Multi-objective design optimization of a multi-generation energy system based on geothermal and solar energy

Energy Conversion and Management 205 (2020) 112426

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Multi-objective design optimization of a multi-generation energy system based on geothermal and solar energy

T

Seyed Mojtaba Alirahmia, Sajjad Rahmani Dabbagha, Pouria Ahmadia, , Somchai Wongwisesb,c ⁎

a

Advanced Energy Systems Lab (AESL), School of Mechanical Engineering, College of Engineering, University of Tehran, P.O. Box 11155-4563, Tehran, Iran Fluid Mechanics, Thermal Engineering and Multiphase Flow Research Lab. (FUTURE), Department of Mechanical Engineering, Faculty of Engineering, King Mongkut’s University of Technology Thonburi, Bangmod, Bangkok, Thailand c The Academy of Science, The Royal Society of Thailand, Sanam Suea Pa, Dusit, Bangkok 10300, Thailand b

ARTICLE INFO

ABSTRACT

Keywords: Multi-generation system Organic Rankine cycle Geothermal Parabolic trough solar collector Exergoeconomic analysis

In this paper, a multi-generation system based on geothermal energy and parabolic trough solar collectors is proposed for the simultaneous generation of power, cooling, freshwater, hydrogen, and heat. Power is generated by a combined steam Rankine cycle and an organic Rankine cycle. Ten different refrigerants are used for the organic Rankine cycle, among which R123 has the best performance. In addition, four fluids are used as the geothermal fluid, among which Therminol 59 has recorded the best performance. Solar intensity, geothermal mass flow rate, geothermal fluid temperature, and steam turbine inlet pressure have proven to be the most prominent parameters affecting the exergy efficiency and cost. After analyzing the proposed system from the energy, exergy and exergoeconomic points of view, a multi-objective-optimization-genetic-algorithm is applied for improving the performance of the system. In order to apply the multi-objective optimization, Engineering Equation Solver and MATLAB software are linked together by the Dynamic Data Exchange method. According to the obtained results. The results show that the exergy efficiency of the system and the total unit cost respectively reach to 29.95% and 129.7 $/GJ at the optimum point.

1. Introduction Design, exergoeconomic analysis, and optimization of co-generation energy systems based on renewable energies have gained significant importance recently due to the adverse environmental repercussions pertinent to fossil fuels [1]. Regarding exergoeconomic analysis, traditional methods of evaluating multi-generation systems performance from thermodynamics and economic perspectives discretely fail to offer comprehensive data for designers and engineers, due to the intricate characteristics of these systems [2]. As a result, exergoeconomic analysis is introduced to draw a meaningful correlation between economic and thermodynamics standpoints by simultaneously analyzing them as a whole, and providing useful information for optimization purposes [3]. Different factors affect the performance of a multi-generation system since many different variables are involved in each system. Thus, optimization is considered as a pivotal stage in the design of cogeneration systems in order to keep a balance between said factors. Different algorithms are available for optimization, each of which has some advantages and drawbacks, such as NSGI-II and IBEA [4]. To shed light on the arrangement of components in the multi-

⁎

generation system and their connections, some information is worth mentioning. Solar energy, as an easy to access and clean resource, has some drawbacks which make it difficult to harness electricity incessantly, as it fluctuates with regards to several factors. Fortunately, this predicament can be surmounted by combining solar methods with storage systems and diverse energy sources [5]. According to literature, 140 MJ/kg of energy can be stored by hydrogen, which makes it an efficacious material compared to representative fuels with an average energy density of 50 MJ/kg. Not to mention that the byproduct of burning hydrogen is water, hence it is an environmentally friendly energy-storing procedure [6]. Additionally, geothermal as clean and sustainable energy source with minimum pollutant emissions can afford 2800 years of consistent power only if 1% of entire existing resources could be utilized [7]. This energy could be used by different methods including Rankine cycles. However, Since the Rankine cycles are not ideal, a considerable amount of input energy is wasted in different parts, especially in the condenser. Hence, this energy can be used as a low-grade thermal source for other heat recovery cycles such as an organic Rankine cycle (ORC) [8]. Using organic fluids not only can enable us to harness wasted heat in relatively low temperatures, but can

Corresponding author. E-mail address: [email protected] (P. Ahmadi).

https://doi.org/10.1016/j.enconman.2019.112426 Received 17 October 2019; Received in revised form 19 December 2019; Accepted 20 December 2019 0196-8904/ © 2019 Elsevier Ltd. All rights reserved.

Energy Conversion and Management 205 (2020) 112426

S.M. Alirahmi, et al.

Nomenclature

Aa Ae C C CP COPC D Ex E ECOPC Ex ExD F F1 FR Gb hx hfi hhv h2 j j0 Jiref K k kw L M mx Nx ncs ncp ne nv P Px Qx R RR S sx Tx TCF T S UL V V0

Vohm W Wx w X Z

Aperture area [m2] RO unit element area [m2] Specific exergy cost [$/GJ] Cost rate [$/h] Specific heat of air at constant pressure [kJ/kg.K] Total cooling coefficient of performance Membrane thickness [m] Exergy input [kW] Energy input [kW] Total cooling exergetic cofficient of performance [\% ] Exergy rate [kW] Exergy destruction [kW] Faraday constant [C/mol] Collector efficiency factor Heat transfer factor Solar radiation intensity [W/m2] Specific enthalpy at point x [kJ/kg] Heat transfer coefficient inside the receiver High heating value of hydrogen [kJ/kg] Current density [A/m2] Exchange current density [A/m2] Pre - exponential factor [A/m2] Ratio of specific heats (CP/CV ) Thermal conductivity[kW m] Membrane water permeability Collector length [m] Mass [kg] Mass flow rate at point x [kg/s] Outlet flow rate of fluid x [kg/s] Number of collectors in series Number of collectors in parallels RO unit number of member elements RO unit number of pressure vessels Osmosis pressure [kPa] Pressure at point x [bar] Heat transfer rate at point x [kW] Overall ohmic resistance Recovery ratio Absorbed solar radiation Specific entropy at point × [kJ/kg.K] Temperature at point × [°C] Temperature correction factor Thermal energy demand [J mol H2] Solar collector overall heat loss coefficient Overpotential[V] Reversible potential [V]

H G (x ) r

(x )

