Exergoeconomic optimization of a new trigeneration system driven by biogas for power, cooling, and freshwater production

Energy Conversion and Management 205 (2020) 112417

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Exergoeconomic optimization of a new trigeneration system driven by biogas for power, cooling, and freshwater production

T

Towhid Gholizadeha, Mohammad Vajdia, , Hadi Rostamzadehb ⁎

a b

Department of Mechanical Engineering, Faculty of Engineering, University of Mohaghegh Ardabili, Ardabil, Iran Department of Aerospace Engineering, Sharif University of Technology, Azadi Ave., Tehran, Iran

ARTICLE INFO

ABSTRACT

Keywords: Biogas Trigeneration Ejector Humidification-dehumidification (HDH) system Exergoeconomic Optimization

Anaerobic fermentation of crop straw/animal dug can be the most appropriate solution for biomass conversion into applicable renewable energy-based fuels. However, due to the imperfection matching between the biogas combustion process and energy conversion system, a painstakingly design procedure is required to devise highefficient energy system for capturing biogas efficiently. For this aim, a new trigeneration system driven by biogas is devised for electricity, refrigeration, and potable freshwater generation. The devised system encompasses a gas turbine (GT) cycle, a new cooling/electricity cogeneration system based on organic Rankine cycle (ORC) and ejector cooling cycle (ECC), and a humidification-dehumidification (HDH) unit. To further enhance performance of the devised system, exergoeconomic optimization of the system is concurred. Five working fluids were screened through the new ORC/ECC system and ultimately Toluene was suggested since in the case the overall integrated trigeneration system had the highest refrigeration load of 249.8 kW and trigeneration-based gainoutput-ratio (TGOR) of 0.894 (as the main performance indicators). Using Toluene as refrigerant in the ORC/ ECC system, it is found that optimization leads to the increment of the net electricity, refrigeration load, TGOR, and exergy efficiency of around 2.58%, 22.69%, 14.04%, and 13.26%, respectively, while unit cost of trigeneration (UCT) is decreased by 6.71%. Among all elements, combustion chamber is recognized as the highly destructive element by exergy destruction of 771.6 kW, followed by vapor generator with exergy destruction of 221.4 kW. At last, an intensive parametric evaluation of some influential parameters is presented.

1. Introduction Galloping consumption of energy around the world has captivated attention of many scholars to design more efficacious energy conversion systems. While many sectors in industry convert the available energy from one form to another more useful form, the conversion of energy in power plants is highly crucial in the developed civilization today. Numerous schemes are devised to further increase power plants efficiency with considering cost aspect of the procedure, where among all using renewable energy has received a well agreement benefit [1,2]. Recent advances in biotechnologies have materialized the provision of more reliable, clean, high-efficient, and low cost biofuels for improving of living standards and promoting industrialization. Biogas, as a typical kind of biofuel, could be regarded as a promising choice for multiple benefits of environmental, industrialization, socio-economic, etc. Many countries like China have realized this fact by investing more on biogas-based developmental projects instead of the fossil fuels or conventional biomass energies [3]. Due to the limited available

⁎

technologies, biomass energy is inappropriately burnt for domestic applications which results in exposure to some serious respiratory illnesses [4]. Due to huge amount of agricultural products for converting into biomass, many regions around the word lack the required technologies for this aim. For instance, in 2009 and in China, 215 out of 687 million ton of crop straw was unused due to the lack of suitable technologies [5]. In many cases, these crop straws are burned in the open air without any use, leading to substantial environmental pollution [6]. Moreover, only 0.9% of the animal dugs are properly collected in harmless way, literally the process is threatening the quality of air and surface water [3,6]. Therefore, anaerobic fermentation of crop straw/ animal dug can be the most appropriate in many circumstances [3]. Another central factor in improving efficiency of biogas-based energy delivery systems is elimination of imperfection matching between the biogas combustion process and energy conversion system. The best solution can be design of high-efficient integrated energy systems to convert as much energy of biogas as possible into different useful forms of energy. Recent investigations have resolved these classified problems

Corresponding author. E-mail address: [email protected] (M. Vajdi).

https://doi.org/10.1016/j.enconman.2019.112417 Received 2 August 2019; Received in revised form 14 December 2019; Accepted 16 December 2019 0196-8904/ © 2019 Elsevier Ltd. All rights reserved.

Energy Conversion and Management 205 (2020) 112417

T. Gholizadeh, et al.

Nomenclature

η ϕr λ μ

Symbols A AC AP c C CC CRF ECC ex Ex fk GA GOR GT h

h HDH IHE ir LHV M MOO m mr n N nr ORC P R rk rAC S s T TGOR TTD U

UCT V VG W w Y yD Z Z R

area (m2 ) Air compressor Air preheater cost per exergy unit ($. GJ 1) cost rate ($. s 1) Combustion chamber capital recovery factor Ejector cooling cycle Exergy per unit mass(kW . kg 1) exergy rate(kW ) Exergoeconomic factor (%) Genetic algorithm Gain-Output-Ratio Gas turbine specific enthalpy per mass(kJ . kg 1)

Subscripts and superscripts AC AP BC cc ch CI cond cr c.v. D DBT Dhum dif DTT ej eva ex f Fu fw GT Hum in is i LMTD mix mf noz net OM ORC out pf ph pp Pr pu q s sf sys tur VG W w 1, 2, … 0

specific enthalpy per mole(kJ . kmol 1) Humidification-dehumidification İnternal heat exchanger interest rate Lower heating value Molar mass(kg . kmol 1) Multi-objective operator mass flow rate(kg . s 1) Seawater/air mass flow rate ratio molar rate(kmol. s 1) annual number of hours (h)/Number of moles componets expected life Organic Rankine cycle pressure (kPa) Universial gases constant (J.kg−1.K−1) Relative cost difference (%) Air compressor ratio Salinity (g/kg) specific entropy(kJ . kg 1. K 1) temperature (K ) Trigeneration-based GOR Terminal temperature difference (K) overall heat transfer coefficient (kW . m 2K 1) unit cost of trigeneration ($/GJ) Velocity (m/s) Vapor generator electricity(kW ) Weight function Molar ratio Exergy destruction ratio (%) investment cost of components ($) investment cost rate of components ($. s 1) Universial gases constant (J.kg−1.K−1)

Greek Symbols ε

efficiency (%) maintenance factor Fuel/air ratio Mass entrainment ratio

effectiveness

and issues by devising more efficient integrated energy system driven by biogas energy. Leonzio [7] devised a new trigeneration system working with biogas energy, using an absorption chiller unit (ACU), a heat pump unit (HPU), and a recovery plant. They combusted 3280 kW of biogas to generate 2523 of kW heating, 925 of kW electricity, and 473 kW of cooling. Gholizadeh et al. [8] devised a new double-evaporator power/refrigeration set-up driven by biogas energy and

Air compressor Air preheater Brayton cycle Combustion chamber chemical capital investment condenser critical control volume destruction Desalination bottom temperature dehumidifier diffuser Desalination top temperature ejector evaporator exergy formation fuel freshwater Gas turbine humidifier inlet isentropic ith component Logarithmic mean temperature difference mixer Mixed fluid nozzle net value operating & maintenance Organic Rankine cycle outlet Primary fluid physical pinch point product pump Heat transfer constant entropy Secondary fluid system turbine Vapor generator work water cycle locations dead state

demonstrated the feasibility of their devised layout from thermodynamics vantage point. They discerned energy and exergy efficiencies of 54.54% an 36.83%, respectively. Later on, they estimated the cost of their devised system by employing thermoeconomic analysis and optimized performance of the system by genetic algorithm (GA) method in Engineering Equation Solver (EES) software [9]. They demonstrated the high capability of the optimization method applied through their 2

