𝐶𝑅𝑄 + 𝑍𝑅𝐸𝐶 = 𝐶14 + 𝐶15 + 𝐶𝐶𝑄 𝑐𝐶𝑂𝑀𝑃 = 25 $/𝐺𝐽 𝐶23 + 𝐶𝑊 ― 𝐶𝑂𝑀𝑃 + 𝑍𝐶𝑂𝑀𝑃 = 𝐶24 𝐶21 = 𝐶22 None 𝐶16 = 𝐶17 None 𝐶25 = 𝐶26 None 𝐶3 + 𝑍𝑇𝑈𝑅 = 𝐶4 + 𝐶𝑊 ― 𝑇𝑈𝑅 𝑐3 = 𝑐4, 𝑐𝑇𝑈𝑅 = 25 $/𝐺𝐽 𝐶19 + 𝐶22 = 𝐶7 None 𝑐 𝐶8 = 𝐶9 + 𝐶11 9 = 𝑐11

Journal Pre-proof

Table 7. The cost equations of hybrid system devices (Couper et al., 2009). Device Heat exchanger

Purchased equipment cost (PEC) functions ($) PEC = 8500 + 409 (A)0.8 𝑊𝑃

PEC = 800 ( 10 )0.26 (

Pump

1 ― 𝜂𝑃 𝜂𝑃

Compressor

PEC = 1810 (HP)0.71

Turbine

PEC = 378 (HP)0.81

Tower

Cb

=

)

PEC = 1.218 [Cb +NCt + Cp], N = number of trays Ct = 457.7 exp (0.1739D), D = diameter of tower 1.218 exp [6.629 + 0.1826 (ln W) + 0.02297 (ln W)2], W = weight of tower Cp = 300D0.7396 L0.7068, L = height of tower

Table 8. Eco-indicators for material types (Dincer et al., 2018). Material Eco-indicator 99 (mPts/kg)

Eco-indicator 99 (mPts/kg)

Steel

86

Steel high alloy

910

Steel low alloy

110

Cast iron

240

Copper

1400

Aluminum (primary material)

780

Table 9. Eco-indicator for materials of hybrid system devices (Cavalcanti and Reviews, 2017). milliPoints per weight Device name

Percent of materials

Weight function (mPts/kg)

Heat Steel (66%), Copper (33%)

519

WHE = 2.14 × Q0.7

Evaporator

Steel (100%)

86

WEva = 0.073 × Q0.99

Condenser

Steel (100%)

86

WCon = 0.073 × Q0.99

Exchanger

Journal Pre-proof

Steel (33%), Steel low alloy (45%), Compressor

131

Equations (25-26)

Cast iron (22%) Pump

Steel (35%), Cast iron (65%)

186

WP = 0.175 × ln (W) 1.06

Turbine

Steel (25%), Steel high alloy (75%)

201

WTur = 4.90 ×W0.73 Calculated by HYSYS

Column

Steel (100%)

86 software.

Table 10. Environmental impact balance equations of the hybrid system equipment. Device HP

Main equations 𝐵1 + 𝐵𝑊 ― 𝐻𝑃 + 𝑌𝐻𝑃 = 𝐵2

LP HRVG GHEX REB EVA CHEX CON SUBC ABS SHEX VHEX REC COMP VAL1 VAL2 VAL3 TUR MIX TEE

𝐵7 + 𝐵𝑊 ― 𝐿𝑃 + 𝑌𝐿𝑃 = 𝐵8 𝐵27 + 𝐵2 + 𝑌𝐻𝑅𝑉𝐺 = 𝐵3 + 𝐵28 𝐵28 + 𝐵12 + 𝑌𝐺𝐻𝐸𝑋 = 𝐵29 + 𝐵13 𝐵4 + 𝑌𝑅𝐸𝐵 = 𝐵5 + 𝐵𝑅𝑄 𝐵26 + 𝐵𝑄 ― 𝐸𝑉𝐴 + 𝑌𝐸𝑉𝐴 = 𝐵23 𝐵24 + 𝐵17 + 𝑌𝐶𝐻𝐸𝑋 = 𝐵18 + 𝐵25 𝐵14 + 𝐵𝑊3 + 𝑌𝐶𝑂𝑁 = 𝐵15 + 𝐵𝑊4 𝐵15 + 𝐵18 + 𝑌𝑆𝑈𝐵𝐶 = 𝐵16 + 𝐵19 𝐵7 + 𝐵𝑊1 + 𝑌𝐴𝐵𝑆 = 𝐵8 + 𝐵𝑊2 𝐵9 + 𝐵20 + 𝑌𝑆𝐻𝐸𝑋 = 𝐵10 + 𝐵21 𝐵5 + 𝐵11 + 𝑌𝑉𝐻𝐸𝑋 = 𝐵12 + 𝐵1 𝐵5 + 𝐵11 + 𝐵𝑅𝑄 + 𝑌𝑅𝐸𝐶 = 𝐵14 + 𝐵15 + 𝐵𝐶𝑄 𝐵23 + 𝐵𝑊 ― 𝐶𝑂𝑀𝑃 + 𝑌𝐶𝑂𝑀𝑃 = 𝐵24 𝐵21 = 𝐵22 𝐵16 = 𝐵17 𝐵25 = 𝐵26 𝐵3 + 𝑌𝑇𝑈𝑅 = 𝐵4 + 𝐵𝑊 ― 𝑇𝑈𝑅 𝐵19 + 𝐵22 = 𝐵7 𝐵8 = 𝐵9 + 𝐵11