C P

Ohmic overpotential of the electrolyte [V] Net output power [kW] Power consumption at point x [kW] Collector width[m] Salt concentration[g/kg] Cost rate of the components [$/h] Absorptivity of receiver Correction factor for diffuse radiation Internal heat exchanger coefficient of performance Total energy required for electrolysis [kJ/kg] Change in Gibbs free energy [J/mol] Ionic conductivity of the membrane Isentropic efficiency Receiver efficiency Water content at location x Density [kg/m3] Transmissivity of the cover glazing Effective transmissivity of the parabolic trough collector

Subscripts

0 a Abs av act b c Con d DWH electric Evp f Gen H2 H2 O HEX HP in out p reacted ri s Tot Tur

also increase the effective lifespan of turbine blades by roughly 10 years, by having a superheated fluid after expansion and avoiding two-phase fluid in the turbine [9]. When the temperature of return fluid is high enough in geothermal power plants, this heat can be used for domestic heating or to drive absorption chillers [10]. Undoubtedly, apart from environmental issues, the unprecedented surge of demand for drinkable water is one of the most paramount challenges nowadays. Statistically speaking, 3.5 million people lose their lives yearly as a consequence of the shortage of clean water, and associated problems with sanitation [11]. In this regard, geothermal power plants can partially address this concern since 20 L/MWh of water is used to produce power in these plants, compared to 1000 L/ MWh of coal-based power plants [12]. On the other hand, desalination technologies, such as reverse osmosis (RO), seem feasible approaches to address this problem [13]. However, RO systems require a substantial

Dead state Anode Absorber Average Activation Brain flow Cathode Condenser Distilled water Domestic Water Heater Electricity Evaporator Feed flow Generator Hydrogen Water Heat Exchanger High pressure Inlet Outlet Pump Entering water of PEM electrolyzer Inlet receiver Isentropic Total Turbine

amount of electrical energy supply to provide the needed pressure on feed water. As a result, it is more cost-efficient to satisfy the RO system’s electrical demand by sustainable technologies [14]. All in all, merging of combined cooling, heating and power (CCHP) systems with novel renewable energy sources and storing technologies bears numerous benefits to the resulted system, including diminishing CO2 emission and higher energy efficiency [15]. In this regard, Ahmadi et al. [16] proposed a co-generation where the ocean’s energy is harnessed by an energy conversion system; additionally, the system was equipped with solar collectors, a polymer electrolysis membrane (PEM) electrolyzer, a single effect absorption chiller, and an RO water desalination system. It is pointed out that the total cost rate of the system and exergy efficiency as a result of multiobjective optimization is 154 $/h and 60%, respectively. Abbasi et al. [17] proposed a solar-driven system with a desalination unit, and 2

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S.M. Alirahmi, et al.

conducted an exergoeconomic optimization. The result of exergy efficiency was about 21.19%. Cardemil et al. [18] examined different combinations of methods of solar and geothermal. It showed that generated power is greater when solar energy superheats geothermal fluid prior to exchange heat with working fluid of power generation cycle. Ahmadi et al. [19] studied the thermodynamic simulation of a flat plate solar collector attached to an ocean thermal energy conversion (OTEC) cycle and a PEM electrolysis. They concluded that the very integrated OTEC cycle can reach an exergy efficiency of 22%. Furthermore, they demonstrated that by an increase in solar radiation, the cycle’s total exergy destruction decreases. As a result, exergy efficiency and the rate of hydrogen production in the electrolyzer. Luqman et al. [20] studied wind and solar-based systems with capability of desalination, cooling, electricity generation, and hydrogen production. The system had a freshwater and hydrogen production rate of 828 m3/day and kg/day. Furthermore, exergy and energy efficiency were 34% and 50% respectively. Kianfard et al. [21] obtained a net cost of 4.257 $/kg and 32.73 cents/m3 for production of hydrogen and water desalination in a combined system which employs an organic Rankine cycle (ORC) with dual fluid, a RO water desalination section, and a PEM electrolyzer unit. Siddiqui et al. [22] evaluated a solar and geothermal based system for cooling, hydrogen production, and electricity generation with energy and exergy efficiency of 19.6% and 19.1% respectively. Yari [23] investigated exergy destruction, first and second-law efficiency in an assortment of ORC cycles such as an organic cycle with an internal heat exchanger (IHE), regenerative ORC, and combined flash binary cycle. The highest first-law efficiency is calculated to be 15.35% based on the input energy to an ORC cycle in the regenerative binary cycle equipped with an IHE and the operating fluid of R123. Moreover, flash-binary cycle with R123 has been estimated to have a maximum first-law efficiency of 11.81%. Also, it is showed that an ORC with an IHE and R123 as the working fluid can reach its zenith first-law efficiency which is 7.65%. Keshavarzzadeh and Ahmadi [4] proposed a novel CCHP system encompassing an ORC cycle, a proton exchange membrane electrolyzer (PEME) section, an absorption chiller, and a thermal-storage section.

They drew a comparison between the indicator-based evolutionary algorithm (IBEA) optimization algorithm and non-dominated sorting genetic algorithm (NSGA-II), and they concluded that despite the fact that exergy efficiency increased by 2.5%, the overall cost rate declined by 7% in the IBEA method. Atiz et al. [24] proposed a geothermal system for low-temperature resources and solar energy. Using n-butane as the cyclic fluid, they calculated 6.92% and 21.06% as the total energy and exergy efficiencies of the system, respectively. Akrami et al. [25] modeled a multi-generation system comprised of an ORC, an absorption chiller, a PEM electrolyzer, and a water heater. Under certain conditions, they monitored 34.98% and 49.17% for the energy and exergy efficiencies, respectively. Hashemian and Noorpoor [26] studied thermodynamic, exergoeconomic, and exergoenvironmental analysis of a multi-generation system, operation with the energy of solar and biomass. Using genetic algorithm and finding optimum working points, they concluded that 0.84 $/s, 14%, and 82.4% are attainable for the proposed system for overall product cost rate, exergy, and energy efficiency, respectively. In the present paper, a novel multi-generation system is developed, simulated, and analyzed in terms of energy, exergy, and exergoeconomic. The proposed system consists of a geothermal pit, linear parabolic solar planes, a steam cycle, a regenerative organic Rankine cycle with an IHE, an absorption chiller, a PEM electrolyzer, and a reverse osmosis unit. According to previous works and the present study, a heat exchanger is used in hybrid systems of PTC and geothermal energy. However, multi-objective optimization for a multigeneration system wherein the geothermal fluid enters the PTC directly has never been addressed to this day. The following is a summary of the primary objectives and innovations of this paper:

• Tailoring a heat exchanger between the steam cycle and the ORC for increasing the productivity of the system and confining energy loss. • Considering various geothermal working fluids for the solar and geothermal cycles.

