Investigation of a novel multigeneration system driven by a SOFC for electricity and fresh water production

Energy Conversion and Management 196 (2019) 296–310

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

Investigation of a novel multigeneration system driven by a SOFC for electricity and fresh water production

T

⁎

Nazanin Chitgara, Mohammad Ali Emadia, Ata Chitsazb, , Marc A. Rosenc a

School of Mechanical Engineering, Iran University of Science and Technology, Tehran 16844, Iran Faculty of Mechanical Engineering, Urmia University, Urmia, Iran c Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, Ontario L1G 0C5, Canada b

A R T I C LE I N FO

A B S T R A C T

Keywords: Solid oxide fuel cell Kalina cycle Desalination Multi-objective optimization Thermodynamic simulation Exergy-economic analysis

An integrated system for the simultaneous production of electricity and fresh water is proposed based on a solid oxide fuel cell (SOFC). In this system, a Kalina cycle is utilized to recover waste heat from the SOFC stack. Furthermore, a thermoelectric generator is employed to recover the heat dissipated in the Kalina condenser. In the proposed configuration, the energy required for reverse osmosis desalination can be supplied by a Kalina cycle and a thermoelectric generator. The system uses methane as its primary fuel. Electrochemical equations for the fuel cell are considered, as are thermodynamic and exergy-economic relations for the components of the system. The effects on the performance of the proposed hybrid system of variations in design parameters such as current density, SOFC inlet temperature, fuel utilization factor, inlet pressure of the Kalina cycle turbine and concentration of water-ammonia solution in the Kalina cycle are examined. The SOFC stack is seen to make the highest contribution to the total exergy destruction of the system. To strive simultaneously for maximum efficiency and minimum total cost, optimization is carried out using a genetic algorithm. The total optimum point of the system is the trade-off between the optimization objectives. At this point, the net electrical power production is about 1.3 MW and the production rate of fresh water reaches 226 m3/day, while the exergy efficiency and total cost rate are 54% and 36.8 $/hr, respectively.

1. Introduction Increasing of energy demand combined with growing environmental concerns has increased interest in innovative, efficient and environmentally benign technologies for energy conversion. The appropriate use of such technologies in energy conversion system can simultaneously improve efficiency while decreasing harmful impacts on the environment. Among innovative energy conversion technologies, fuel cells garnered much attention. Fuel cells have advantages such as relatively high efficiency, and low pollutant emission and noise [1]. In a fuel cell, reacts electrochemically to generate direct current (DC). Campanari [2] conducted energy and exergy analyses of a system composed of a micro gas turbine (MGT) and an SOFC. The results showed that the MGT efficiency can be considerably increased when coupled with a SOFC, reaching an electrical efficiency of 63%. Moreover, the thermal efficiency of the SOFC-MGT increased to 86% when used for combined heat and power (CHP). Al-Sulaiman et al. [3] studied a hybrid system

consisting of an SOFC and an organic Rankine cycle (ORC) integrated by a single-stage absorption refrigerator. Their results indicated that trigeneration efficiency of the integrated system exceeded that of the SOFC-ORC by 22%. Akkaya and Sahin [4] performed an energy analysis of a hybrid system composed of a SOFC and an ORC. They found that the energy efficiency of the system can be increased by 14–25% if the ORC is used for heat recovery from the SOFC. The Kalina cycle (KC) for recovering and using waste heat is an alternative to an ORC [5]. A limited number of studies have addressed the use of a KC to recover heat from a SOFC or SOFC-GT system. Ma et al [6] proposed a CCHP system based on a SOFC in which the GTSOFC-induced waste heat was used in a Kalina cycle. The results revealed that the thermal efficiency of the proposed system can be as high as 80%. Moreover, a parametric study was conducted on design parameters such as fuel utilization factor, ammonia-water concentration and turbine input pressure to assess their effects on system performance. Tan et al [7] investigated the energy efficiency of a hybrid system composed of a SOFC, a gas expander (GE) and a KC. They found

⁎

Corresponding author. E-mail addresses: [email protected] (N. Chitgar), [email protected] (M.A. Emadi), [email protected] (A. Chitsaz), [email protected] (M.A. Rosen). https://doi.org/10.1016/j.enconman.2019.06.006 Received 5 April 2019; Received in revised form 2 June 2019; Accepted 3 June 2019 0196-8904/ © 2019 Elsevier Ltd. All rights reserved.

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π ρ ψ

Nomenclature Surface area (m2) Capital recovery factor Specific exergy (kJ/kg) Exergy rate (kW) Exergy destruction rate (kW) −0 Δg Change in molar Gibbs free energy (kJ/kmol) h Specific enthalpy (kJ/kg) H Enthalpy (kJ) ΔH Molar enthalpy change of reaction (kJ/kmol) i Current density (A/m2) k Thermal conductivity (W/m K) Kp,ref , Kp,sh Equilibrium constant (Pa2), (−) l Thickness (m) ṁ Mass flow rate (kg/s) MW Molecular weight (kg/kmol) ṅ Molar flow rate (mol/s) P Pressure (kPa) P0 Environmental dead state pressure (kPa) Heat transfer rate (kW) Q̇ R Electrical resistance (Ω) − R Universal gas constant (8.314 kJ/kmol K) s Specific entropy (kJ/kg.K) T Temperature (K) T0 Environmental dead state temperature (K) Ua Air utilization ratio Uf Fuel utilization ratio Vcell Cell voltage (V) VN Reversible cell voltage (V) Vloss Loss voltage (V) Ẇ Power (kW) x Molar fraction ẋ Extent of steam reforming reaction (mol/s) ẏ Extent of water gas shift reaction (mol/s) y Mass fraction Z Capital cost of a component ($) Extent of electrochemical reaction (mol/s) ż Ż Capital cost rate ($/hr) A CRF ex Eẋ Eẋ D

Subscripts 0 * a act AC APH b c ch conc CI e elec f FC FPH G in int N Ohm ov out OM P ph surr T

Environmental condition Restricted dead state Anode Activation Air compressor Air preheater Brine Cathode Chemical Concentration Capital investment Electrolyte Electrochemical Feed water Fuel compressor Fuel preheater Exhaust gas Inlet Interconnect Nernst Ohmic Overall Outlet Operation and maintenance Pump Physical Surroundings Turbine

Abbreviations DC GT HT KC LT ORC RO SOFC

Greek symbols

ζ η µ

Osmotic pressure (kPa) Electrical resistivity of cell component (Ωm) Exergy efficiency

Voltage losses (V) Energy efficiency Chemical potential (J/kg)

Direct current Gas turbine High temperature Kalina cycle Low temperature Organic Rankine cycle Reverse osmosis Solid oxide fuel cell