Auxiliary equations 𝑚𝑃𝑡𝑠 𝐺𝐽

(Manesh et al., 2014) 𝑏𝐿𝑃 = 6206 𝑚𝑃𝑡𝑠/𝐺𝐽 𝑏27 = 𝑏28 𝑏29 = 𝑏28 𝑏4 = 𝑏5 None 𝑏24 = 𝑏25 𝑏14 = 𝑏15, 𝑏𝑊3 = 0 𝑏16 = 𝑏15 𝑏7 = 𝑏7𝑎, 𝑏𝑊1 = 0 𝑏20 = 𝑏21 𝑏5 = 𝑏1 𝑏14 = 𝑏20 𝑏𝐶𝑂𝑀𝑃 = 6206 𝑚𝑃𝑡𝑠/𝐺𝐽 None None None 𝑏3 = 𝑏4, 𝑏𝑇𝑈𝑅 = 6206 𝑚𝑃𝑡𝑠/𝐺𝐽 None 𝑏9 = 𝑏11

𝑏𝐻𝑃 = 6206

Table 11. The values of exergy of the hybrid system streams. Stream ID 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Physical exergy (kW) 2.45 3.73 80.71 44.48 18.31 13.74 1.03 1.76 1.06 20.56 20.56 0.70 13.47 22.67 22.68 27.38 24.23

Chemical exergy (kW) 772.46 772.46 772.46 772.46 772.46 2972.83 2972.83 2972.83 1785.10 1785.06 1785.10 1187.73 1187.73 1187.70 1187.73 1504.52 1504.52

Total exergy (kW) 774.91 776.18 853.17 816.94 790.77 2986.57 2973.85 2974.59 1786.15 1805.62 1805.65 1188.43 1201.20 1210.37 1210.41 1531.90 1528.74

Stream ID 18 19 20 21 22 23 24 25 26 27 28 29 W1 W2 W3 W4

Physical exergy (kW) 8.65 8.24 30.11 4.64 4.16 25.01 43.03 50.69 47.11 130.17 41.64 30.04 0.35 8.65 0.18 4.64

Chemical exergy (kW) 1504.52 1504.52 1470.74 1470.74 1470.74 109.55 109.55 109.55 109.55 111.07 111.07 111.07 346.38 346.38 173.19 173.19

Total exergy (kW) 1513.17 1512.76 1500.86 1475.38 1474.90 134.56 152.57 160.24 156.65 241.23 152.70 141.10 346.73 355.03 173.37 177.83

Table 12. The exergetic parameters of each device of the hybrid system. Equipment HP LP HRVG GHEX REB EVA CHEX CON SUBC ABS SHEX VHEX REC COMP VAL1 VAL2 VAL3 TUR

(kW) 1.63 0.97 88.53 11.6 26.17 22.1 1680.39 5.31 3041.91 12.72 25.48 15.86 32.82 29.55 1475.38 1528.74 160.24 36.23

(kW) 1.28 0.74 76.98 9.21 21.6 18.48 1673.4 3.15 3041.5 8.29 19.5 12.76 16.76 18.02 811.46 901.96 89.73 32.27

ε (%)

IP (kW)

𝑦𝐷 (%)

78.06 75.82 86.96 79.41 82.53 83.61 99.38 59.35 99.19 65.2 76.54 80.46 51.08 60.98 55 59 56 89.08

0.08 0.06 1.51 0.49 0.8 0.59 0.03 0.88 0 1.54 1.4 0.61 7.85 4.5 0.22 0.38 1.58 0.43