Fig. 1. Schematic diagram of the multi-generation energy system based on geothermal and solar. 3

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• Producing fresh water and hydrogen from the novel integrated energy system. • Applying multi-objective optimization to determine the optimal

Table 1 Input parameters for the system modeling. Parameters

design parameters.

Value

Unit

2314 0.07 0.066 3.82 180 300 16 850 0.96 0.94 0.96 0.95 5.76 12.27

J/kg°C m m W/m2°C °C W/m2 °C W/m°C W/m2 – – – – m m

1500 5 501.2 35 0.8

kPa °C kPa °C –

45 7 0.85 0.3 42

g/kg – – – –

Jaref

101.325 101.325 80 76 18 14 10 100 1.7 × 105

kPa kPa °C kJ/mol kJ/mol – – μm A/m2

Jcref F

4.6 × 103

A/m2

96.486

C/mol

PTC [27,28]; Specific heat of the working fluid (CP, C) Receiver outside diameter (Do,r) Receiver inside diameter (Di,r) Collector heat loss coefficient (UL) Receiver inlet temperature (Tri) Heat transfer coefficient inside the receiver (hfi) Thermal conductivity of the receiver (k) Total solar radiation Transmissivity of the cover glazing Effective transmissivity of PTC Absorptivity of receiver Correction factor for diffuse radiation Single collector width Single collector length Steam & organic Rankine cycle P7 Pinch point temperature of the Steam generator P12[extraction] Tc εIHE Reverse osmosis [29,30]; Salinity43 Number of elements Fouling factor Recovery ratio Number of pressure vessels PEM electrolysis [21,31]; Po2 PH2 TPEM Eact,a Eact,c

2. System description Fig. 1 shows the schematic diagram of an integrated multi-generative system, presented in this paper, based on geothermal and solar energy, which comprises a PEM electrolyzer, an RO desalination unit, an absorption cooler system, a steam cycle, and an ORC cycle. The operating fluid in the steam cycle absorbs the required heat from a flow of hot steam to run a turbine, using a steam generator at point 2. The mentioned hot steam is obtained from production wells and absorbs further heat in solar collectors. Then, the exited hot water from Steam generator, at point 3, is used in order to exchange its remaining thermal energy to preheat the feed water of a PEM electrolyzer at point 37 via a domestic water heater (DWH), and to drive the generator of an absorption cooling system at point 4. Also, the ORC cycle consists of an open feed-organic heater (OFOH) and IHE to enhance the efficiency of the system. This cycle acquires the necessary heat through a heat exchanger at point 11. In the other part of the system, the generated electric energy from both the Rankine cycle and the steam cycle is collected to be used in a reverse osmosis desalination system, and a PEM electrolyzer to produce hydrogen for later uses. At point 46, a small turbine is placed to harvest the electricity from the RO unit’s brine water, which is going to be discharged back to the sea. Fig. 2 represents S-T diagrams of the aforementioned processes. 3. Thermodynamic analysis In order to model the system, some inputs are needed. Input values for different parameters are listed in Table 1 [21,27–31].

a c

D

3.1. Steam cycle and organic Rankine cycle In this paper, 4 different geothermal fluids namely Therminol 59, Therminol VP1, Syltherm 800, and Marlotherm SH, are compared to determine which one has better performance. This system uses a binary geothermal cycle where the geothermal fluid from production wells with an initial temperature of roughly 180 °C (state 1) gain extra heat from a parabolic trough collector (PTC) and reaches the temperature of approximately 380 ℃ (state 2). Then, this fluid transfers its thermal energy to the operating fluid of the steam cycle, which is water in this case, in order to drive the steam turbine. Steam enters a heat exchanger after the turbine to transfer its heat to an organic fluid. A heat exchanger, a turbine, a pump, a condenser, an OFOH, and an IHE are

constituents of the ORC. IHE unit recovers heat from the low-pressure steam after the turbine (state 13). The saturated vapor enters the turbine (state 11) and is expanded isentropically in an ideal ORC cycle (state 12). An OFOH mixes organic fluid in pump’s discharge with the portion of steam extracted from the turbine in intermediate pressure (state 18). The rest of the vapor expands in the turbine to reach the condenser pressure (state 13) [32]. The equation presenting energy balance in the steam generator is as:

Fig. 2. S-T diagrams of processes in (a) the steam cycle and (b) the ORC. 4

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S.M. Alirahmi, et al.

m2 (h2

h3) = m6 (h7

(1)

h 6)

where, according to Table 1, PEM temperature is 80 °C. When hydrogen ions move across the membrane, the membrane’s resistance brings about ohmic over-potential in the proton exchange membrane. Different factors are responsible for the ionic resistance of the membrane, such as humidification degree, thickness, and temperature of the membrane. The membrane’s local ionic conductivity can be calculated by experimental equation [35]:

The following equation describes the energy balance in the heat exchanger, between the steam cycle and the ORC:

m8 ( h 8

h9) = m10 (h11

(2)

h10)

The proposed cycle is designed based on mass balance, energy, and isentropic efficiency. Also, Engineering Equation Solver (EES) is used to solve equations, conduct exergy and exergoeconomic analysis, and to determine thermodynamic properties at all points. The subsequent assumptions are made in this paper:

[ (x )] = [0.5139 (x )

• This system operates under steady-state conditions. • Isentropic efficiency is proposed for pumps and turbines. • Pressure drop in pipelines and heat exchangers are neglected. • The fluid enters the turbine as saturated vapor (x = 1), and as saturated liquid (x = 0) in the pump inlet. • The isentropic efficiency of the pump and the turbine, are assumed

Q

W =

(mx )out

(mh)out

(mh)in

J 2J0, i

2

+1 ,

i = a, c

Eact , i , RT

(3)

J0, i = Jiref exp

(4)

For supplementary information for PEM electrolysis, visit ref. [19,31,35].