Energy Conversion and Management 205 (2020) 112417

T. Gholizadeh, et al.

Fig. 1. Schematic of the devised new trigeneration system operated by biogas.

simulation. Lamidi et al. [10] used market wastes to generate biogas for operation of a new trigeneration system for power, food drying, cooling storage. They found a payback period of 2.1–7.19 years for the proposed set-up. Gazda and Stanek [11] recommended the use of biogas integrated with photovoltaic system for trigeneration of heat, cold, and power. They reported a huge amount of CO2 emission reduction. Gao et al. [12] designed a new trigeneration system for heat, cold, and power for different gases for anaerobic digestion and thermal cracking. They showed that the decisive factors in determining performance of their designed system are efficiency of gas engine, its cost, and the required heat and cold. Su et al. [13] used solar heat for biogas steam reforming designed for a new trigeneration system. They concluded that using a high biogas conversion process for enhancing reforming temperature is not commendable solution for an energy system aspect. Bruno et al. [14] used biogas in gas turbine (GT) cycle to cogeneration of power and cooling by employing a ACU for waste heat capturing of the GT cycle. They highly recommended biogas utilization of power and cooling cogeneration due to address full demand of their system. According to the presented literature review in the above paragraphs, it could be concluded that devising a high-efficient trigeneration system for power, freshwater, and cooling load driven by biogas energy is not extensively investigated up to now. For this aim, a new trigeneration set-up on the basis of an ORC (organic Rankine cycle), an ECC (ejector cooling cycle), and a humidification-dehumidification (HDH) unit is planned to generate power, cooling, and freshwater. Various renewable energy-based heat sources can be recommended for the devised packed trigeneration system in which biogas is proposed due to its high mobility demonstrated in the previous works. To capture heat of biogas due to its high temperature feature, a GT cycle is used, where its waste heat is used to drive the trigeneration. This deliberation has also led to a remarkable increment in power production. As a result, a new trigeneration system operated by biogas is achieved. In this study, the term trigeneration system refers to the whole system including a GT cycle, an ORC, an ECC, and a HDH unit. The rest of the report is systematized as follows. In section 2, an intensive description of the devised trigeneration system is presented. In section 3, methods, assumptions, relations used for modeling of the devised unit, input data, first and second laws and economic relations, and extended central performance criteria are elaborated. In section 4 optimization procedure used through the simulation is presented. In the subsequent section, results are displayed and computational preciseness is demonstrated through a verification process. Ultimately, a conclusion is drawn.

and freshwater production is displayed in Fig. 1. Overall, the devised set-up encompasses two main subsets of: a GT cycle, a new cooling/ electricity system, and a HDH unit. Each subset is expounded descriptively as follows. Layout of a simple and conventional GT cycle is used here. As air passes from an air compressor (AC), it is entered into an air preheater (AP) in the compressed form and then is mixed with fuel in the CC (combustion chamber) at high temperature and leaved the chamber with composition of gases. Due to the high temperature of composition gases, they are expanded high enough to generate electricity via a gas turbine. Next, the high temperature of flue gases is used again in two stages. First to preheat the entered air stream in the GT cycle, and second to run the VG (vapor generator) of the integrated ORC/ECC. In the integrated cooling/electricity system based on an ORC and an ECC, following thermodynamic processes can be observed. The saturated vapor is directed into a turbine and rotates through it to generate electricity, and then is split into two streams. One stream flows through the ejector as primary flow of this element and the rest is liquefied through the condenser 2 to supply required thermal heat of the HDH unit. As primary flow sucks the secondary flow inside the ejector, the mixed flow leaves it and then is preheated through two processes. The first precooling process occurs through an internal stream via an internal heat exchanger (IHX), while the second precooling process occurs through an external water circulation process in a condenser. The liquid refrigerant leaves the condenser 1 and then is split into two streams. One stream is used for cooling aim after throttling through an expansion device by employing an evaporator and the rest of stream is pressurized by pump 1 and then is directed into the IHX. The heated-up stream is mixed with the liquid stream at a mixer and then is pressurized via pump 2 and returns to the VG. The thermal energy of the condenser 2 is fed into the HDH system as a heat source of the unit to generate freshwater. In this element, the seawater with specific salinity is directed to an open loop, whilst air stream circulates in a closed circuit. The seawater goes through an evaporation process with air and the remains are discarded from the humidifier in forms of brine, whilst air is humidified through the humidifier. In the end, distilled water is produced as air quits the humidifier and goes into to the dehumidifier and the cold air sets back to the humidifier.

2. System description

Some presumptions are pondered in order to accomplish an intensive thermal modeling of the devised trigeneration set-up as follows [15,16]:

3. Materials and methods 3.1. Thermodynamic assumptions

Layout of the devised new trigeneration system for power, cooling, 3

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• Steady state condition is governed. • Turbine, pump, and compress each operate with an isentropic efficiency. • Inflow and outflow of the expansion valve are related to each other isenthalpically. • Evaporator and condensers outlets are assumed saturated. • Temperature of the freshwater is set on the average of the exit air • • • • • •

T T P 1 ln + (1 + 1.608 ) Ra T0 ln + Ra T0 T0 T0 P0 1 + 1.608 0 (1 + 1.608 ) ln + 1.608 ln 1 + 1.608 (7) 0

ex da = (cp, a + cp, v ) T0

where, ω is the humidity ratio:

dry-bulb temperature and the inlet air dew-point temperature in the dehumidifier [17–19]. The exiting and entering air relative humidity is set at 90% [17]. Only physical and chemical exergies are pondered through exergy assessment [20]. Based on ideal gas laws available in air and combustion products, gas mixture are manipulated [21,22]. The role of the combustion chamber in losing heat is accounted by setting it into 2% of LHVbiogas [12]. Drop of pressure in the CC and AP is reckoned 4% and 5%, respectively [9]. Elements of air are assumed as follows: 77.48% of N2 , 20.59% of O2 , 0.03% of CO2 , and 1.9% of H2 O [8,9].

=

ex , k

Cq, k +

(1)

Qout + W = 0

(2)

In terms of second law of thermodynamics, the balance relation of a unit may be articulated as:

Ex out , i

(3)

i=1

The overall exergy of fluid stream is declared as: (4)

Exk = Ex ph, k + Exch, k where,

h0

Ex ch, k = nk (

yi ex i k

T0 (s ch,0

(5)

s0 ))k

+ RT0

yi lnyi ) i

Parameter

value

Ref.