0.43 0.28 13.85 2.86 5.48 4.34 8.37 2.59 0.49 5.31 7.17 3.72 19.25 13.83 0.58 1.12 4.30 4.74

(kW) 0.35 0.23 11.55 2.39 4.57 3.62 6.98 2.16 0.41 4.43 5.98 3.1 16.05 11.53 0.48 0.93 3.58 3.96

Table 13. The values of exergy, unit exergy cost and unit exergy environmental impact of the hybrid system. Stream 𝐸 (kW)

c ($/GJ)

ID 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

774.91 776.18 853.17 816.94 790.77 2986.57 2973.85 2974.59 1786.15 1805.62 1805.65 1188.43 1201.20 1210.37 1210.41 1531.90

17

1528.74

20.61 20.63 20.61 20.61 20.61 238.00 238.00 237.95 237.95 238.80 237.95 235.82 234.31 236.15 236.15 236.15 236.29

$ 𝐶( ) ℎ

b (Pts/GJ)

57.49 57.65 63.30 60.61 58.67 2558.84 2547.94 2548.04 1530.02 1552.26 1546.73 1008.94 1013.25 1028.97 1029.00 1302.31 1300.43

5.53 5.53 5.53 5.53 5.53 35.54 35.54 35.54 35.54 35.65 35.54 35.24 35.01 35.24 35.24 35.24 35.26

𝐵 (𝑃𝑡𝑠/ℎ) 15.42 15.45 16.97 16.25 15.73 382.16 380.54 380.56 228.51 231.76 231.01 150.75 151.41 153.56 153.57 194.36 194.07

Stream ID 18 19 20 21 22 23 24 25 26 27 28 29 W1 W2 W3 W4

𝐸 (kW) 1513.17 1512.76 1500.86 1475.38 1474.90 134.56 152.57 160.24 156.65 241.23 152.70 141.10 346.73 355.03 173.37 177.83

c ($/GJ) 239.38 239.55 236.15 236.15 236.22 164.48 138.99 138.99 142.17 15.90 15.90 15.90 0.00 17.96 0.00 9.43

b

$ 𝐶( ) ℎ

(Pts/GJ)

1317.42 1317.56 1286.39 1286.04 1276.34 873.59 737.99 67.33 78.09 9.17 8.97 13.81 0.00 11.47 0.00 3.20

35.79 35.80 35.24 35.24 35.25 43.08 36.79 36.79 37.63 4.73 4.73 4.73 0.00 1.28 0.00 0.64

𝐵 (𝑃𝑡𝑠/ℎ) 196.99 196.92 191.98 191.93 190.48 228.82 195.35 17.82 20.67 2.73 2.67 4.11 0.00 1.64 0.00 0.41

Table 14. The outcomes of exergoeconomic evaluation of the hybrid system. Device HP LP HRVG GHEX REB EVA CHEX CON SUBC ABS SHEX VHEX REC COMP TUR

𝑐𝐹 ($/GJ) 25.00 25.00 15.90 15.90 20.61 278.00 138.99 199.31 236.15 238.00 236.15 20.61 222.92 25.00 20.61

𝑐𝑃 ($/GJ) 33.73 35.55 20.39 130.27 28.13 280.37 322.37 236.15 285.52 384.09 317.36 117.06 414.5 254.5 25.00

𝐶𝐷 ($/h) 0.03 0.02 0.66 0.14 0.34 3.62 3.49 1.83 0.35 3.79 5.08 0.23 1.32 1.04 0.29

𝑍 ($/h) 0.008 0.007 0.583 0.545 0.246 0.369 0.531 0.526 0.578 0.570 0.580 0.585 2.812 0.669 0.217

𝐶𝐷 + 𝑍 ($/h) 0.04 0.03 1.24 0.68 0.58 3.99 4.02 2.36 0.92 4.36 5.66 0.81 4.14 1.71 0.51

𝑟 (%) 34.91 42.21 28.22 719.13 36.49 0.85 131.94 18.48 20.9 61.39 34.39 467.99 85.94 918 21.31

𝑓 (%) 19.50 24.44 46.84 79.95 42.01 9.17 13.19 22.27 62.57 13.07 10.25 71.78 67.98 39.19 42.49

Table 15. The outcomes of exergoenvironmental assessment of the hybrid system. Device HP LP HRVG GHEX REB EVA CHEX CON SUBC ABS SHEX VHEX REC COMP TUR

𝑏𝐹 (mPts/GJ)

𝑏𝑃 (mPts/GJ)