(5)

i = a, c

(17)

3.4. Parabolic trough collector Geothermal fluid gains more heat passing through the PTCs, as shown in Fig. 1. The useful energy-producing rate by collectors can be calculated as [27]:

Qu = ncp ncs FR [SAa

Ar UL (Tri

T0)]

(18)

where S can be written as [36]:

As can be seen in Fig. 1, an electrical generator provides power for reactions in the electrolyzer. Having preheated in the domestic water heater, water enters the electrolyzer to produce hydrogen. The resulted hydrogen exits the cathode and loses its heat to reach the ambient temperature. Subsequently, the mixture of oxygen and water exits anode in order to separate oxygen, and the remaining water is used again in the electrolyzer. The required energy for the electrolysis process can be determined by:

C P

(20)

mc Cp, c Ar UL

1

exp 1

1 UL

+

Do, r hfi

Ar UL F1 mc Cp, c

(21)

)

(22)

UL

+

(

Do, r 2k

ln

Do, r Di, r

The surface of the aperture is [36]:

A a = (w

Do, r ) L

(23)

3.5. Reverse osmosis desalination An RO system usually takes in seawater at the first stage of the process, then the water goes through a pre-treatment procedure, and finally, the water enters the main RO system [5]. Using the mass flow rate of distillate m45 and the recovery ratio (RR), the feed flow rate m43 can be calculated:

(9)

also, ref. [35] expresses V as: (10)

where V0 is calculated by Nernst equation:

298)

=

F1 =

The electrolyzer rate of electrical energy input can be obtained by [19]:

V = V0 + Vact , a + Vact , c + Vohm

(19)

FR =

(8)

Ex electric = Eelectric = JV

r

The following equations can be used to determine FR and F1:

where the properties of oxygen, hydrogen, and water are presented in thermodynamic tables [32]. Hydrogen’s outlet flow rate can be calculated by [35]:

J = NH2 O, reacted 2F

S = Gb r

(7)

H= G+T S

8.5 × 10 4 (TPEM

1 RT 1 = ln + 2J0, i F 2J0, i

1

(16)

3.3. PEM electrolysis

V0 = 1.229

(14) (15)

RT sinh F

Vact , i =

Further information for analyzing each element of the absorption chiller is available in sources [33,34].

NH2, out =

0

An electrode’s activation over-potential and exchange current density equation can be written as follows [35]:

(6)

h29)

(13)

c

Vohm = JRPEM

The cooling capacity of the absorption chiller is obtained by:

Qcooling = m (h30

(12)

Also, Vohm can be defined using the following equation:

Considering each component of the absorption chiller system as a control volume, mass balance, mass conservation, momentum, and the first and the second law of thermodynamics equations are employed in order to analyze the single-effect absorption chiller. Mass balance in steady-state conditions and constant flow are as follows [33]:

(mx )in =

x+

1 T

dx [ (x )]

L

RPEM =

3.2. Absorption chiller

mout

c

D

1 303

As a result, the total ohmic resistance can be described by [35]:

to be 90% and 80%, respectively.

min =

a

(x ) =

0.326] exp 1268

m43 =

(11) 5

m45 RR

(24)

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S.M. Alirahmi, et al.

Also, the volume flow rate of brine water is expressed by:

m46 = m43

Table 3 Formulation of cost balance and auxiliary equations for each component.

(25)

m45

Auxiliary equation

The salt concentration of distilled water and rejected water and the average salt concentration are as follows, respectively [30]:

Xd = Xf × (1

Xb =

Xav =

(26)

SR)

m43 × Xf

m45 × Xd (27)

m46 m43 × Xf

m45 × Xb (28)

m45

The equation for the factor of temperature correction is [30]:

1 1 TCF = exp 2700 × + Tk 298

(29)

The following equation determines water permeability of membrane:

kw =

6.84 × 10

8

× (18.6865 Tk

(0.177 × Xd ))

Three equations below calculate the average osmosis pressure on the feed side, net osmosis pressure across the membrane, and the net pressure difference through the membrane, respectively [30]:

Pav = 37.92 × (Xf + Xb)

(31)

Pnet = Pav

(32)

75.84 × Xd

Component PTC field

c1 = c2 , csun = 0

Csun + C1 + ZPTC = C2

c 2 = c3

C2 + C6 + ZS, ge = C3 + C7

c 7 = c8

C7 + ZSteam, T = C8 + CSteam, T

c11 = c12 , c11 = c13

C11 + ZORC, T = C12 + C13 + CORC,T

c8 = c9

C8 + C10 + ZHE = C11 + C9

Steam generator Steam turbine

cP1 = cSteam, t

C9 + CP1 + ZP1 = C6

cP 2 = cORC , t

C18 + CP 2 + ZP 2 = C10

cP 3 = cORC , t

C15 + CP3 + ZP3 = C16

c14 = c15 , c19 = 0

C14 + C19 + Zcond = C15 + C20

c3 = c4

C3 + C37 + ZDWH = C38 + C4

c39 = c38 , cPEM = cORC, t

C39 + CPEM + ZPEM = C40 + C42

N A

C43 + ZRO = C46 + C45

ORC turbine Heat exchanger Pump 1 Pump 2 Pump 3

Condenser 1

C4 + C23 + ZG, LiBr = C24 + C27 + C5

Domestic water heater PEM electrolyzer RO desalination unit Generator

c27 = c28

C27 + C31 + ZC, LiBr = C28 + C32

Condenser 2

c29 = c30

C29 + C30 + ZE, LiBr = C30 + C34

C24 Ex 24

(30)

Cost balance

c4 C23 Ex 23

C26 + C30 Ex 26 + Ex 30

CP , LiBr WP , LiBr

=

c24 = c25

= c5 =

=

C27 Ex 27

C21 Ex 21

CORC , t WORC , t

C23 Ex 23

Evaporator

C26 + C30 + C35 + ZA,LiBr = C21 + C36

Absorber

C21 + CP, LiBr + ZP, LiBr = C22

Pump 4

C24 + C22 + ZHEX , LiBr = C23 + C25

HEX

Table 2 Energy balance and Exergy destruction rate equations for the system’s elements. Component Parabolic trough collector Steam generator Domestic water heater Steam turbine ORC turbine Heat exchanger

Energy balance equations

m1 h1 + Qu = m2 h2

QS, ge = m6 (h7

WT , ORC = m11 (h11 T = (h11

Pump 3 Open feed organic heater Internal heat exchanger Condenser1 LiBr generator LiBr absorber LiBr condenser2 LiBr evaporator LiBr pump4

h 9) = m10 (h11

y )(h12 h12s )

Ex3

ExD, DWH = Ex3 + Ex37

h37)

h8 ) h8s )

h12) + (1 h12) (h11

Ex1 + Qsolar (1

ExD, S ,ge = Ex2 + Ex 6

h3)

h4 ) = m37 (h38

WT , Steam = m7 (h7 h8) (h7 T = (h7

m8 (h8

ExD, PTC = Ex2

h6) = m2 (h2

QDWH = m3 (h3

Pump 1 Pump 2

Exergy destruction rate equations

h13 )

h10)