Reference state pressure, P0 (kPa) Reference state temperature, T0 (K) Isentropic efficiency of GT, GT (%) Isentropic efficiency of AC, AC (%) Preheated air temperature, T3 (K) Air compressor pressure ratio, rAC Pump isentropic Efficiency, pu (%)

101.3 298.15 86 86 700 10 0.95

[9] [9] [9] [9] [9] [9] [9]

Net power output of Brayton cycle based of biogas, WBC (kW) Turbine outlet pressure, P20 (kPa) Vapor generator temperature, TVG (K) Turbine isentropic efficiency, tur (%) Mixer efficiency of ejector, mix (%) Evaporator 1 temperature, Teva (K) Condenser 1 temperature, Tcond 1 (K) TTD of vapor generator , TTDVG\; (K) TTD of condenser 2 , TTDcond 2\; (K) TTD of IHX, TTDIHX \; (K) Mass extraction ratio, MER Nozzle efficiency of ejector, naz (%)

1250 1000

750 Tcrit 20 0.90 0.90 265 303.15 10 10 5 0.5 0.85

[9] [9]

[9] [9] [9] [9] [9] – – – [9]

Desalination bottom temperature, TDBT (°C) Desalination top temperature, TDTT (°C) Salinity of seawater, S (g/kg) Humidifier effectiveness, Hum (%) Dehumidifier effectiveness, Dhum (%)

25 60 35 85 85

[15] [15] [15] [15] [15]

Gas turbine inlet temperature, T4 (K)

k

Ex ph, k = m (h

(11)

Table 1 Input parameters for thermodynamic simulation of the devised trigeneration set-up.

mout = 0

i=1

(10)

The overall cost rate of the k th constituent of a system is articulated as [20]:

The general form of governing equations at steady state for thermodynamic evaluation of a unit can be articulated as:

Ex in, i

Cout , k

Ck = ck Exk

3.4. Energy and exergy evaluation

k

Cin, k + Zk = Cw, k +

where, utilized parameters are: Cin, k : stands for the cost rate of the incoming stream of the kth constituent, Cout , k: stands for the cost rate of the outcoming stream of the kth constituent, Cw, k : stands for the cost rate of work and Cq, k: stands for the cost rate of heat transfer Exergy and cost rate are related as [20]:

Moreover, the relations employed to accurately model ejector are used from our previous studies that are listed in Table 3 [24,25]. Considering Eqs. given in Table 3, iteration method is used to obtain mass entrainment ratio of ejector.

ExD, k =

(9)

The balance equation based on cost of the kth constituent of a system is articulated as [20]:

3.3. Ejector formulae

Qin

ExP, k Ex out = Exin ExF , k

3.5. Exergoeconomic evaluation

A complete and intensive elaboration of the GT cycle is delivered in our previous works [8,9,23]. Hence, only a brief description of the process occurring through the GT cycle is presented in Table 2.

(mh)out +

=

Some mass-, energy-, and exergy-based balance relations to each constituent of the reckoned set-up are enumerated in Table 4.

3.2. GT cycle formulae

(mh)in

(8)

The exergetic efficiency of the kth element is declared as:

Meantime, some major input data, prerequisite of simulation of the devised trigeneration system, are given in Table 1.

min

mv ma

Desalination mass flow rate ratio, mr Diffuser efficiency of ejector, dif (%)

(6)

ch,0

where, ex i is known as the standard chemical exergy found in Refs. [27,28] and yi is concentration of the ith constituent. Exergy of humid air is computed from Eq. (7) [26]: 4

2 0.85

[9]

[15] [9]

Energy Conversion and Management 205 (2020) 112417

T. Gholizadeh, et al.

Table 2 A brief utilized mathematical relations for modeling of GT cycle [23]. Constituent

Target parameter

Air compressor

Isentropic efficiency of air compressor Consumption electricity of compressor Air preheater efficiency

Air preheater

Combustion chamber

Pressure loss across air preheater Fuel/air ratio on the molar basis Chemical equation in terms of fuel/air ratio

Formulae

=

AC

h¯in h¯ out , S h¯in h¯ out

WAC = mair AP

=

Pair , out Pair , in

¯=

(h¯ out h¯in) Mair

mair (h¯ air , out h¯ air , in ) mgas (h¯ gas, in h¯ gas, out )

=1

PAP

nFu nair

nPr n air

or

=1+ ¯

¯ [0.6CH4 + 0.4CO2] + [0.7748N2 + 0.2059O2 + 0.0003CO2 + 0.019H2 O]

YN2 =

0.7748 1+ ¯

[1 + ¯][YN2 N2 + YO2 O2 + YCO2 CO2 + YH2 O H2 O] ,

,

0.2059 1.2 ¯ , 1+ ¯ 0.0003 + ¯ YCO2 = , 1+ ¯

YO2 =

YH2 O = Energy balance equation

Enthalpy of air Enthalpy of products

Qc . v

LHV of the biogas combustion Pressure loss across combustion chamber Isentropic efficiency of gas turbine Gas turbine generated electricity

Gas turbine

+ nFu h¯Fu

¯ 0.02nFu LHV

nPr h¯Pr + nair h¯ air = 0

OR ¯ h¯Fu

¯ (1 + ¯) h¯Pr + h¯ air = 0.02 ¯ LHV h¯ air = [0.7748h¯ N2 + 0.2059h¯ O2 + 0.0003h¯ CO2 + 0.019h¯ H2 O] T = Tair , in h¯Pr = ¯=

Enthalpy of biogas

0.019 + 1.2 ¯ 1+ ¯

[0.7748h¯ N2 + (0.2059

1.2 ¯) h¯ O2 + (0.0003 + ¯ ) h¯CO2 + (0.019 + 1.2 ¯ ) h¯ H2 O] T = TPr 1+ ¯

0.7748 h¯ N2 + 0.2059 h¯O 2 + 0.0003 h¯CO2 + 0.019 h¯ H2 O ¯ h¯Fu 0.02 ¯ LHV [ 1.2 ¯ h¯ O2 + h¯ CO 2 + 1.2 ¯h¯ H2 O] T = TPr

h¯biogas = 0.4h¯ CO2 + 0.6h¯ CH4

LHVbiogas = HPr PPr , out Pair , in GT

=

=1

Hreact =

o

NPr h¯ f , Pr

o

o

o

Nreact h¯ f , react = (NPr h¯ f )CO2 + (NPr h¯f ) H2 O

o

(Nh¯ f )CH4

o

(Nreact h¯ f )CO2

PCC

h¯in h¯ out h¯in h¯ out , S

WGT = mPr

(h¯in

h¯ out ) MPr

CRF: stands for the capital recovery factor. CRF is attained from Eq. (13) [20]:

Table 3 Mathematical relations employed for ejector [25]. Parameter name

Formulae

Ejector mass entrainment ratio

µ=

CRF =

msf mpf

k (1 + k )nr (1 + k )nr 1

(13)

Energy balance between nozzle and primary fluid sections

hpf

Momentum conservation in the mixing section

Vmf =

Vnoz 1+µ

here: k: stands for the interest rate and nr : stands for the total operating period of the system The cost rate of exergy destruction of the kth constituent is articulate as [20]:

h out =

hpf + µhsf 1+µ

CD, k = cFu, k ExD, k (IfExPr , k = constant )

Isentropic efficiency of motive nozzle

Energy balance for the ejector

noz

Mixing efficiency mix

Energy balance equation between mixing and outlet sections Diffuser efficiency

Zk =

CI Zk

+

OM Zk

= CRF ×

r

× 365 × 24 × Zk N

=

1 2

2 hnoz = Vnoz

=

V2 mf , is 2 Vmf 1 2

=

hout , is hout

(14)

The relative cost difference (rk ) and exergoeconomic factor ( fk ) for the k th component of a system may be expressed respectively as [20]:

2 hmf = Vmf , is

h out dif

hpf hnoz hpf hnoz, is

rk = (cPr , k

hmf hmf

cFu, k )/ cFu, k

fk = Zk /(Zk + CD, k )

(15) (16)