SOFC. Ziapour et al [12] integrated an ORC and a TEG to enhance the electricity production of a solar plant with two approaches. First, the ORC condenser was replaced by a TEG. Second, a TEG was used as a heat exchanger in the ORC. The results indicated that the thermal efficiency of the plant can be increased by 21.9% and 12.7% with the first and second approaches, respectively. Due to rising living standards and increased demand for fresh water in domestic, industrial and agricultural sectors, parts of the world are facing fresh water shortages. To overcome this problem, the desalination of seawater has found considerable use for producing drinking water [13]. Fuel cell-based hybrid systems are a potentially advantageous option for coupling with water desalination units. Various studies have addressed the integration of these units. Eveloy et al [14] combined SOFT and GT systems with a reverse osmosis (RO) unit. Seven types of working fluids were investigated for heat recovery from the SOFC-GT system. Al Hallaj [15] reported that the required energy of the RO system was reduced about 8 percent by pre-heating the feed water using the waste heat of the MCFC. Lisbona

that if the KC uses the heat from a gasoline engine, the total energy efficiency can be increased by 10.3%. Wang et al [8] carried out energy and exergy analyses of a combined system based on an SOFC. The system included an SOFC, an afterburner, a gas turbine, a heat exchanger, compressors and a Kalina cycle. A parametric study showed that increasing the air circulation enhanced the electric efficiency of the SOFC and the total electric and exergy efficiencies of the hybrid system. The results showed that the overall electrical and exergy efficiencies are 70% and 60%, respectively. Recently, thermoelectric generators (TEGs) have begun to be used in electricity production systems to improve energy efficiency. TEGs can produce electricity without greenhouse gas emissions [9]. Zare and Palideh [10] proposed a Kalina-TEG integrated system whose major driving force is geothermal energy. They showed that the application of the TEG increased the exergy efficiency by 7.3%. Zhang et al examined the recovery of waste heat from an SOFC system by a thermoelectric generator and thermoelectric coolers [11]. The results revealed that the energy efficiency of the proposed system is 4.6% more than that for the 297

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produce combustion gases in the afterburner. The output gases of the afterburner, after passing through the preheaters to preheat the SOFC stack inlet, enter the KC evaporator for heat recovery and then are released to the atmosphere. The KC includes the following: steam generator, separator, turbine, valve, high- and low-temperature heat exchangers, mixer and pump. The high-pressure two-phase mixture receives the required energy from the SOFC exhaust and passes to the separator of the steam generator. There, the flow is divided into a saturated stream of ammonia-rich water-ammonia mixture and a saturated fluid of ammonia-water mixture with reduced water mass fraction. The saturated stream is expanded in a turbine to produce electricity. In the meantime, the saturated fluid is conveyed to the high-temperature heat exchanger to preheat the high-pressure mixture; its pressure drops after passing through the valve. The two-phase output flow of the turbine is mixed with the fluid exiting the valve in the mixer and the mixture enters the heat exchanger. In this system, a thermoelectric generator is used instead of a Kalina cycle condenser. A water-ammonia mixture enters the warm side of the TEG and produces electricity by transferring heat to the inlet water on the cool side. The saturated flow is pumped and preheated and returned to the evaporator. The Kalina cycle turbine produces electricity and the TEG product is used by the RO unit. The RO unit is integrated with the hybrid system to produce fresh water, i.e., water with a salinity of < 500 ppm. Seawater is pumped into the system with a low-pressure pump. It passes through a filter to remove suspended particles and then is divided into two parts. A small amount of seawater bypasses the RO unit to provide the required salinity of the RO products. The rest of water passes through a static mixer in which specific chemicals are added. The added chemicals are required to prepare the feed water for a condition that permits use in the RO membrane modules without causing damage to them. The high-

et al [16] used the electricity of a SOFC for an RO unit and the heat of a SOFC to preheat the RO input seawater. It was shown that the combined SOFC-RO is more economic than use of SOFC exhaust to produce the required steam for a multi-stage flash desalination unit. Since the use of a KC for recovery and use of SOFC waste heat has been investigated in a limited number of studies, a KC is used in the present study to recover waste heat from an atmospheric SOFC system and to use an RO unit to produce drinking water. A TEG is also used to consume a part of waste heat dissipated by the KC condenser. A mathematical model is used to simulate the energy production system under steady state conditions. The overall thermodynamic performance of the system is evaluated. An exergy analysis is conducted along with an economic analysis to investigate the possibility of varying key parameters to improve the system performance thermodynamically and economically. The contribution of each component to the total exergy destruction is determined. Finally, multi-objective optimization is used to obtain the optimum performance of the proposed system with respect to two objectives: high exergy efficiency and low rate of total cost. 2. System description Fig. 1 shows the SOFC-KC-TEG-RO hybrid system considered in this study. The operation of the combined system is as follows. Methane and air separately enter their compressors. After evaporation, water is mixed with methane in a heat exchanger. In the SOFC stack, anode inputs experience shifting and reforming reactions, which produce the required hydrogen for the electrochemical reaction. A part of the produced heat from the exothermic electrochemical reaction is used to provide the required energy of the endothermic reforming reaction. The other part is utilized to heat the products of the fuel cell. The output air of the cathode and unused fuel of the anode are completely burnt to

Fig. 1. Schematic of the proposed integrated system. 298

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Table 1 Molar flow rates for each species in the fuel cell group.

Uf =

Anode

Cathode

̇ 4,j = x ̇ nCH

̇ 2,i ṅN2,i = 3.76nO

(6)

where Pcell and Tcell are the pressure and temperature of the fuel cell −0 −0 and ṅ is mole rate. Also, Δ greforming and Δ gshifting are the changes in Gibbs free energy and can be written as:

̇ 4,j ṅH2O,j = rsc × nCH

̇ 2,l = nO ̇ 2,i − 0.5z ̇ nO

ṅH2,k = 3x ̇ + y ̇ − z ̇ ̇ nCO,k = ẋ − ẏ ̇ 2,k = y ̇ nCO ṅH2O,k = ṅH2O,j − x ̇ − y ̇ + z ̇

ṅN2,l = ṅN2,i ̇ ̇ 2,i + ṅN2,i ntotal,i = nO ̇ ̇ 2,l + ṅN2,l ntotal,l = nO

Ua =

ż 3x ̇ + y ̇

−

−0

−

Δgreforming = Δhreforming − Tcell Δsreforming −

−

−

−

−

Δh reforming = 3hH2 + hCO − hCH4 − hH2O

ż

−

̇ 2,i 2nO

−

−

−

−

Δsreforming = 3sH2 + sCO − sCH4 − sH2O

̇ ̇ 4,j + ṅH2O,j ntotal,j = nCH ̇ ̇ ̇ 2,k ntotal,k = ṅH2,k + ṅH2O,k + nCO,k + nCO