Ex 4

Ex8

WT , Steam

ExD, T ,ORC = Ex11

Ex12

Ex13

ExD, HE = Ex8 + Ex10

Ex 9

ExD, P1 = Ex 9

P1

WP 2 = m18 (h10 h18 ) = v18 (P10 P18) (h10 h18)

ExD, P 2 = Ex18

Ex10 + WP 2

P2

WP3 = m15 (h16 h15 ) = v15 (P16 P15) (h16 h15)

ExD, P3 = Ex15

Ex16 + WP3

P3

h18 h12

h17 h17

QIHE = (h13 = (T13 QC = m14 (h14 (m 4 h4

ExD, IHE = Ex13 + Ex16

h15) = m19 (h20

h19)

m5 h5) + m23 h23 = m27 h27 + m24 h24

Ex11

ExD, C = Ex14 + Ex19

Ex18

Ex14 Ex20

Ex15

Ex5

Ex24

Ex27

Qabs = m30 h30 + m26 h26 + m21 h21

ExD, ABS = Ex26 + Ex30 + Ex35

Ex36

Ex21

QC, LiBr = m27 h27

ExD, C , LiBr = Ex27 + Ex31

Qeva, LiBr = m29 h29

m28 h28

ExD, G, LiBr = Ex 4 + Ex23

Ex17

ExD, eva, LiBr = Ex29 + Ex33

m30 h30

WLiBr , P = m21 (h22 h21 ) P21) (h22 h21) LiBr , P = v21 (P22

Ex32

Ex22 + WLiBr ,P

h28 = h29

ExD, valve1 = Ex28

Ex29

h25 = h26

LiBr HEX

ExD, valve2 = Ex25

Ex26

m22 (h23

PEM electrolyzer

WPEM = m39 h39

RO pump

WRO,P = m 43 (h44

h 43)

ExRO, P = Ex 43

Ex 44 + WRO,P

WRO,T = m 46 (h46

h 47)

ExRO, T = Ex 46

Ex 47 + WRO,T

m 40 h 40

h25)

ExD, HEX = Ex24 + Ex22

m 41 h41

ExD, PEM = WPEM + Ex39

6

Ex34

ExD, LiBr , P = Ex21

LiBr valve 2

h22) = m24 (h24

Ex28

Ex30

LiBr valve 1

RO turbine

WT , ORC

Ex 6 + WP1

ExD, OFOH = Ex12 + Ex17

h14) = (h17 h16 ) T14 ) (T13 T16)

Ex38

ExD, T ,Steam = Ex7

WP1 = m 9 (h6 h9 ) = v9 (P6 P9) (h6 h9)

y=

T0 TPTC )

Ex7

Ex23 Ex 40

Ex25 Ex 41

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S.M. Alirahmi, et al.

m45 + Pnet 3600 × TCF × FF × Ae × ne × n v × k w

P=

(33)

The high-pressure pump’s required power is expressed by:

1000 × m43 × P 3600 × f × p

WHP =

(34)

Finally, the multi-generation system’s efficiency of energy and exergy can be expressed by: en, tot

Wnet, steam + Wnet, ORC + Qcooling + (hhv h2 × m40 )

=

WPEM + QRO

Wnet , RO

QPTC + (m1 × h1)

(35) ex , tot

=

Wnet , steam + Wnet , ORC + Ex 40 + Ex 42 + Ex cooling + Ex38

Ex37 + Ex 45

Exsun + Ex1

(36)

Fig. 3. Comparison of the present model with experimental data.

4. Exergoeconomic analysis

5. Validation

In energy conversion systems, the precise magnitude and the kind of irreversibility of each point can be defined by exergy analysis in order to utilize existing energy sources in the most productive means. To be more specific, system exergy is defined as keeping the equilibrium of the environment and the highest usable power of a control volume in a certain process. In this regard, having considered every element as a control volume, exergy balance equations are presented as follows [32]:

Since the proposed multi-generation system has not been studied in the preceding literature, the calculated results for subsystems have been validated individually, using experimental and theoretical data in the pertinent literature. Accordingly, the results for PEM electrolysis have been compared with the results of Ioroi et al. [43], Fig. 3, and the RO unit’s results with the work of Nafey and Sharaf [30], Table 4. Considering the negligible errors for each part, the model and the results are acceptable.

ExQ +

Ex in =

Exout + ExW + ExD

in

(37)

6. Results and discussion

wherein, subscripts D and out, are the control volume’s inlet and outlet flow, and exergy destruction rate, respectively. Equations determining the first law of thermodynamics and exergy destruction rate of all of the multi-generation system’s components are presented in Table 2. Simultaneous evaluation of economic and exergy issues in complicated energy systems can prove to be problematic. Hence, exergoeconomics, as a new area of engineering, has been introduced to address these concerns by combining information about exergy based on price analysis, which can assist project designers and managers to select the most cost-efficient method to enhance the system’s performance [25]. In this regard, equations for cost balance, which are applied to each system element, are listed as follows [21]:

Ce, k + Cw, k = Cq, k + e

Ci, k + Zk i

Cj = cj Ej

Different refrigerants exist in the market, each of which possesses a variety of distinct features compared to others, such as being environmentally friendly, lower cost, and so forth. Having examined energy and exergy efficiencies of a variety of working fluids for the proposed ORC in this paper, the details of resulted data, shown in Fig. 4, are listed in Table 5. According to this information, R123 yields the best efficiency of energy and exergy under the conditions of this study, in comparison to the other refrigerants which are assessed. Geothermal fluid as the main input of the entire system has a profound impact on the overall outcome of the system. Thus, the results of using different fluids on the net overall power output have been determined and depicted in Fig. 5. As can be seen, the fluid Marlotherm SH provides better results by producing a superior power output compared to others. As a result, Marlotherm SH is chosen to be used in the present study. Furthermore, the geothermal source’s initial temperature can significantly affect the power produced by this multi-generation system. According to Fig. 5, the more the geothermal fluid temperature increases, the more the power production capacity of the whole system increases. The underlying reason for this result is that when a geothermal fluid with a higher temperature enters the solar collector, the fluid at the outlet of the collectors, which is the inlet of the steam generator, has a higher temperature. With respect to the parametric study principles, all parameters in Eq. (1) are assumed to be constant, except the flow rate of the steam cycle. Therefore, according to Eq. (1), an increase in the inlet geothermal fluid temperature at point 2, will result in an increase in the flow rate of the steam cycle; correspondingly, since the ORC and the steam cycle are linked together by a heat exchanger, ORC mass flow rate will increase as well. As shown in Table 2, by the equations of work done by the steam and the working fluid of the ORC, the higher the mass flow rate in both the ORC and the steam cycle results in a higher power production rate, as demonstrated in Fig. 5.