The detail cost balance relations and purchase equipment cost (PEC) for each constituent of the devised trigeneration system are presented in Table 5. Some crucial cost indices used through estimating cost of the set-up are listed in Table 6. The total area related to heat transfer process of a heat exchanger can be estimated on the basis of using the total heat transfer coefficient and LMTD (logarithmic mean temperature difference) as:

(12)

where: CI Zk : stands for the capital investment cost of the k th constituent, OM Zk : stands for the operating and maintenance cost of the k th constituent, N : stands for the annual number of operation, r : stands for the maintenance factor, Zk : stands for the purchase cost of the k th constituent and

Ak =

5

Qk Uk TLMTD

(17)

6

(1 +

AC

=

h1 h2S h1 h2

GT

=

h 4 h5 h4 h5S

h14 ) = m26 (h27

Dehumidifier

Humidifier

Pump 2

Pump 1

Mixer

Internal heat exchanger

h26)

h32)

h26)

mAir (h30

m27 h27

h23) ,

h17) , pu2

pu1

h29) = m25 (h26

h29)m28 = m25

h18s h17 h18 h17 h24s h23 h24 h23

m31 30

= max

h30 h29 h30. ideal h29

29) Dhum

= max

mf / Mf

Hum

h25) + m31 h31m31 = mAir (

=

=

m28 h28 = mAir (h30

Wpu2 = m23 (h24

Wpu1 = m17 (h18

QIHX = m12 (h12 h13) = m19 (h19 h18)T12 T19 = 5(k ) m23 h23 = m19 h19 + m22 h22.m23 = m19 + m22

h14) = m32 (h33

Qcond2 = m12 (h13

h9 h20 h9 h20s

Qcond1 = m12 (h13

=

Condenser 1

h15)

tur

-

h20)

h7) ,QVG = m9 (h 9

h5) ,

Qeva = m11 (h11

Condenser 2

h5)

) hprod + h air = 0.02 LHV , Qcc = LHV

h3) , Q AP = m5 (h 6

h1) ,

Evaporator

Wtur = m 9 (h 9

QVG = m6 (h6

WGT = mP (h4

hfuel

Q AP = m1 (h2

WAC = m1 (h2

Energy balance equations

Ejector

Turbine

New cogeneration system Vapor Generator

Gas turbine

Combustion chamber

Air preheater

GT cycle Air compressor

Component

Table 4 Exergy, energy, and mass balance equations for different components of the devised set-up.

.

h30 h29 h30 h29. ideal

.

h27 h28 h27 h28. ideal

h26 h25 h26. ideal h25

Ex5)

(Ex2

(Ex3

Ex1)

Ex20

Wtur

ExD, Dhum = (Ex30

ExD, Hum = (Ex27

ExD, pu2 = Wpu2

ExD, pu1 = Wpu1

(Ex26

(Ex30

Ex23)

Ex17)

Ex23

Ex29)

Ex28)

(Ex24

(Ex18

ExD, mix = Ex19 + Ex22

Ex13) (Ex19

Ex22) (Ex27

ExD, IHX = (Ex 12

Ex15) -(Ex33

ExD, cond2 = (Ex 21

Ex15) -Qeva ( ExD, cond1 = (Ex11

ExD, eva = (Ex11

Ex24 )

Ex2)

1)Troom, eva = Teva + 3

Ex25 + Ex31)

Ex29)

Ex18)

Ex26)

Ex32)

T0 Troom, eva

WGT

Ex7) (Ex 9

Ex 4)

ExD, ej = (Ex10 + Ex11) Ex12

ExD, tur = Ex 9

ExD, VG = (Ex 6

ExD, GT = (Ex5

ExD, CC = (Ex3 + Exfuel ) Ex 4

ExD, AP = (Ex 6

ExD, AC = WAC

Exergy balance equations

T. Gholizadeh, et al.

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Table 5 Exergoeconomic relations developed through thermoeconomic modelling of the devised trigeneration set-up for different elements [9,15]. Equipment cost function GT cycle

ZAC = (75\;m1/(0.92

sc )\;)(P2 / P1)

ZAP = 4122 × (m5 (h5

h6)/U Tlmtd .AP )0.6

ln(P2/P1)

Auxiliary equations

Cost balance equations

Components

cW , AC = cW , GT c1 = 0

C1 + ZAC = C2

Air compressor

c5 = c6

C2 + C5 + ZAP = C6 + C3

Air preheated

C3 + Cf + ZCC = C4

Combustion chamber

c4 = c5

C4 + ZGT = C5 + CW ,GT \;

Gas turbine

ZVG = 309.143 × AVG + 231.915

c6 = c7

C6 + C24 + ZVG = C9 + C7

Vapor generator

Ztur = 6000 × (Wtur )0.7

c20 = c18

C9 + Ztur = C20 + CW , tur

ZCC = (46.08\;m3/(0.995

P4/P3 )\;)[1 + exp (0.018T4

26.4)]

ZGT = (1536\;m 4 /(0.93 st )\;) ln(P5/ P4 )[1 + exp (0.036T4 New cooling/electricity cogeneration system

CFu = FP ×

54.4)]

LHVFu 106

Zej = 0

Turbine Ejector

C10 + C11 + Zej = C12

c15 = c11

Zeva = 6000 × (Aeva /100)0.7

Evaporator

C15 + Zeva = C11 + Zprod,eva

Zcond 1 = 1773 × m12

c13 = c14 ;c32 = 0

Zcond 2 = 6000 × (A econd 2 /100)0.7

c22 = c21

C21 + C26 + Zcond 2 = C27 + C22

Condenser 1

ZIHX = 1.3 × (190 + 310AIHX )

c12 = c13

C12 + C18 + ZIHX = C19 + C13

C13 + C32 + Zcond 1 = C14 + C33

Zmixer = 0

Condenser 2

Internal heat exchanger Mixer

C19 + C22 + Zmixer = C23

Pump 1

Zpu 1 = 3540 × (Wpu 1 )0.71

cW , pu 1 = cW , tur

CW , pu 1 + C17 + Zpu 1 = C17

Zpu 2 = 3540 × (Wpu 2 )0.71

cW , pu 2 = c W ,tur

CW , pu 2 + C23 + Zpu 2 = C24

c27 = c28

C27 + C29 + ZHum = C28 + C30

Humidifier

Dehumidifier

ZHum=746.749× m27 0.79 × R0.57 × A R = T27 T28 A = T27 Twb .30

0.9924

× (0.022 × Twb .30 + 0.39) 2.447

ZDhum = 2143 × (Adhum )0.514

c30 = c28 ; c29 = 26 ;c25 = 0

C25 + C30 + ZDhum = C29 + C26 + C31

c15 = c16 = c15

C14 = C17 + C16

c21 = c10

C20 = C21 + C10

Value ex , sys

1.06 8000 7.36 20 0.05

Maintenance factor, r Annual number of hours, N (hr) Fuel price, FP ($/Gj) Components expected life, nr (years) Interest rate, ir

=

Table 7 The overall heat transfer coefficient for employed heat exchangers. U (W /m2K )

Air preheater Vapor generator Internal heat exchanger Condenser 2 Evaporator Dehumidifier

30 750 750 750 1000 1400

costindexfortheoriginalyear costindexforthereferenceyear

WPu1

Cw, net + CQ, eva + C31

(

Wnet + QEva 1

T0 Troom, eva

) + Ex

(22)

31

1

T0 Troom, eva

).