−

−0

(7)

−

Δgshifting = Δhshifting − Tcell Δsshifting − −

−

−

(10)

Vloss = ζ ohm + ζact + ζ conc

(11)

Table 2 Electrochemical equations. Voltage

In this study, the required hydrogen is supplied by the reforming reaction, in an internal reformer to the methane-fueled SOFC. The reactions occurring in a fuel cell with a reformer are:

Z ̇ [H2 + 1/2O2 → H2 O] Overall electrochemical reaction

(9)

Vcell = VN − Vloss

Nernst voltage

(2)

(8)

Ohmic overvoltage

Relation − °

⎛ Δg VN = ⎜− s ⎜ ne F ⎝

⎞ ⎟− ⎟ ⎠

(12) RTcell ⎛ P H2 O ln ⎜ ne F P H2 P O2

⎝

(14)

−1

(15)

⎝

⎠

6

(16)

−1

−10300 ⎞ ⎞ ρe = ⎛3.34 × 10 4exp ⎛ ⎝ Tcell ⎠ ⎠ ⎝

(3)

(17)

−1

9.3 × 10 −1100 ⎞ ⎞ ρint = ⎛ exp ⎛ ⎝ Tcell ⎠ ⎠ ⎝ Tcell

Activation overvoltage

Concentration overvoltage

(4)

ζact,a =

RTcell ⎛Sinh−1 ⎛ j ⎞ ⎞ F ⎝ 2joa ⎠

ζact,c =

RTcell ⎛Sinh−1 ⎛ j ⎞ ⎞ F ⎝ 2joc ⎠

299

⎝

(19)

⎠

⎝

(20)

⎠ (21)

ζ conc = ζconc,a + ζ conc,c ζ conc,a =

−RTcell ⎛ ⎜ln ⎛1 2F ⎝

−

j ⎞ jas ⎠

ζ conc,c =

−RTcell ⎛ln ⎛1 4F ⎝

−

j ⎞ ⎞ jcs ⎠ ⎠

jcs =

(5)

(18)

ζact = ζact,a + ζact,c

jas =

0

ṅCO2,k × ṅH2,k ⎛ Δg¯shigting ⎞ = ecp ⎜ RT ¯ cell ⎟ ṅCO2,k × ṅH2O,k ⎝ ⎠

(13)

42 × 10 −1200 ⎞ ⎞ ρc = ⎛ exp ⎛ ⎝ Tcell ⎠ ⎠ ⎝ Tcell

0

Kp,sh =

⎟

−1 6 ⎛ 95 × 10 exp ⎛ −1150 ⎞ ⎞ Tcell ⎝ Tcell ⎠

6

ṅH32,k × ṅCO,k ⎛ Pcell ⎞2 ⎛ Δg¯reforming ⎞ ⎜ ⎟ = exp ⎜ RT ¯ cell ⎟ ṅCH4,k × ṅH2O,k ⎝ ṅtotal,k ⎠ ⎠ ⎝

⎞ ⎠

ζ ohm = (ρa la + ρc l c + ρe l e + ρint lint ) j ρa =

Hydrogen is produced through methane reforming and shifting reactions shown in Eqs. (1) and (2). It is then consumed in the electrochemical reaction shown in Eq. (3) to produce power. The molar conversion rates for the reforming, shifting and electrochemical reactions in Eqs. (1)–(3) are denoted by ẋ, ẏ and ż, respectively. These variables can be obtained by solving simultaneously the equations for the equilibrium constants of the reforming (Kp,reforming) and shifting reactions (Kp,shifting), and the fuel utilization factor (Uf), which are expressed as follows:

Kp,reforming =

−

Here, VN and Vloss are the cell reversible voltage and the sum of the Ohmic, activation and concentration overvoltages, respectively. The calculations of the Nernst voltage and the overvoltages are described in Table 2. The operating temperature of the fuel cell, Tcell, is unknown at this

3.1. Solid oxide fuel cell

ẏ [CO+H2 O↔ H2 + CO2] Shifting

−

The fuel cell voltage can be expressed as:

2

(1)

−

ẆSOFC = iAact Ncell Vcell

2

ẋ [CH 4 + H2 O↔ 3H2+CO] Reforming

−

Note that the relevant thermodynamic parameters, such as g , h and − s , are written in molar units. After calculation of ẋ, ẏ and ż, the molar flow rates of the gases are determined (see Table 1). The electric power produced by the SOFC stack can be written as the product of the current density (i), the active surface (Aact), the number of fuel cells in the stack (Ncell) and the fuel cell voltage.

• The entire system operates at a steady condition and changes in kinetic and potential energies can be ignored. • Pressure drops in the heat exchangers and pipelines are neglected. • All gases behave as ideal gases. • Air is composed of N (79%) and O (21%). • Each system components is considered as a control volume. • Radiative heat transfer between the gas channels and solid structures can be ignored. • The equipment is completely insulated, so that there is no thermal dissipation into the environment • Air and fuel enter the SOFC stack at the same temperature. • Only hydrogen reacts in the electrochemical reaction and CO and H O are converted to H and CO in a shift reaction. • Unreacted gases are completely burnt in the afterburner. 2

−

−

Mathematical models are used for the thermodynamic analysis of the system components. The following assumptions are made:

2

−

Δsshifting = sH2 + sCO2 − sCO − sH2O

3. Modeling

2

−

Δh shifting = hH2 + hCO2 − hCO − hH2O

pressure pump is used to increase the water pressure to the design pressure. The design pressure of the RO system is determined based on the osmosis pressure calculated in system analysis section. The brine provides a part of RO required power by passing through a Pelton turbine.