(38) (39)

Some essential parameters to evaluate the system performance from an exergoeconomic perspective, such as unit cost rate, product unit cost, and exergy destruction cost rate, can be expressed as follows [37,38]:

cF , k =

Cf , k Ef , k

(40)

CP , k EP, k

(41)

CD, k = cF , k × Ef , k

(42)

cP, k =

Table 3 consists of supplementary equations and applied cost balance equations. In order to calculate the Zk of components in Table 3, references [39–42] are used.

7

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Table 4 Validation of the results obtained from the present work with data reported by Nafey [30]. Difference (%)

Unit

Nafy [30]

Present study

0.97

kW

1131

1120

0 0 0 0.8 0.1

m3/h – ppm ppm kPa

485.9 0.9944 64,180 250 6850

485.9 0.9944 64,180 252 6843

Variable

Wpump.RO

Mf SR Xb Xd ΔP

Fig. 5. Effect of temperature of geothermal fluid on produced power.

Fig. 4. Energy and exergy efficiencies of different operating fluids in the ORC.

Apart from the geothermal fluid’s initial temperature, the flow rate of the geothermal fluid is also a decisive variable. Although it is conceivable that the power production of the system may rise by increasing the amount of the inlet geothermal fluid, calculations suggest otherwise. Since the number and capacity of solar collectors are assumed to be constant despite the flow rate, increasing the amount of the geothermal fluid passing collectors results in lower temperature at the outlet of collectors and lower power production as well. As Fig. 6 demonstrates, raising the flow rate can drastically reduce the power output. Cooling capacity is substantially important for this research because of the reason that it is one of the key purposes of this system. As mentioned previously, an increase in the flow rate of the geothermal fluid has a negative impact on the output power. In contrast, the corresponding impact on the cooling capacity of the absorption chiller is completely the opposite. Fig. 7 indicates that the Therminol 59 has a higher performance than other fluids, but also an increase in flow rate can enhance the cooling capacity of the chiller because by doing so, the amount of hot flow in the generator of the absorption chiller increases, which culminates in an improvement in cooling capacity. According to the early mentioned paragraphs, the system exergy evaluation is of great prominence because of economic considerations. Another parameter which can challenge system performance is the correlation of steam turbine inlet pressure with exergy efficiency. Fig. 8 represents how the exergy efficiency increases by raising steam turbine inlet pressure to a peak. Nonetheless, after a critical point, this relation

Fig. 6. Effect of geothermal mass flow rate on produced power.

Fig. 7. Effect of the mass flow rate of geothermal fluid on the cooling capacity.

between the parameters is reversed, such that the exergy efficiency diminishes by further increasing the inlet pressure. This behavior can be explained by considering two factors that affect power production. Firstly, enthalpy of a fluid is proportional to its temperature and pressure, which can be obtained from thermodynamic properties tables. According to those tables, increasing the inlet pressure of the fluid

Table 5 Energy and exergy efficiencies of different operating fluids in the ORC.

Second law efficiency [%] Thermal efficiency [%]

Isobutene

Neopentane

n-Pentane

R11

R114

R123

R141b

R142b

R245fa

R600

28.68 22.94

29.3 23.78

28.89 23.22

29.3 23.7

28.99 23.36

29.35 23.84

29.09 23.49

28.43 22.59

29.33 23.82

28.98 23.34

8

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Fig. 11. Effect of solar intensity on the hydrogen production and water desalination unit.

Fig. 8. Effect of inlet pressure of the steam turbine on the system exergy efficiency.

lower inlet pressures, effect of enthalpy increase is dominant, so power production is amplified. However, at higher inlet pressures, decrease in flow rate is more effective on power production, than increase in enthalpy. Due to this transition, the steam turbine inlet pressure needs to be optimized to reach an acceptable number, which is presented in the optimization section. Moreover, steam turbine inlet pressure can influence the exergy destruction rate in the system. Fig. 9 suggests that regardless of the type of geothermal fluid, an increase in the inlet pressure results in an increase in the exergy destruction rate of the system. This is due to the fact that, as elaborated upon in preceding paragraphs, temperature and pressure of the geothermal fluid are assumed to be constant, and the rise in inlet pressure of the steam turbine is equal to the temperature increase of the working fluid in the steam cycle. Thus, a more significant temperature gradient will be present in the steam generator between the working fluid of the steam cycle and the geothermal fluid, which brings about a higher exergy destruction rate at higher inlet pressures. Solar energy, as a supplementary energy source for geothermal fluid in the proposed system, can produce a higher efficiency for the system. As demonstrated in Fig. 5, an increase in the temperature of the geothermal fluid has a positive correlation with power production. Fig. 10 explains two important features of Therminol 59; first, the higher initial temperature of geothermal fluid means better exergy efficiency for the same fluid; second, greater solar radiation intensity can culminate in improved exergy efficiency. This is due to the fact that intensifying solar radiation will increase the outlet temperature of the geothermal fluid from collectors, and consequently, the flow rate of the steam cycle and the ORC, according to Eq.1 and Eq.2. Furthermore, equations of work in Table 2 suggest that a rise in the flow rate of the cycles augments the power production, which means better exergy efficiency, considering Eq. (36).

Fig. 9. Effect of inlet pressure of steam turbine on the exergy destruction.

Fig. 10. Effect of solar intensity on the exergy efficiency for different temperatures of geothermal fluid.

means an increase in enthalpy. Equations from Table 2 show that increase in enthalpy causes an increase in power production. Secondly, temperature of geothermal fluid is directly related to geological features of the area, so it is out of our control. Since the temperature of the geothermal fluid is constant, the amount of energy that comes to steam generator from geothermal fluid is constant. Increasing inlet pressure of the turbine and the resulting increase in enthalpy of steam misbalances Eq. (1). To balance this equation, since the energy from the geothermal source is constant at one side of the equation, the mass flow rate of the steam cycle should decrease to compensate the increase in enthalpy. According to Eq. (2), reduction of flow rate causes reduction of power production. Therefore, considering both factors simultaneously, at

Fig. 12. Effect of temperature of the absorption chiller on COP. 9

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Fig. 13. Exergy destruction rate percentage of the system. Fig. 15. Effect of solar intensity on the cost rate for different temperatures of geothermal fluid.