4. Optimization method To augment performance of an energy system it is highly important to design the devised set-up around an optimum condition since the best performance of the system can be obtained and any deliberation and changes can be carried out after that. Normally, optimization based on thermodynamic equations can be achieved by defining energy and exergy efficiency as objective functions. Later on, the best performance of the set-up can be attained by maximizing these two parameters as “objective functions”. However, in exergoeconomic optimization the cost index is also included as another main index. This duty is reckoned in this study by employing genetic algorithm (GA) scheme in a single way or by aggrandizing each parameter into a single operator. The proficiency of each proposal is demonstrated in our previous works [9,27]. Regarding that, Table 8 has listed some important parameters employed through the optimization process. Three decisive parameters, encompassing TGOR, exergy efficiency, and UCTsys are chosen as objective operators, whilst the seawater/air mass flow rate ratio, evaporator temperature, vapour generator temperature, desalination top temperature, AC pressure ratio, GT outlet pressure, PA temperature, and GT inlet temperature are enrolled as the decisive decision variables. The chief target is maximization of TGOR

(18)

(19)

WPu2

(21)

+ Ex25 + Ex1

[23] [23] [23] [23] [23] [23]

where,

WAC

31

Cw, net is the cost rate of the net electricity.

WNet + Qeva + m31 hfg @T31

WNet = WGT + WTur

) + Ex

where, CQ, Eva and C31 are the cost rate of the released cold exergy of the

For the devised trigeneration system, trigeneration-based GainOutput-Ratio (TGOR) is defined as below:

nBiogas . LHVBiogas

0 nBiogas . exch, Biogas

T0 Troom, eva

evaporator and freshwater, respectively (CQ, eva = cQ, Eva × QEva

3.6. Performance criteria

TGOR =

(

WNet + QEva 1

Reference

The total heat transfer coefficients for each heat exchanger are categorized in Table 7. The cost rates are updated for each element as:

Originalcost = costatreferenceyear ×

Division point 2

Unit cost of trigeneration (UCT) for the recommended biogas fueled trigeneration set-up may be written as:

UCTsys =

Component

Division point 1

The exergy efficiency of the recommended biogas fueled trigeneration system may be stated as follows:

Table 6 Some decisive cost economic parameters employed through the economic analysis [23]. Parameters

Pump 2

(20) 7

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Table 8 Adjustaed key parameters in the GA [9,15].

Max MOO = w1 × TGOR + w2 ×

Parameter

Value

Number of generations Individuals number in the population Minimum mutation rate Crossover probability Maximum mutation rate Initial mutation rate

64 32 0.0005 0.85 0.25 0.25

w1 + w2 + w3 = 1, 0

mr

Teva1 (K )

550

TVG (K )

590

330

T27 (K )

345

5

rAC

P20 (kPa)

650

T3 (K )

1200

T4 (K )

c3

1

,

(24) (25)

5.1. Model justification To testify the attained findings resulted from thermodynamic analysis of the devised trigeneration systems, Engineering Equation Solver (EES) software is used to expand an appropriate code. To validate the accuracy of the HDH unit modeling, a CAOW-HDH unit with a humidifier effectiveness of 80%, minimum temperature of 30 °C and maximum temperature of 80 °C are chosen. While, the dehumidifier effectiveness and mass flow rate ratio are varied and the GOR value is recorded in each step. The results then are compared with those of Narayan et al. [17] and this analogous results are displayed in Fig. 2. On the basis of this comparison, the data of our simulation are in well agreement with those of Narayan et al. [17] within the displayed range. Due to the theoretical method of present study, it is highly imperative to testify the accuracy of the developed code for the GT cycle. Once the accuracy of the simulation is attained, it can be claimed that the subsequent results of this study- including basic results, optimum results, and parametric study, to name but a few- are accurate enough. In this part, we have compared simulation results of the present study with those of manufacture’s data presented by Nikpey Somehsaraei et al. [28]. The results of this comparison are presented in Table 9,

273

(23)

15

550

UCTsys

5. Results and discussion

3

260

+ w3 × 1

here, w1, w2 and w3 are the weight coefficients for the TGOR, exergy efficiency, and UCT, respectively.

and exergy efficiency and minimization of UCTsys . The range of decision variables are given below:

1

w1, w2, w3

ex , sys

950 750 1550

A multi-objective operator (MOO) is defined by weighing TGOR, exergy efficiency, and UCTsys and aggrandizing all in a single operator. For the devised system, the MOO is ariticulated as follows:

Fig. 2. Variation of GOR Vs. of HDH mass flow rate ratio at various dehumidifier effectivenesses for present study and Narayan et al. [17]. 8

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Table 9 Performance comparison of a GT cycle between present study and real manufacturing data [28]. Parameter

Unit

Reference value

Simulated value

Error (%)

Power output Electrical efficiency Fuel consumption Exhaust gas flow rate Compression ratio Turbine inlet temperature Turbine outlet temperature Recuperator outlet temperature

kW % kW Kg/s – °C °C °C

100 30 333 0.8 4.5 950 650 270

100 30.5 327.9 0.8 4.707 928.7 650 270

0 0.5 1.529 0 4.608 2.24 0 0

Table 10 Themophysical and environmental properties of the selected working fluid. Fluid

Pcrit (MPa)

Tcrit (K)

ODP

Safety group

GWP

Type

Ref

R245fa R123 N-pentane Toluene R141b

3.65 3.66 3.37 4.12 4.21

426.16 456.83 469.7 591.75 477.5

0 0.02 0 0 0.12

B1 B1 A3 – –

1050 77 20 3 725

isentropic isentropic isentropic isentropic Isentropic

[29] [29] [29] [30] [31]

GWP: Global warming potential; ODP: Ozone depletion potential.

35.45%. Therefore, considering power of ORC and exergy efficiency, R141b may be a suitable choice. However, it should be noted that the GT cycle produces enough power for the users, and hence in this study due to the main role of refrigeration load, freshwater, and TGOR, Toluene is recommended as the best selection. In this evaluation, the values of UCT and freshwater rate are excluded since all refrigerants result in the same value for both these parameters.

underlining the fact that the present study is in well agreement with these real data. To further substantiate the accuracy of the simulation results, the variation of the compressor work, turbine power, and fuel mass flow rate with different methane fractions under a constant input data is displayed in terms of Fig. 3. The results are presented for the current study and experiment one conducted by Nikpey Somehsaraei et al. [28]. As Fig. 3 indicates, the present results are in well agreement with those of experiment.