⎝

⎝

4FP H2 Daeff RTcell la 4FP O2 Dceff P O2 ⎞⎟ RTcell lc ⎛⎜1 − P0 ⎠ ⎝

− ln ⎛1 − ⎝

P H2 j P H2 O jas

⎞⎞ ⎠⎠

(22)

⎟

(23) (24) (25)

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point. But it can be determined by a trial and error method using the energy equilibrium equation of the SOFC. As a result of hydrogen oxidation in the electrochemical reaction and its conversion to electricity, heat is released. The heat produced by the electrochemical and shifting reactions provides the heat required for the reforming process and heats the mixture of the produced gases. The enthalpy variation of the electrochemical reaction, the heat consumed for reforming and the heat released in shifting, can be calculated as follows:

(

)

Q̇reforming = x ̇ hCO + 3hH2 − hCH4 − hH2O

(

)

̇ Qshifting = y ̇ hCO2 + hH2 − hCO − hH2O

(

ΔHelec = z ̇ hH2O − hH2 − 0.5hO2

Table 3 Relations used in energy analysis of the KC. Component Turbine

(26) (27)

)

Energy equations

ηis,T =

Ẇ T , Ẇ is,T

Ẇ T = ṁ 1 (h1 − h2)

Evaporator

ṁ G (hp − hq ) = ṁ 8 (h9 − h8)

Separator Condenser Pump

ṁ 9 h9 = ṁ 10 h10 + ṁ 11 h11 ṁ 4 (h4 − h5) = ṁ W (h14 − h13)

HT heat exchanger LT heat exchanger Mixer Throttle valve

ṁ 7 (h8 − h7) = ṁ 10 (h10 − h11) ṁ 6 (h7 − h6) = ṁ 3 (h3 − h4 ) ṁ 2 h2 + ṁ 12 h12 = ṁ 3 h3 h11 = h12

ηis,P =

Ẇ is,P , Ẇ P

Ẇ P = ṁ 5 (h6 − h5)

(28)

̇ = ΔHelec + Qsurr ̇ Qelec + ẆSOFC

(29)

principles are applied to each of these control volumes. The energy conservation principle can be expressed as:

̇ = zT ̇ FC,new Δs + jVloss Qelec

(30)

Q̇ +

− PH2O ⎞ Δs = (sH2O − sH2 − 0.5sO2) − R ln ⎜⎛ 0.5 ⎟ P H ⎝ 2 PO2 ⎠

∑ ṁ in hin = Ẇ

+

∑ ṁ out hout

(32)

The energy equations for the components of the KC are listed in Table 3.

(31)

The reforming process is endothermic (Qref > 0). Conversely, shifting and electrochemical processes are exothermic (ΔHelec < 0 and Qsh < 0) and can provide the heat required for the reforming reaction in the fuel cell. Moreover, waste heat to the environment (Qsurr > 0) reduces the recoverable heat from the SOFC stack. The trial and error method used to find the stack temperature is shown in Fig. 2.

3.3. Thermoelectric generator The thermoelectric generator is a unique heat engine, in which charge carriers serve as the working fluid. The device converts a heat flow to electricity. TEGs have numerous advantages including high reliability, no moving parts and silent operation, environmental compatibility, ease of repair and maintenance and a long life cycle (> 100,000 h in a steady state) [17] compared to conventional power technology. As shown in the proposed system, a thermoelectric generator replaces the condenser in a typical Kalina cycle. A water-ammonia mixture enters the warm side of the TEG and cooling water enters the cold side. The temperature difference is exploited to produce

3.2. Kalina cycle To analyze the performance of the KC from the viewpoint of the first law of thermodynamics, each component is considered as a control volume operating at steady state. Energy and mass conservation

Fig. 2. Trial and error algorithm to determine the SOFC stack temperature. 300

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occurring in form of exergy destruction or waste can be identified by exergy analysis. The exergy destruction rate of a process (Eẋ D) can be determined from the difference between the fuel exergy and product exergy rates (Eq. (42)). The exergy efficiency is defined as the ratio of product exergy rate to fuel exergy rate, which can be calculated using Eq. (43) for kth component and Eq. (44) for the entire system, as follows [21]:

electricity. To evaluate the energy efficiency of the TEG, the following equations reported in literature can be used [17]:

ηTEG = ηCarnot

1 + ZTM − 1 1 + ZTM +

TL TH

(33)

The TEG energy efficiency can also be be expressed as:

ηTEG =

ẆTEG Q̇ TEG

(34)

In these equations, TL and TH denote the temperatures of cold and warm sides, respectively, while ZTM represents a figure of merit multiplied by average temperature, which is an important parameter as it influences the conversion efficiency of the TEG. The terms ηCarnot, Q̇ TEG and ZTM can be expressed as follows [18]:

Eẋ D = Eẋ F − Eẋ P

(42)

Eẋ P,k Eẋ F,k

(43)

ψk =

ψtot =

Eẋ P,tot Eẋ F,tot

(44)

TL TH

(35)

5. Economic analysis

Q̇ TEG = ṁ cold (h cold,out − hcold,in )

(36)

The economic analysis accounts for capital, operation and maintenance and fuel costs. Applying a cost rate balance to the entire system, we can write:

ηCarnot = 1 −

ZTM =

α 2TM (37)

kR

̇ ̇ + Ctotal = Cfuel

Here, k and R are the thermal conductivity coefficient and electrical resistance, respectively. Further, TM and α can be defined as:

TM =

1 (TH + TL ) 2

α=−

The fuel cost rate can be determined based on the natural gas cost (cf), as follows:

(38)

̇ = c f × LHV × ṁ f Cfuel

ΔV ΔT

ṁ 4 (h4 − h5) = ṁ cold (h cold,out − hcold,in ) + ẆTEG

The capital cost (ŻCI) and operation and maintenance costs (ŻOM) of component k can be determined by:

(40)

̇ + ZOM ̇ = ZCI

(47)

Exergy analysis was conducted using exergetic parameters such as exergy destruction and efficiency for each component and the entire system. To start, the product and fuel exergy rates of each component are determined. The product exergy rate (Eẋ p ) is defined as the rate of exergy of a part or a system which is in accordance with its target; the fuel exergy rate (Eẋ f ) refers to usage rate of the exergy to obtain the exergy of the required product. Table 5 lists the fuel and product exergy rates of each component in the hybrid system. The physical and chemical specific exergies of water and seawater in the RO process can be calculated by the equation proposed and validated by Sharqawy et al. [20] (with maximum deviation of 1.5%):

s ∗)

+

∑ i

wi (μi∗

−

μi0 )

Parameter

Relation

Seawater source Feed mass flow rate

ṁ f = ṁ p/ Rr

Molar fraction of salt in seawater source

4. Exergy analysis

− T0 (s −

Zk × φ CRF t

Table 4 Basic equations for reverse osmosis modeling.