𝐵𝐷 (mPts/h)

𝑌 (mPts/h)

𝐵𝐷 + 𝑌 (mPts/h)

𝑟𝑏 (%)

𝑓𝑏 (%)

6206.00 6206.00 4727.57 4727.57 5526.10 5100.00 36791.21 25346.37 35242.33 35544.71 35242.33 5526.10 111285.14 6206.00 5526.10

7976.29 8230.74 5485.50 20092.20 6707.76 5320.00 55224.26 35242.33 45136.33 54921.15 46263.00 6682.63 623486.81 7203.5 6206.00

8.01 5.24 196.52 40.64 90.95 66.49 924.69 273.81 51.56 566.31 758.33 61.66 6430.76 257.57 78.68

0.136 0.120 13.539 4.190 0.979 0.654 7.700 7.740 1.328 12.179 9.508 7.093 25.200 0.159 0.315

8.15 5.36 210.06 44.83 91.93 67.15 932.39 281.55 52.89 578.49 767.84 68.75 6455.96 257.73 79.00

28.53 32.63 16.03 325.00 21.38 4.31 50.10 28.08 28.07 54.51 31.27 20.93 460.26 16.07 12.30

1.67 2.23 6.45 9.35 1.07 0.97 0.83 2.75 2.51 2.11 1.24 10.32 0.39 0.06 0.40

Table 16. The comparison between the economic and exergetic parameters of some devices of this investigation and Reference (Mosaffa et al., 2016). Name of device Compressor Evaporator Condenser Cascade heat exchanger

f (%) 39.19 9.17 22.27 13.19

Values of the Paper ε (%) 60.98 83.61 59.35 99.38

Values of the Reference f (%) 56.53 45.03 66.52 3.85

ε (%) 55.83 79.63 3.76 87.21

Table 17. The comparison of technical parameters of this process with previous investigations. This study

Ref 1. (Pourfayaz et al., 2019)

Ref 2. (Mosaffa et al., 2016)

Ref 3. (Khani et al., 2016)

Overall exergy efficiency (%)

69

29

31.52

60

Column exergy efficiency (%)

51.08

35.53

29

-

Overall exergy destruction rate (kW)

83.4

820

222.5

417.6

Figures

Figure 1. PFD of the hybrid system, which is simulated by Aspen HYSYS simulator.

Figure 2. Expected relationships among capital investment, construction-of-component related environmental impact and irreversibility, for the kth device of a thermodynamic system.

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Figure 3. Percentile contributions of the heat exchangers of the hybrid system to exergy destruction rate.

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Figure 4. Percentile contributions of the devices of the hybrid system to exergy destruction rate.

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Figure 5. Exergy destruction pie chart in the subsystems of the hybrid system.

Figure 6. Sankey diagram of the hybrid system for total exergy balance.

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Figure 7. The exergetic efficiency of each device of the hybrid system.

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Figure 8. Comparison between the two types of cost (exergy destruction and the component itself) for hybrid system equipment.

Figure 9. Comparison between the two types of environmental impact (exergy destruction and the component itself) for hybrid system devices.

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Figure 10 (a). Interaction between the three variables (𝑍‚ 𝑌‚ 𝑎𝑛𝑑 𝐸𝐷) versus the variation of isentropic efficiency for COMP compressor.

Figure 10 (b). Interaction between the three variables (𝑍‚ 𝑌‚ 𝑎𝑛𝑑 𝐸𝐷) versus the variation of pressure ratio for COMP compressor.

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Figure 11 (a). Interaction between the three variables (𝑍‚ 𝑌‚ 𝑎𝑛𝑑 𝐸𝐷) versus the variation of isentropic efficiency for TUR turbine.

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Figure 11 (b). Interaction between the three variables (𝑍‚ 𝑌‚ 𝑎𝑛𝑑 𝐸𝐷) versus the variation of pressure ratio for TUR turbine.

Figure 12 (a). Interaction between the three variables (𝑍‚ 𝑌‚ 𝑎𝑛𝑑 𝐸𝐷) versus the variation of minimum temperature approach for HRVG heat exchanger.

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Figure 12 (b). Interaction between the three variables (𝑍‚ 𝑌‚ 𝑎𝑛𝑑 𝐸𝐷) versus the variation of inlet pressure for HRVG heat exchanger.

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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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

Evaporation temperature of this system is -54.62 °C.



Overall exergy destruction rate is obtained by 83.4 kW.



Evaporator has the lowest exergoeconomic factor (f).



Largest value of overall cost rate is related to the SHEX (5.66 $/h).