5.3. Optimization results In order to success in performance evaluation of the devised trigeneration system, it is more desirable to report the thermodynamic properties at each stream of the devised system. This duty is done in here by presenting Table 11 for the best working fluid selected in the previous section, namely Toluene. It should be noted that these data are given at multi-objective optimization design (MOOD) mode. Fig. 5 displays the results of optimization for four different scenarios of TGOR optimization design (TGOROD) mode, exergy efficiency optimization design (EEOD) mode, MOOD mode, and cost optimization design (COD) mode. Comparing results of TGOROD and base modes, it is found that the freshwater rate, refrigeration load, TGOR, and UCT are increased by 50.77%, 99.87%, 17.85%, and 10.25%, respectively. While, the net electricity and exergy efficiency are decreased by 1.15% and 14.41%, respectively. The freshwater rate, net electricity, refrigeration load, TGOR, exergy efficiency, and UTC in TGOROD mode are computed 80.77 m3/day, 1111 kW, 499.3 kW, 1.05, 30.04%, and 22.37 $/GJ, respectively. To achieve this scenario, we should set the unit on the seawater/air mass flow rate ratio of 1.58, evaporator temperature of 273 K, vapour generator temperature of 550 K, desalination top

5.2. Working fluid selection Selection of a proper working fluid is the central concept in the design of high-efficient energy systems. Once the mathematical model of the devised trigeneration system was finalized, several appropriate working fluids can be recommended which are screened through the developed code. Based on results of this laborious task, five working fluids are selected including N-pentane, Toluene, R141b, R245fa, and R123. Table 10 listed some environmental and thermophysical properties of the suggested working fluids. In order to select an appropriate working fluid used in the combined ORC/ECC system, Fig. 4 is presented. The illustrated data are around the base mode. According to Fig. 4, using Toluene as refrigerant leads to the highest refrigeration load of 249.8 kW and TGOR of 0.894, and also its other parameters are competitive. Using R141b as refrigerant has resulted in the highest ORC-power of 172 kW and exergy efficiency of

Fig. 3. Variation of compressor power, turbine power, and fuel mass flow rate with methane fraction of a GT cycle for present study and experiment [28]. 9

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Fig. 4. Main performance criteria for different working fluids around the base mode.

temperature of 330 K, AC pressure ratio of 5, GT outlet pressure of 950 kPa, PA temperature of 650 K, and GT inlet temperature of 1550 K. Comparing results of EEOD and base modes, it is found that the freshwater rate, refrigeration load, and UCT are decreased by 5.5%, 23.97%, and 8.42%, respectively. While, the net electricity, TGOR, and exergy efficiency are increased by 2.84%, 6.38%, and 13.64%,

respectively. The freshwater rate, net electricity, refrigeration load, TGOR, exergy efficiency, and UTC in TGOROD mode are computed 50.62 m3/day, 1156 kW, 189.9 kW, 0.951, 30.06%, and 18.58 $/GJ, respectively. To achieve this scenario, we should set the unit on the seawater/air mass flow rate ratio of 2.16, evaporator temperature of 261.3 K, vapour generator temperature of 590 K, desalination top

Table 11 Thermodynamic properties of the devised trigeneration system at MOOD mode. Point

Fluid

T (K )

P (kPa)

h (kJkg 1)

s (kJkg 1K 1)

m (kg /s )

Ex (kW )

C ($/h )

c ($/GJ )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Air Air Air Gas flow Gas flow Gas flow Gas flow Fuel Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Seawater Seawater Seawater Seawater Air Air Freshwater Water Water

298.15 648.02 750.00 1550.00 1005.86 921.77 385.09 298.15 590.00 495.05 273.00 420.06 325.06 303.15 273.00 303.15 303.15 303.29 415.06 495.05 495.05 329.28 373.91 375.09 298.15 319.28 330.03 308.82 305.05 323.01 312.98 298.15 303.15

101.3 1234 1172 1125 114.9 109.1 101.3 1200 4059 550 0.8902 4.893 4.893 4.893 0.8902 4.893 4.893 550 550 550 550 550 550 4059 101.3 101.3 101.3 101.3 101.3 101.3 101.3 101.3 101.3

−257.7 111.5 224 −288.4 −1010 −1116 −1745 −6366 595.8 535.2 227.3 420.8 286.4 −149.7 −149.7 −149.7 −149.7 −149 64.88 535.2 535.2 −103.3 −19.19 −14.52 99.77 184.3 227.5 142.2 101.9 247.4 166.8 104.8 125.8

6.995 7.08 7.256 8.524 8.64 8.545 7.553 6.974 1.181 1.195 0.9549 1.36 0.9993 −0.4361 −0.4265 −0.4361 −0.4361 −0.436 0.161 1.195 1.195 −0.2914 −0.05217 −0.05154 0.3498 0.6239 0.7569 0.4895 5.962 6.427 0.5699 0.3669 0.4365

2.5060 2.5060 2.5060 2.6684 2.6684 2.6684 2.6684 0.1624 2.7527 1.3763 0.8130 2.1893 2.1893 2.1893 0.8130 0.8130 1.3763 1.3763 1.3763 2.7527 1.3763 1.3763 2.7527 2.7527 20.3596 20.3596 20.3596 19.7484 12.8798 13.4910 0.6112 45.6437 45.6437

0 861.4 1012 3271 1254 1047 156.5 3031 724.7 273.3 −30.76 76.37 17.6 −0.0894 −2.378 −0.0332 −0.0562 0.8193 50.2 546.6 273.3 4.416 43.92 56.26 0 57.5 129.3 14.05 2.991 88.26 2.39 0 7.916

0 42 50.39 126.6 48.55 40.53 6.059 76.11 45.84 17.29 −4.964 12.33 2.841 −0.01443 −0.3839 −0.005359 −0.009071 0.1012 9.737 34.58 17.29 0.2794 10.02 11.29 0 38.51 55.53 6.035 2.003 59.11 18.98 0 2.897

0 13.54 13.83 10.75 10.75 10.75 10.75 6.976 17.57 17.57 44.83 44.83 44.83 44.83 44.83 44.83 44.83 34.32 53.88 17.57 17.57 17.57 63.35 55.75 0 186 119.3 119.3 186 186 2206 0 101.6

10

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Fig. 5. Results of simulation at base and various optimized modes of the devised trigeneration system.

temperature of 345 K, AC pressure ratio of 12.31, GT outlet pressure of 550 kPa, PA temperature of 750 K, and GT inlet temperature of 1550 K. Comparing results of COD and base modes, it is found that the freshwater rate, TGOR, and UCT are decreased by 32.36%, 5.62%, and 17.22%, respectively. While, the net electricity, refrigeration load, and exergy efficiency are increased by 2.13%, 21.69%, and 11.84%, respectively. The freshwater rate, net electricity, refrigeration load, TGOR, exergy efficiency, and UTC in TGOROD mode are computed 36.23 m3/day, 1148 kW, 304 kW, 0.844, 38.44%, and 16.79 $/GJ, respectively. To achieve this scenario, we should set the unit on the seawater/air mass flow rate ratio of 1.5, evaporator temperature of 273 K, vapour generator temperature of 577.3 K, desalination top temperature of 345 K, AC pressure ratio of 10.15, GT outlet pressure of

550 kPa, PA temperature of 750 K, and GT inlet temperature of 1472 K. In this study, MOOD mode is recommended as the optimum mode due to the highest trade-off improvement in all performance factors. Comparing results of MOOD and base modes, it is found that the UCT is decreased by 6.71%. While, the net electricity, refrigeration load, TGOR, and exergy efficiency are increased by 2.58%, 22.69%, 14.04%, and 13.26%, respectively. Also, the freshwater rate is remained constant through this mode of optimization. The freshwater rate, net electricity, refrigeration load, TGOR, exergy efficiency, and UTC in TGOROD mode are computed 43.29 m3/day, 1153 kW, 306.5 kW, 1.02, 38.93%, and 19.14 $/GJ, respectively. To achieve this scenario, we should set the unit on the seawater/air mass flow rate ratio of 1.57, evaporator temperature of 273 K, vapour generator temperature of 11