Water desalination is a type of separation process in which salt is separated from feed water (f). The produced water (p) and brine (b) are the two flows in a water desalination plant. Based on the process characteristics, the feed water salinity and fresh water salinity can be calculated using the mass flow rate and the molar and mass fractions of salt and water at any point of the system. The corresponding equations are provided in Table 4 [19]:

h∗)

(46)

(39)

3.4. Reverse osmosis

= (h −

(45)

k

An energy balance for the TEG can be written as:

e ph,ch

̇ + ZOM ̇ )k ∑ (ZCI

Product water Salt mass flow rate in product water

ṁ s,p = ys,p ṁ p x s,p =

MWw ⎡⎛ 1 ⎞ ⎤ MWw + MWs ⎢ ⎜ − 1⎥ y ⎟ ⎢ ⎥ ⎣ ⎝ s,p ⎠ ⎦

Molar fraction of water in product water

x w,p = 1 − x s,p

Mass fraction of water in product water

yw,p = 1 − ys,p

Brine Brine mass flow rate Molar fraction of salt in brine

y

ṁ b = ṁ t − ṁ p

x s,b =

MWw ⎤ ⎡⎛ 1 ⎞ − 1⎥ MWw + MWs ⎢ ⎜ y ⎟ ⎦ ⎣ ⎝ s,b ⎠

x w,b = 1 − x s,b

Mass fraction of water in brine

yw,b = 1 − ys,b

Salinity Salinity = ys × 106

−y

s,p s,RO ⎞ ṁ bypass = ṁ p ⎛ ⎝ ys,f − ys,RO ⎠

Molar fraction of water in brine Mass fraction of salt in brine

Molecular weights of source, product water and brine MWi = x s,i MWs + x w,i MWw

301

⎡⎛ 1 ⎞ ⎤ − 1⎥ MWw + MWs ⎢ ⎜ y ⎟ ⎣ ⎝ s,t ⎠ ⎦

x w,f = 1 − x s,f yw,f = 1 − ys,f

Bypass water Bypass mass flow rate

Here, h, s, μ and w denote specific enthalpy, specific entropy, chemical potential and weight fraction, respectively. Also, properties with “*” are at the ambient pressure and temperature (T0, P0), with the initial flow concentration. This condition is called the restricted dead state. Properties with the superscript “0” are determined at ambient temperature, pressure and concentration (T0, P0, w0), a condition called dead state. As mentioned previously, source and magnitude of exergy wastes

MWw

Molar fraction of water in seawater source Mass fraction of water in seawater source

Molar fraction of salt in product water

(41)

x s,f =

ys,b =

ys,f − Rr ys,RO 1 − Rr

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Table 5 Definitions of exergy rate of fuel and exergy rate of product for each component. Component Fuel cell group SOFC stack Air compressor Fuel compressor Water pump

Exergy rate of fuel (EẋF,k )

Exergy rate of product (EẋP,k )

ch ch ch ch Eẋ j + Eẋ i − Eẋ k − Eẋ l

Eẋ kph − Eẋ jph + Eẋ lph − Eẋ iph

ẆAC Ẇ FC

Eẋ f − Eẋ c Eẋ e − Eẋ b Eẋ d − Eẋ a

Fuel preheater

Ẇ WP Eẋ o − Eẋ p Eẋ n − Eẋ o

Water preheater

Eẋ m − Eẋ n

Mixer

Eẋ D = Eẋ g + Eẋ h − Eẋ j

Afterburner

Eẋ k + Eẋ l

Eẋ m

Eẋ p − Eẋ q Eẋ D = Eẋ 9 − Eẋ 10 − Eẋ 1 Eẋ 1 − Eẋ 2

Eẋ 9 − Eẋ 8

Air preheater

Kalina and TEG system Evaporator Separator Turbine HT heat exchanger LT heat exchanger Pump Throttling valve Mixer TEG Reverse osmosis unit LP pump HP pump Filter

Eẋ i − Eẋ f

Eẋ h − Eẋ e Eẋ g − Eẋ d

Eẋ 10 − Eẋ 11 Eẋ 3 − Eẋ 4

Eẋ 6 − Eẋ 5

Ẇ WP Eẋ D = Eẋ 11 − Eẋ 12 Eẋ D = Eẋ 12 + Eẋ 2 − Eẋ 3 ̇ ) Eẋ 5 − Eẋ 4 + (Eẋ 14 − E13

Ẇ TEG

Ẇ LPP Ẇ HPP

Eẋ 16 − Eẋ 15 Eẋ 19 − Eẋ 18

RO

Eẋ D = Eẋ 16 − Eẋ 17 Eẋ D = Eẋ 18 − Eẋ 20 Eẋ 19 + Eẋ 20

Pelton turbine

Eẋ 22 − Eẋ 23

Throttling valve

Ẇ T Eẋ 8 − Eẋ 7 Eẋ 7 − Eẋ 6

Eẋ 21 Ẇ PT

Table 6 Capital cost for each component of the system. Component Air compressor Fuel compressor Water pump Air preheater Fuel preheater Water preheater

Capital cost

Ref

( )

ZAC =

P 71.1ṁ c P f ln f 0.9 − ηAC Pc Pc

ZFC =

71.1ṁ b Pe P ln ⎛ e ⎞ 0.9 − ηFC P b ⎝ P b ⎠ 0.2 0.71 ⎞ (442Ẇ WP ) 1 − η WP ⎠

ZWP = 1.41 ⎛1 + ⎝

AAPH 0.78 0.093 AFPH 0.78 0.093 AWPH 0.78 0.093

( ) = 130 ( ) = 130 ( )

ZAPH = 130 ZFPH

ZWPH

SOFC stack Afterburner

ZSOFC = Aact Ncell (2.96Tcell − 1907)

KC evaporator

0.89 ZEva = 1397AEva

KC turbine

ZTur = 4405Ẇ Tur

KC pump

ZPump = 1120Ẇ Pump

KC HT heat exchanger

0.514 ZHT = 2143AHT 0.514 ZLT = 2143ALT

KC LT heat exchanger

ZAB =

46.08ṁ l P 0.995 − m Pl

(1 + exp(0.018Tm − 26.4))

[25] [26]

[27]

0.7

0.8

KC separator

ZSep = 280.3ṁ Sep

KC throttling valve TEG

ZTV = 114.5ṁ TV ZTEG = 1000Ẇ TEG

SWIP RO Pelton turbine

ZSWIP = 996Q̇f log10 (ZHPP) = 3.3892 + 0.0536log10 (Ẇ HPP) + 0.1538[log10 (Ẇ HPP )]2 log10 (ZPT ) = 2.2476 + 1.4965log10 (Ẇ PT ) − 0.1618[log10 (Ẇ PT )]2

RO permeator

ZRO = 10N . Am

RO HP pump

[24]

[28]

302

[29]

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respectively. The values used in Eqs. (46)–(48) are provided in Table 7. By thermodynamic simulation of the SOFC-KC-TEG-RO integrated system and calculation of the system properties, exergy and energy efficiencies can be determined for each subsystem. Tables 8 and 9 list energy and exergy efficiencies of the entire system as well as its components.