Another indirect impact of solar radiation intensity is on the hydrogen production of the PEM electrolyzer. As monitored in Fig. 11, even though for solar intensities lower than 300 W/m2, the amount of hydrogen production is approximately equal for different types of geothermal fluids, as the solar intensity increases, the outcome of hydrogen production unit varies considerably for each fluid. This association is applicable to the RO unit and water production as well, as can be seen in Fig. 11. This is because of the inextricable connection of the production rate of both the PEM electrolyzer and the RO unit with the power produced by the ORC. Since the electricity from the ORC is utilized to run these units, the increase of electricity production as a result of higher solar intensities, as elaborated on in the previous paragraph, can positively affect the production rate of hydrogen and freshwater. According to the conducted calculations in this paper, the electricity production of the ORC can vary from 52.93 kW to 399.4 kW, for solar intensities 300 W/m2 and 900 W/m2 respectively. The coefficient of performance (COP) is one of the most prevalent terms to measure the efficiency of cooling systems. Several factors can affect the COP of a system, where the evaporator temperature plays a more crucial role due to its direct impact on the performance of the cooling system. Fig. 12 demonstrates the energetic and exergetic COPs of the absorption chiller, simultaneously. On one hand, the energy COP of the cooling system increases subtly by augmenting the evaporator temperature. The underlying reason is that a higher evaporator temperature can raise its heat input, which in turn can enhance the energy COP of the system. On the other hand, the exergy COP of the system falls at higher temperatures of the evaporator, since this temperature is

(

a decisive factor in calculating the exergy COP. Qeva 1

T0 Teva

6.1. Results of exergy and economic analysis Fig. 13 is represented to unify all calculated exergy destruction data in a single chart and determine which parts of the system are responsible for the highest exergy destruction. This figure reveals that the PTC unit alone, brings about nearly 39% of the total exergy destruction rate of the proposed system, followed by DWH, absorption chiller, and the steam turbine account for 15%, 14%, and 9%, respectively. Fig. 14 shows the correlation of different geothermal fluid temperatures with both the exergy efficiency and the total cost rate. According to this figure, regardless of the fluid type, an increase in the temperature of the fluid reduces the cost rate of power production of the entire system. As elucidated formerly in this paper, this is because a higher geothermal temperature not only leads to a higher flow rate in both the steam cycle and the ORC, but also rises the power production of the entire system. Since the geothermal energy is considered a costfree energy source, if more power is produced by the same system, just by increasing geothermal fluid temperature, the cost rate of power production declines. Furthermore, as clarified earlier in this paper, this temperature increase enhances the exergy efficiency of the system. In this respect, it can be concluded that Therminol 59 and Marlotherm SH yields the lowest cost rate, and Syltherm 800 produces the best exergy efficiency. Fig. 15 focuses on Therminol 59′s cost rate, as the selected fluid of the proposed system, based on solar radiation intensity and the fluid’s initial temperature. According to this figure, for solar intensities lower than 300 W/m2, there is a surge of cost rate for colder geothermal fluids. As a result, the higher geothermal temperature is required for areas with weak solar intensity in order to avoid excessive cost rates. On the contrary, the cost rates decrease in higher solar intensities, and reach almost a constant value for solar intensities above 700 W/m2, despite the initial temperature of the geothermal fluid. To shed more light on this issue, this reduction of cost rate stems from the fact that solar energy is a cost-free source, thus if the solar intensity rises, the total power production increases. Consequently, the total cost rate of

) is the

numerator of the COP exergy equation, where an increase in evaporator temperature, raises the heat output of the evaporator and reduces the exergy COP of the system.

Table 6 Optimization variables and constraints. Upper bound

Lower bound

Parameter

180 20

150 15

Tgeo (℃) mgeo (kg)

12.27 10 2000 40

Fig. 14. Effect of temperature of geothermal fluid on both the cost rate and the exergy efficiency.

10

9 3 500 30

Collector Length (m) PPSteam generator P7 (kPa) T15 (℃)

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7. Optimization Exergy efficiency and cost rate are two of the most important parameters in the proposed system in this paper. In order to apply multi-optimization, the EES and MATLAB software have linked together by the Dynamic Data Exchange (DDE) method. NSGA-II, as one of the well-known evolutionary algorithms (EA), has some merits such as the strategy of fast crowded distance estimation [4]. Using a genetic algorithm, the Pareto frontier, which is a well-converged diagram solution, can be obtained to determine the optimum values. This diagram comprises points that draw a correlation between cost rate and exergy efficiency to find out the best working condition. Subsequently, the outcome of different parts of the system can be calculated using the obtained data. In this paper, six design variables are considered for optimization as: 1. 2. 3. 4. 5. 6.

Fig. 16. Pareto frontier (optimum points obtained for the multi-generation system).

the whole system dwindles. The constraint of solar collectors’ technology, however, restrains the capacity of solar collectors to harness the wholly available solar radiation. Therefore, for higher solar intensities, the efficacy of solar collectors, for different initial temperatures of the geothermal fluid, happens to be the same.

The inlet temperature of the geothermal fluid The flow rate of the geothermal fluid Length of the solar collector pinch point temperature of the steam generator Steam turbine inlet pressure The temperature of the ORC’s condenser

Constraints for the abovementioned variables are presented in Table 6. This optimization aims to maximize the exergy efficiency, and to minimize the cost rate, as two objective functions.

Fig. 17. Scatter distribution of the effective parameters. 11

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Table 7 Exergy efficiency and cost rate for points A, B, and C on the Pareto curve. mH2

( )

2.65 2.27 0.40

kg h

Wnet (kW)

Ctot ($/GJ)

860.3 772.2 129.3

317 129.7 58.66

exergy (%)

31.99 29.95 19.72

T15 (oC)

P7 (kPa)

PP (oC)

Collector Length (m)

mgeo

37.48 32.56 31.48

1095.67 1632.63 1925.47

4.0 6.9 9.2

11.44 12.17 9.89

19.87 19.42 18.28

The Pareto frontier of the optimum points is presented in Fig. 16. Also, the scattered distribution of the decision variables is depicted in Fig. 17. By Contemplating data on the Pareto frontier, the importance of multi-objective optimization can be realized. All points on the Pareto frontier are optimum points. The point C is the best point considering the cost rates as the only decisive factor, neglecting exergy. On the other hand, point A represents the best exergy efficiency of the system, disregarding the cost rate. Thus neither of the points A and C is the ideal point. The ultimate goal of multi-objective optimization is to find the best possible balance between different important factors of the system. However, due to inevitable irreversibilities in energy systems, the ideal point, at the corner of the Pareto frontier, is not reachable. Hence, point B, as the closest point to the ideal point, is selected as the operating condition of the system. Detailed information of the points A, B, and C are listed in Table 7.