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590 K, desalination top temperature of 330 K, AC pressure ratio of 12.05, GT outlet pressure of 550 kPa, PA temperature of 750 K, and GT inlet temperature of 1550 K. Table 12 shows different elements role in destruction of the overall exergy of the system for MOOD mode. Combustion chamber is recognized as the highly destructive element by exergy destruction of 771.6 kW, constituting around 46.2% of the overall exergy destruction of 1670 kW. The overall investment cost and destruction cost are obtained 19.58 $/h and 100.5 $/h, respectively. Humidifier has the highest investment cost of 7.62 $/h, followed by turbine by 2.29.

electricity (which is consistent with study of Badran [32] and Nikpey Somehsaraei et al. [28,33], and Khaljani, et al. [22]) and refrigeration load due to the increment of saturated vapor mass flow rate at the inlet of turbine. Consequently, more freshwater will be generated since more thermal heat can be directed into the HDH unit. As GT inlet temperature increases, input thermal heat of the combustion process along with its exergy rate are reduced considerably and hence energy and exergy efficiencies augment. The UCT, however, is minimized at T4 = 1480K to the value 19.25 $/GJ. 5.4.3. Impact of preheated air temperature on performance of the system Fig. 8 displays influence of the preheated air (PA) temperature on the net electricity, refrigeration load, freshwater rate, energy and exergy efficiencies, and UCT of the devised trigeneration set-up. The mass flow rate of the saturated organic fluid at the inlet of turbine is decreased with the rise of PA temperature since the enthalpy difference through the vapor generator drops, leading to the decrement of net electricity (since ORC-turbine power decreases), refrigeration load (due to the drop of the primary flow mass flow rate), and freshwater rate (due to the drop of thermal energy delivered to the HDH unit). Additionally, as PA temperature increases, thermal energy and exergy through the combustion process experiences a downward trend. Since decrement rate of outputs speaks louder than the decrement of input thermal heat, thus TGOR will decreases as PA temperature goes upward. By contrast, the decrement rate of input exergy rate is higher than the decrement of exergy of outputs and net electricity, and hence exergy efficiency increases as PA temperature rises up (which is consistent with study of S. E. Hosseini, et al. [21] and Khaljani, et al. [22]). Economic evaluation also indicated that UTC drops as PA temperature increases due to the low consumption of energy required as prime mover (which is consistent with study of Khaljani, et al. [22]).

5.4. Parametric study This sub-part measures impact of CH4 molar ratio, GT inlet temperature, AC pressure ratio, preheated air temperature, seawater/air mass flow rate ratio, vapor generator temperature, desalination top temperature, evaporator temperature, and turbine outlet pressure on refrigeration load, net electricity, freshwater rate, TGOR, exergy efficiency, and UCT. 5.4.1. Impact of methane molar ratio on performance of the system The impact of CH4 molar ratio on the refrigeration load, net electricity, freshwater rate, energy efficiency, exergy efficiency, and UCT of the devised trigeneration set-up is sketched in Fig. 6. On the basis of the layout, giving a rise to the CH4 molar ratio leads to the increment of net electricity due to the reality that the thermal heat discarded from the GT cycle to the bottoming system is raised up (the gas turbine power capacity is designed constant). As a result, more primary flow will be injected into ejector to suck more refrigerated flow inside of ejector, and hence more refrigeration load will be extracted at high CH4 molar ratios. The increment of mass flow rate of the outlet stream of turbine also leads to the increment of discarded heating to the HDH unit via condenser 2, causing to the increment of freshwater mass flow rate as well. In spite of the increase of all outputs, the TGOR is decreased as CH4 molar ratio increases since the input thermal energy of fuel injected to the GT cycle is drastically augmented. However, in terms of exergy, increment rate of exergy of input thermal energy of fuel is low in comparison with net electricity increment, and hence exergy efficiency increases as CH4 molar ratio augments. In terms of cost evaluation and by considering a constant fuel price for any CH4 molar ratios, it is found that UCT is also increased as CH4 molar ratio rises up.

5.4.4. Impact of air compressor pressure ratio on performance of the system Fig. 9 depicts the impact of AC pressure ratio on the net electricity, freshwater rate, refrigeration load, TGOR, exergy efficiency, and UCT. Net electricity, freshwater rate, refrigeration load, TGOR, and UCT have the minimum value of 1121.65 kW, 52.5 m3/day, 244.8 kW, 0.894, and 20.01 $/GJ, respectively at rAC = 8, while exergy efficiency increases at first up to the point of 34.72% and then decreases with rAC . This finding is in consistent with that of Hosseini et al. [22], and Nemati et al. [34], and Khaljani, et al. [22]). The findings can be justified as follows. A precise parametric evaluation unravels that the capture thermal energy from fuel consumption in the combustion chamber has a minimum value at rAC = 8 and due to its dominant effect on the main performance factors, the trend of outcomes and performance parameters resemble its trend.

5.4.2. Impact of GT inlet temperature on performance of the system Influence of GT inlet temperature on the net electricity, freshwater rate, refrigeration load, energy and exergy efficiencies, and UCT is sketched in Fig. 7. Rising up the GT inlet temperature increases the net

Table 12 Exergoeconomic factors for defferent elements of the devised trigeneration system when Tuluene used as refrigerant around MOOD mode. Components

ED, k (kw)

CD, k ($/h)

ZD ($/h)

fk (%)

r k (%)

ex , k

Air compressor Air preheater Combustion chamber Gas turbine Vapor generator Turbine Ejector Evaporator Condenser 1 Condenser 2 Internal heat exchanger Mixer Pump 1 Pump 2 Humidifier Dehumidifier Total system

63.6 57.66 771.6 91.68 221.4 11.21 166.2 3.784 9.776 197.2 9.392 10.69 0.04526 0.5107 30.01 25.31 1670

2.816 2.232 24.14 3.549 8.572 0.7084 8.44 0.6104 1.577 12.46 1.515 1.96 0.003676 0.04147 14.89 16.99 100.5

0.9989 0.3761 0.1496 7.154 0.0826 2.293 0 0.06462 0.04127 0.005696 0.1502 0 0.0355 0.2306 7.621 0.3806 19.58

26.18 14.42 0.6158 66.84 0.9544 76.4 0 9.573 2.551 0.04568 9.02 0 90.62 84.76 33.85 2.191 16.31

10.06 43.94 23.75 14.4 33.44 28.45 217.6 17.01 126.7 274.9 20.9 24.35 55.09 27.16 17.2 43.21 139.1

93.08 72.67 80.9 95.44 75.12 93.71 31.48 86.67 44.75 26.68 84.02 80.42 95.08 96.02 73.95 70.29 38.93

12

(%)

yD (%) 3.808 3.453 46.2 5.489 13.26 0.6709 9.952 0.2266 0.5853 11.81 0.5623 0.6404 0.00271 0.03058 1.797 1.516

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Fig. 6. Variation trend of freshwater rate, net electricity, refrigeration load, TGOR, exergy efficiency, and UCT with an alteration in the CH4 molar ratio.