Table 7 Parameters used in economic equations [30–33]. Value

Parameter

20 year 12% 1.06 7500 h 3.5 USD/MMBTU

N i ϕ t cf

6. System optimization 6.1. Definition of objective functions

Table 8 Energy efficiency definitions and relations for system and its components. Term

Exergy efficiency and total cost of the system are considered as the objective functions in this study. Multi-objective optimization is employed to maximize the exergy efficiency and minimize the cost. These objective functions can be expressed as follows: Objective function I: overall exergy efficiency

Relation

SOFC input energy rate

Q̇in = ṁ CH4,in LHVCH4

SOFC AC power

ẆSOFC,AC = ηinv ẆSOFC ̇ We,SOFC = ẆSOFC,AC − (ẆAC + Ẇ FC + Ẇ WP)

Net electrical power of stack SOFC efficiency

ηSOFC =

̇ We,SOFC Q̇in

ψoverall =

× 100

KC-TEG input energy rate

Q̇in,KC − TEG = ṁ G (hp − hq )

Net electrical power of KC-TEG

̇ We,KC − TEG = Ẇ T + Ẇ TEG − Ẇ KC,P

KC-TEG efficiency RO power input RO efficiency Overall system efficiency

ηKC − TEG =

̇ We,KC − TEG Q̇in,KC − TEG

ṁ frw hfrw Ẇ in,RO + ṁ sw hsw

ηov =

̇ We,SOFC + ṁ frw hfrw Q̇in + ṁ sw hsw

̇ ̇ + Ctotal = Cfuel

× 100

Relation

SOFC input exergy rate

ch,0 Eẋ in = ṁ CH4,in ex CH 4

SOFC exergy efficiency KC-TEG input exergy rate KC-TEG exergy efficiency RO minimum work rate of separation RO exergy efficiency Overall system exergy efficiency

ψSOFC =

̇ We,SOFC Eẋ in

6.2. Design parameters The design parameters selected to optimize the hybrid system follow: SOFC stack inlet temperature (Tcell,in), SOFC stack flow rate (i), fuel utilization factor (Uf), ammonia concentration (x), Kalina evaporator operating pressure (Peva) and RO recovery ratio (Rr). The allowable variation ranges of the parameters are given in Table 10.

× 100

Eẋ in,KC − TEG = ṁ G [(hp − hq ) − T0 (sp − sq )]

ψKC − TEG =

̇ We,KC − TEG Eẋ in,KC − TEG

6.3. Optimum point selection in the multi-objective optimization

× 100

In multi-objective optimization for choosing the final solution, there is a need for a decision-making process. In this paper, two methods of LINMAP and TOPSIS are used to find the optimal final point. In this methods two points are defined as ideal and non-ideal points which are the best and the worst points, respectively. In the LINMAP approach, the closest point to the ideal point on the Pareto front is chosen as the optimal final solution. In this method, each objective function is normalized according to the following equation:

̇ Wmin,RO = Eẋ 21 + Eẋ 23 − Eẋ 15

ψRO = ψov =

Ẇ min,RO Ẇ in,RO ̇ We,SOFC + Ẇ min,RO Eẋ in

Decision variable

Low

High

SOFC inlet temperature (K) Current density (A/m2) Fuel utilization factor (-) Ammonia concentration (-) Kalina evaporator pressure (kPa) RO recovery factor (-)

900 3000 0.6 0.70 2500 0.5

1040 5000 0.9 0.86 5000 0.7

Fijn =

Fij m 2 ∑ i=1

(Fij )2

(51)

Where i, j and m are respectively the index of each point on the Pareto front, the index of objective function and the point numbers on the Pareto front, respectively. The distance of each point on the Pareto front to the ideal point is calculated as follows:

d i+ =

where Zk denotes the capital cost of component k. Values for system of the component capital costs are reported in Table 6. In Eq. (47), φ is the operation and maintenance factor and t is the number of annual working hours. The capital recovery factor (CRF) is defined by:

i (1 + i) N (1 + i) N − 1

(50)

In multi-objective optimization, a decision making procedure is required for the selection of final optimal solution in the Pareto front. There are various methods to determine the final optimal solution, such as the LINMAP and TOPSIS methods.

Table 10 Decision variables and their allowable variation ranges.

CRF =

̇ + ZOM ̇ )k ∑ (ZCI k

Table 9 Exergy efficiency definitions and relations for system and its components. Term

(49)

Objective function II: total cost rate

Ẇin,RO = Ẇ HPP + Ẇ LPP

ηRO =

̇ ̇ + Wmin,RO We,SOFC Eẋ in

2

n )2 ∑j =1 (Fijn − Fideal,j

(52)

In TOPSIS, in addition to the ideal point, a non-ideal point is also defined. Therefore, along with the solution distance from the ideal point, di+, the solution distance from the non-ideal point (di−) is also calculated as follows:

d i− =

(48)

2

n )2 ∑j =1 (Fijn − Fnon_ideal,j

(53)

To find the final answer in TOPSIS, a criterion is defined as follows:

where i and N denote the interest rate and the lifetime of the system, 303

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Table 11 Comparison of present model results with experimental data reported by Tao et al. [22] and Ziapour et al. [12] Current density (A/m2)

1000 2000 3000 4000 5000 6000

SOFC Cell voltage (V)

ZTM

Present model

Experiment [22]

Difference (%)

0.78 0.74 0.69 0.65 0.59 0.52

0.86 0.76 0.68 0.62 0.57 0.52

9.3 2.6 1.5 4.8 3.5 0.0

0.8 0.9 1.0 1.1 1.2 1.3

TEG power output (kW) Present model

Experiment [12]

Difference (%)

1.48 1.61 1.74 1.85 1.96 2.07

1.47 1.62 1.75 1.88 1.99 2.11

0.68 −0.61 −0.57 −1.60 −1.51 −1.89

Table 12 Input parameters used in system modeling [12,34–37].

Fig. 3. Validation results for (a) SOFC modeling, considering results reported in [22], and (b) TEG modeling, considering results reported in [12].