Point

177.77 176.92 151.76

A B C

Declaration of Competing Interest 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. References [1] Keshavarzzadeh AH, Ahmadi P, Safaei MR. Assessment and optimization of an integrated energy system with electrolysis and fuel cells for electricity, cooling and hydrogen production using various optimization techniques. Int J Hydrogen Energy 2019;44(39):21379–96. https://doi.org/10.1016/j.ijhydene.2019.06.127. [2] Javan S, Mohamadi V, Ahmadi P, Hanafizadeh P. Fluid selection optimization of a combined cooling, heating and power (CCHP) system for residential applications. Appl Therm Eng 2016;96:26–38. https://doi.org/10.1016/j.applthermaleng.2015. 11.060. [3] Khanmohammadi S, Atashkari K, Kouhihamali R. Exergoeconomic multi-objective optimization of an externally fired gas turbine integrated with a biomass gasifier. Appl Therm Eng 2015;91:848–59. https://doi.org/10.1016/j.applthermaleng.2015. 08.080. 112320. [4] Keshavarzzadeh AH, Ahmadi P. Multi-objective techno-economic optimization of a solar based integrated energy system using various optimization methods. Energy Convers Manag 2019;196:196–210. https://doi.org/10.1016/j.enconman.2019.05. 061. [5] Ahmadi P, Dincer I, Rosen MA. Transient thermal performance assessment of a hybrid solar-fuel cell system in Toronto, Canada. Int J Hydrogen Energy 2015;40(24):7846–54. https://doi.org/10.1016/j.ijhydene.2014.11.047. [6] Chi J, Yu H. Water electrolysis based on renewable energy for hydrogen production. Cuihua Xuebao/Chinese J Catal 2018;39:390–4. https://doi.org/10.1016/S18722067(17)62949-8. [7] Olasolo P, Juárez MC, Morales MP, Damico S, Liarte IA. Enhanced geothermal systems (EGS): a review. Renew Sustain Energy Rev 2016;56:133–44. https://doi. org/10.1016/j.rser.2015.11.031. [8] Marami Milani S, Khoshbakhti Saray R, Najafi M. Exergo-economic analysis of different power-cycle configurations driven by heat recovery of a gas engine. Energy Convers Manag 2019;186:103–19. https://doi.org/10.1016/j.enconman.2019.02. 030. [9] Quoilin S, Van Den Broek M, Declaye S, Dewallef P, Lemort V. Techno-economic survey of organic rankine cycle (ORC) systems. Renew Sustain Energy Rev 2013;22:168–86. https://doi.org/10.1016/j.rser.2013.01.028. [10] Anderson A, Rezaie B. Geothermal technology: Trends and potential role in a sustainable future. Appl Energy 2019;248:18–34. https://doi.org/10.1016/j.apenergy. 2019.04.102. [11] Ahmed FE, Hashaikeh R, Hilal N. Solar powered desalination–Technology, energy and future outlook. Desalination 2019;453:54–76. https://doi.org/10.1016/j.desal. 2018.12.002. [12] Wong KV, Tan N. Feasibility of Using More Geothermal Energy to Generate Electricity. J Energy Resour Technol 2016;137:1–6. https://doi.org/10.1115/1. 4028138. [13] Kim J, Park K, Yang DR, Hong S. A comprehensive review of energy consumption of seawater reverse osmosis desalination plants. Appl Energy 2019;254:113652https://doi.org/10.1016/j.apenergy.2019.113652. [14] Shayesteh AA, Koohshekan O, Ghasemi A, Nemati M, Mokhtari H. Determination of

• Among the fluids considered for the organic Rankine cycle, R123 boasts the highest energy and exergy efficiencies. • While assuming a constant number of solar panels, when the inlet

• •

Tgeo (oC)

We would like to mention that, the output of this research is based our team work. In this regard, the first author did the simulation and thermodynamic modeling of the integrated system while the second and third authors applied both exergy and economic analyses to the system. Forth authors, wrote some parts of the manuscript and was responsible for the optimization and discuss about the results. Once the paper was written, third author carefully went through the paper one more time and render some parts. Meanwhile, the forth author did some comments to enhance the analysis and took care of the multiobjective optimization.

In the present research paper, a multi-generation system is considered and energy, exergy, and exergoeconomic analysis along with a multi-objective optimization are performed. Products of the proposed system include cooling by absorption refrigeration cycle, hot water generated by the domestic water heater, hydrogen production by PEM electrolysis, as well as freshwater and electricity generation. The performance of the system is highly dependent on geothermal fluid initial temperature, flow rate, solar intensity, steam turbine inlet pressure, Steam generator pinch point temperature, and the number of solar panels. Judging by the acquired results, PTCs cause the most exergy destruction, thereby meaning it is of high importance to improve the performance of this part. The proposed system has been optimized using an NSGA-II algorithm. For optimal results, three points are considered, the best point on the Pareto curve has an exergy efficiency of 31.99% and the energy efficiency is 18.69%. The total cost rate was 317 $/GJ for Therminol 59 as the geothermal fluid, as well as the R123 as organic fluid. The output products of the system were hydrogen with a mass flow rate of 2.648 kg/h, freshwater at a rate of 32.68 m3/h, as well as a cooling load of 275.6 kJ/s, and hot domestic water at a rate of 13.36 kg/s. Other results of the study are as follows:

•

kg s

9. Authors contributions sections

8. Conclusion

•

( )

flow rate increases, the outlet work of the system decreases, and the cooling load increases. One of the essential parameters is the solar intensity, which affects the exergy efficiency up to 9% when Therminol 59 is used as the geothermal fluid at the temperature of 160°Celsius. An increase in the geothermal fluid temperature causes an increase in the exergy efficiency. Marlotherm SH has the highest exergy efficiency, and Therminol 59 has the lowest cost. An increase in the turbine inlet pressure increases exergy destruction. PTC, DWH, absorption chiller, and the steam turbine are responsible for a considerable portion of exergy destruction. Hence, enhancing their performance is of great importance in order to promote the overall efficiency of the multi-generation system. 12

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[40]

[41]

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