5.4.5. Impact of seawater/air mass flow rate ratio on performance of the system Fig. 10 is sketched to understand variation trend of freshwater rate, net electricity, refrigeration load, TGOR, exergy efficiency, and UCT with an alteration in the seawater/air mass flow rate ratio for the devised new trigeneration system. According to Fig. 10, the freshwater, net electricity, refrigeration load, TGOR, and exergy efficiency reached their highest value of 57.83 m3/day, 1124.14 kW, 249.82 kW, 0.932, and 34.37%, respectively at mr = 1.69 . This trend is mainly because of the trend of the seawater temperature entering condenser 2 which is maximized at this point. Since terminal condenser 2 outlet temperature is related to this temperature via a constant value of terminal temperature difference, thus temperature profile at the outlet of condenser 2 also experiences a similar trend, affecting outputs in the same way. This finding is very consistent with previous studies [15,17,35–37]. However, UCT of the system is increased as mr rises up since supplying more seawater required more thermal energy and humidifier/dehumidifier with higher heat capacity, and hence cost of the product increases.

be explained by the fact that at low VG temperatures ejector sucks high mass flow rate of the secondary flow, while its suction power drops at very high VG temperatures due to its constant thermodynamic properties. Therefore, achieving a minimum value for the mass flow rate of the secondary flow led to a minimum value of refrigeration load as well. In terms of freshwater, condenser 2 duty decreases as VG temperature increases since is liquefied refrigerant mass flow rate has been decreased, and hence less freshwater can be distilled due to the low thermal load supply to the HDH unit. Due to the dominant impact of net electricity on the exergy efficiency, increasing VG temperature will also increase net electricity of the system. However, due to the impact of all aforementioned parameters on TGOR and UCT, they are minimized by 0.894 (at TVG = 577.2K ) and 249.4 $/GJ (at TVG = 582.7K ), respectively. 5.4.7. Impact of desalination top temperature on performance of the systems Fig. 12 shows variation trend of refrigeration load, net electricity, freshwater rate, TGOR, exergy efficiency, and UCT with an alteration in the desalination top temperature for the devised trigeneration system. According to Fig. 12, freshwater rate has a maximum of 55.77 $/GJ at desalination top temperature of 341 K, which can be justified by previous studies [15,17,35]. Due to the dominant impact of freshwater rate on the TGOR, TGOR has also maximum value of 0.911 at the same desalination top temperature. Also, augmenting desalination top temperature slightly increases condenser 2 outlet temperature and hence turbine output power and refrigeration load will rise up. Consequently, net electricity and exergy efficiency augments at high desalination top temperatures due to the substantial impact of net electricity on the exergy efficiency. and hence net electricity increases slightly as desalination top temperature augments. In terms of economic, UCT is decreased as desalination top temperature moves upward.

5.4.6. Impact of vapor generator temperature on performance of the system Fig. 11 is sketched to understand variation trend of output net power, refrigeration load, freshwater rate, TGOR, exergy efficiency, and UCT with an alteration in the vapor generator (VG) temperature for the devised trigeneration system. According to Fig. 11, the net electricity increases as VG temperature goes up since enthalpy drop through the ORC-turbine increases dramatically in spite of the fact that the saturated vapor mass flow rate decreases. However, the refrigeration load reached its nadir value of 249.4 kW at VG temperature of 579.4 K, (which is consistent with study of Rostamzadeh, et al. [38]) while freshwater decreases continuously as VG temperature experiences an upward trend. The minimum value of refrigeration load achieved can

Fig. 7. Variation trend of freshwater rate, net electricity, refrigeration load, TGOR, exergy efficiency, and UCT with an alteration in the GT inlet temperature. 13

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Fig. 8. Variation trend of freshwater rate, net electricity, refrigeration load, TGOR, exergy efficiency, and UCT with an alteration in the preheated air temperature.

Fig. 9. Variation trend of freshwater rate, net electricity, refrigeration load, TGOR, exergy efficiency, and UCT with an alteration in the AC pressure ratio.

Fig. 10. Variation trend of freshwater rate, net electricity, refrigeration load, TGOR, exergy efficiency, and UCT with an alteration in the seawater/air mass flow rate ratio.

Fig. 11. Variation trend of freshwater rate, net electricity, refrigeration load, TGOR, exergy efficiency, and UCT with an alteration in the vapor generator temperature.

14

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Fig. 12. Variation trend of freshwater rate, net electricity, refrigeration load, TGOR, exergy efficiency, and UCT with an alteration in the desalination top temperature.

Fig. 13. Variation trend of freshwater rate, net electricity, refrigeration load, TGOR, exergy efficiency, and UCT with an alteration in the evaporator temperature.

Fig. 14. Variation trend of freshwater rate, net electricity, refrigeration load, TGOR, exergy efficiency, and UCT with an alteration in the turbine outlet pressure.

5.4.9. Impact of turbine outlet pressure on performance of the system Fig. 14 shows variation trend of refrigeration load, output power, freshwater rate, TGOR, exergy efficiency, and UCT with an alteration in the turbine outlet pressure for the devised trigeneration system. The freshwater rate and refrigeration load are augmented as turbine outlet pressure rises up since primary flow pressure increases and sucks more refrigerated flow inside the ejector and also condenser 2 discards more thermal heat to the desalination unit. The augmentation in freshwater and refrigeration load is achieved at the expense of power reduction since turbine expansion ratio decreases. TGOR resembles variation trend of refrigeration load due to its dominant impact, while exergy efficiency follows trend of output power due to the dominant impact of output power in exergy definition. As a result, TGOR will increase with the rise of turbine outlet pressure, while exergy efficiency decreases through this alteration. In terms of economic, with the rise of turbine outlet pressure UCT is slightly increased due to the drop of net electricity and low cost associated with it.

5.4.8. Impact of evaporator temperature on performance of the system Fig. 13 shows variation trend of refrigeration load, net electricity, freshwater rate, TGOR, exergy efficiency, and UCT with the change of the evaporator temperature. According to Fig. 13, the refrigeration load is increased as evaporator temperature rises up since the enthalpy rise through the evaporator increases, which can be justified by previous studies [15,17,35]. However, freshwater rate and net electricity are slightly decreased as evaporator temperature increases since the mass flow rate at the outlet of turbine decreases leading to the decrement of condenser 2 duty. Due to the substantial increment of the refrigeration load TGOR is also increases. However, exergy efficiency is increased at low evaporator temperatures (due to the dominant impact of refrigeration load) and is decreased at high evaporator temperatures (due to the dominant impact of net power in comparison with other effective exergy parameters). Exergy efficiency is maximized to 34.37% at evaporator temperature of 267.1 K. Thermoeconomic results indicated that an increase in the evaporator temperature causes a drop in UCT, too. 15

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6. Concluding remarks

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A new trigeneration system for freshwater, power, and cooling production is devised based on a biogas-fueled GT cycle. As reviewed in literature survey of present study, biogas-based power plants have a great potential to be extended to trigeneration systems, nonetheless less attention is paid with this regard in terms of freshwater production. Therefore, present study is carried out to develop a new trigeneration system for this aim and its feasibility is investigated from energy, exergy, and economic viewpoints. Exergoeconomic optimization is later performed and results are elaborated in detail. Following concluding remarks can be drawn based on our simulation:

• MOOD mode was recommended as the optimum mode of design. • Five working fluids were screened through the new ORC/ECC • •

system and ultimately Toluene was suggested since, in the case the overall integrated trigeneration system , it had the highest refrigeration load of 249.8 kW and TGOR of 0.894. Using Toluene as refrigerant in the ORC/ECC system, optimization led to the increment of the net electricity, refrigeration load, TGOR, and exergy efficiency of around 2.58%, 22.69%, 14.04%, and 13.26%, respectively, while UCT was decreased by 6.71%. Among all elements, combustion chamber was recognized as the highly destructive element by exergy destruction of 771.6 kW, followed by vapor generator with exergy destruction of 221.4 kW.

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