Cl i =

d i−

d i− + d i+

(54)

Variable

Value

General Ambient temperature (K) Ambient pressure (kPa) Air composition (molar fraction): O2, N2

298 101.3 0.79, 0.21

SOFC system Inlet temperature, T (K) Active surface area, Aact (m2) Number of cells, Ncell (−) Fuel utilization factor, Uf (% ) Current density, j (A/m2) Number of electrons, ne (−) Exchange current density of anode, joa (A/m2) Exchange current density of cathode, joc (A/m2) Effective gaseous diffusivity through anode, Daeff (m2/s) Effective gaseous diffusivity through cathode, Dceff (m2/s) Thickness of anode, la (m) Thickness of cathode, lc (m) Thickness of electrolyte, le (m) Thickness of interconnect, lint (m) DC-AC inverter efficiency (% ) Steam- to- carbon ratio, rsc (−) Fuel compressor isentropic efficiency (% ) Air compressor isentropic efficiency (% ) Fuel cell pressure drop (% ) Heat exchangers pressure drop (% ) Afterburner pressure drop (% )

900 0.01 55,000 85 3500 2 6500 2500 0.2 × 10−4 0.05 × 10−4 0.05 × 10−2 0.005 × 10−2 0.105 × 10−2 0.3 × 10−2 97 2.5 85 85 2 2 3

Kalina and TEG Inlet pressure of Kalina turbine (MPa) Inlet mass fraction of Kalina turbine (−) Inlet temperature of Kalina pump (K) Isentropic efficiency of Kalina turbine (% ) Isentropic efficiency of Kalina pump (% ) Pinch point temperature difference of evaporator (°C) Figure of merit, ZTM (1/K)

4 0.84 310 85 85 5 0.8

Reverse osmosis Salinity of product water (ppm) Seawater salinity (ppm) Seawater feeding temperature (K) High pressure pump efficiency, ηHPP (% ) Low pressure pump efficiency, ηLPP (% ) Pelton turbine efficiency, ηPT (% ) Membrane recovery ratio, Rr

450 35,000 298 85 85 85 0.55

The point with maximum Cl i is considered as the final solution. TEG, Fig. 3b and Table 11 are presented. In Table 11 compares the simulated results of the TEG with the results of Ziapour et al [12], and Fig. 3b demonstrates good agreement between results. To compare the present KC simulation results, the net electrical output power, 2190 kW, is compared with the results of Ogriseck et al [23], 2200 kW. Again, good agreement is seen.

7. Results and discussion 7.1. Model verification To validate the simulated results, the proposed system is divided into three subsystems: SOFC, KC and TEG. The simulated data of each subsystem are compared with available numerical and experimental data. To validate the methane-consuming SOFC model, data reported by Tao et al [22] are compared with the present results in Table 11, and Fig. 3a, shows a maximum difference of 10% between presented model and experimental data. Also, to certify the accuracy of the modeling of

7.2. Modeling results and parametric study This proposed SOFC-based hybrid system is examined, in which a SOFC is integrated with KC-TEG and RO cycles. Before implementation of a new technology or a new combination of the available 304

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Table 13 Simulation results of integrated power generation system. Parameter

Value

SOFC subsystem SOFC voltage (V) SOFC operating temperature (K) Afterburner combustion temperature (K) SOFC net electrical power (kW)

0.76 968 1011 1300

Kalina-TEG subsystem Ammonia-water mass flow rate (kg/s) Ammonia-water turbine inlet temperature (K) KC-TEG Net electrical power output (kW)

0.4 393 32

RO subsystem Product water flow rate (m3/day) Work rate of separation (kW)

225 10.2

SOFC-Kalina-TEG Thermal efficiency (%) Exergy efficiency (%)

55.5 53.4

SOFC-Kalina-TEG-RO Thermal efficiency (%) Exergy efficiency (%) Total annual cost ($/year)

55.2 52.8 41.5

Fig. 4. Comparison between the performance of KC-TEG system and the conventional KC.

technologies, a comprehensive analysis of its performance is helpful. For this purpose, the effects of some of the design parameters, such as current density, fuel input temperature and fuel utilization factor, are investigated here. The parameters for cycle modeling are reported in Table 12. Additionally, the thermodynamic simulation results are presented in Table 13. To compare thermodynamically the performance of KC and KC-TEG systems, three parameters of net output power, energy efficiency, and exergy efficiency are considered and shown in Fig. 4. It shows that the energy efficiency and exergy efficiency of the integrated KC-TEG system is higher by 4.6% than the corresponding values in the KC due to the excessive electricity generation. Also, the integrated KC-TEG system can produce 1.4 kW more than KC in the same operating conditions. The SOFC produces 1300 kW and the KC-TEG subsystem produces 32 kW, increasing the total power generation by 1%. The impact of current density on the net power production and the fresh water production is depicted in Fig. 5a. Increasing the current density causes the molar input rate of fuel to increase in a linear manner; hence more chemical potential is converted to electricity, enhancing the power production of the SOFC stack. However, increasing the cell fuel input rate increases the waste heat rate of the afterburner;

Fig. 5. Influence of current density on (a) net power output and product fresh water rate, (b) exergy efficiency and energy efficiency, and (c) total cost rate, of the proposed systems.

therefore, more energy enters the KC-TEG cycle, which raises its production power and increases the RO system water production rate. Fig. 5b shows that an increase of current density reduces the energy and exergy efficiencies of the SOFC and the hybrid system. Based on Eqs. (13), (18) and (21), an increase in current density results in a voltage loss and consequently decreases the cell efficiency. Increasing the current density raises the molar rate of fuel flow, which enhances the power production of the SOFC and KC-TEG. The increase of energy input, however, is greatly exceeds the net electric power, leading to a decrease in the energy and exergy efficiencies. The variation in the total cost of trigeneration system with current density is shown in Fig. 5c. As mentioned before, an increase in j enhances the power production by 305

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Fig. 6. Effect of the cell inlet temperature on (a) net power produced and fresh water production rate, (b) system exergy and energy efficiencies, and (c) total cost rate of the proposed systems.

Fig. 7. Effect of the fuel utilization factor on (a) net power output and fresh water production rate, (b) system exergy and energy efficiencies, and (c) total cost rate of the proposed system.

the SOFC and KC-TEG, which requires high-capacity systems and leads to higher capital investments. Fig. 6a illustrates the effect of varying the SOFC inlet temperature on the power and fresh water produced. An increase in the SOFC inlet temperature increases the activation and concentration waste voltages but decreases the Ohmic waste voltage. Therefore, the cell voltage first increases with increasing SOFC inlet temperature and then decreases. Thus, there is an optimum temperature at which the cell voltage (or the power production) is maximum. This maximum power is 2070 kW and it occurs at 956 K. On the other hand, by increasing the inlet

temperature, the amount of heat dissipated from the afterburner increases. As a result, the input thermal energy to the Kalina cycle increases and consequently more electrical power is provided for the RO system, which increases the amount of water production. The variations of the energy and exergy efficiencies of the SOFC and the hybrid system are shown in Fig. 6b. As varying inlet temperature does not affect the input mass rate of fuel, the variations in energy and exergy efficiencies are dependent on the net power production. As shown in Fig. 6a, the power production first increases and then decreases with increasing fuel 306

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Fig. 9. Effect of ammonia mass fraction on (a) net power output and fresh water production rate, and (b) system exergy and energy efficiencies.

Fig. 8. Effect of Kalina turbine inlet pressure on (a) net power output and fresh water production rate, and (b) system exergy and energy efficiencies.

Fig. 8a presents the variations in system power production and fresh water production rate with Kalina turbine inlet pressure. By increasing the turbine input pressure at a fixed output pressure, the specific enthalpy difference between the turbine input and output increases, which increases the power production and consequently the production rate of water by the RO system. Moreover, with increasing inlet pressure to the turbine, the temperature of the saturated fluid exiting the evaporator increases. But, for a constant pinch point temperature, the hot stream leaves the evaporator at a higher temperature, which reduces the amount of heat transferred to the water-ammonia mixture. According to an energy balance, the mass flow rate of the KC-TEG cycle then decreases. Yet, the power production of the turbine is proportional to the mass flow rate of fluid through it. Thus, a decrease in the mass flow rate will reduces the rate of power production because of the inlet pressure increase. Thus, as shown in Fig. 8b, a rise in turbine input pressure leads to an increase in system power production and a decrease in the mass flow rate, as well as an increase the energy and exergy efficiencies of the system. The effects of increasing ammonia mass fraction on the power output and fresh water production rate are shown in Fig. 9a. As the boiling point is lower for ammonia than water, increasing the ammonia mass percentage lowers the boiling temperature of the mixture. Therefore, an increase in ammonia concentration, for a fixed pinch point temperature, causes the hot flow to exit the heat exchanger at a lower temperature, which leads to an increase in the heat transfer rate and correspondingly the mass flow rate of the Kalina cycle. Since power production in a turbine is proportional to the mass flow rate of fluid through it, an increase in ammonia mass fraction raises the power production and the fresh water production rate. The variations of

cell inlet temperature, which explains the ascending trend of energy and exergy efficiencies. The influence of input temperature on the total system cost is illustrated in Fig. 6c. Increasing the input temperature raises the thermal energy of the KC, which in turn results in greater power production. Moreover, the SOFC power production first increases with increasing cell inlet temperature and then decreases. Therefore, the increase in the total cost of the system with temperature is less than cost increase with current density. As observed, an increase in input temperature from 900 to 1040 K results in an increase in system cost from 77.3 to 83.7 $/h. The effect of varying fuel utilization factor in the range of 0.6–0.9 at constant current density and input temperature is depicted in Fig. 7. According to Fig. 7a, an increase in fuel utilization factor decreases both the net power output and fresh water production rate. This descending trend can be explained by the decrease in molar input rate of fuel to the SOFC and the increase in the molar input rate of air to the SOFC cathode with increasing fuel utilization factor; this lowers the Nernst voltage and hence the cell voltage, giving rise to the reduction of SOFC power production. The variations in energy and exergy efficiencies with fuel utilization factor variation are shown in Fig. 7b. As an increase in fuel utilization factor reduces the power production as well as fuel input rate, maximum energy and exergy efficiencies are expected for an optimum value of the fuel utilization factor. This maximum value is observed at Uf = 0.85. However, due to the reduction of fuel input to the system with increasing fuel utilization factor, fuel cost is expected to decline, which has a significant role in determining the total cost of the system. The decreasing trend of total cost with increasing Uf is shown in Fig. 7c. 307

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Fig. 10. Comparison of energy and exergy efficiencies and exergy destruction rate for the main subsystems of the considered system. Table 14 Optimal values of system design parameters obtained from both single- and multi-objective optimization solutions. Design parameter

Exergetic optimization (Objective function I)

Economic optimization (Objective function II)

Multi-objective optimization selected point by LINMAP/ TOPSIS

Tcell,in (K) i (A/m2) Uf X9 Peva (kPa) Rr

900.7 3040 0.85 0.86 3000 0.66

900.0 3050 0.85 0.71 3003 0.69

900.6 3040 0.85 0.82 3001 0.65

Table 15 System capital costs (in $) for both single- and multi-objective optimizations.

Fig. 11. Exergy efficiency and exergy destruction rate in components of the SOFC.

Component

Exergetic optimization (Objective function I)

Economic optimization (Objective function II)

Multi-objective optimization selected point by LINMAP/ TOPSIS

AC FC APH FPH WPH SOFC AB KC-TEG RO Total

1678 12.3 4138 620 1571 492,310 10,258 4423 17,980 94,864

1683 12.2 4147 621 1574 491,360 10,288 4213 15,124 91,670

1677 12.3 4136 620 1570 492,260 10,254 4406 17,537 94,396

7.3. Exergy analysis The energy and exergy efficiencies and exergy destruction rate are determined for each of the subsystems of the proposed cycle and hybrid system (see Fig. 10). As shown in Fig. 10, the energy and exergy efficiencies of SOFC are 54.2% and 52.1% respectively, which can be improved by recovering the SOFC waste heat by KC-TEG by 2.4% and 2.5%, respectively. By adding a RO unit to produce fresh water, the electricity produced by the KC-TEG system is used in this system. The energy and exergy efficiency achieved for the SOFC-KC-TEG-RO hybrid system is 55.2% and 52.8%, respectively, with only 1.8% and 1.3% increases, as compared to SOFC. Although the hybrid efficiency is lower than the SOFC-KC-TEG integrated mode, it should be noted that in this case, fresh water has been produced instead of power. The SOFC stack makes the most significant contribution to the exergy destruction rate

Fig. 12. Pareto optimal frontier obtained from multi-objective optimization of the hybrid system.

energy efficiency and exergy efficiencies with variation of ammonia mass fraction are shown in Fig. 9b. Although increasing the concentration of ammonia tends to enhance the net power production of the cycle, the increase in the energy input to the system is relatively higher, which reduces the energy and exergy efficiencies.

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Table 16 Stream data for the SOFC system at the optimal design point. State

a b c d e f g h i j k l m n o p q

T (K)

298.15 298.15 298.15 298.15 314.84 316.02 900.62 900.62 900.62 900.62 946.62 946.62 1007.6 946.62 935.62 393 353.5

P (bar)

Constituent molar flow rate (mol/s)

ṅ (mol/s)

1.01 1.01 1.01 1.21 1.21 1.21 1.18 1.18 1.18 1.18 1.16 1.16 1.12 1.10 1.08 1.06 1.06

6.50 2.50 197.7 6.50 2.50 197.7 6.50 2.50 197.7 9 14.30 193.3 206.8 206.8 206.8 206.8 206.8

CH4

H2O

H2

CO

CO2

O2

N2

0 2.50 0 0 2.50 0 0 2.50 0 2.50 0 0 0 0 0 0 0

6.50 0 0 6.50 0 0 6.50 0 0 6.50 10.2 0 11.7 11.7 11.7 11.7 11.7

0 0 0 0 0 0 0 0 0 0 1.53 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0.2 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 2.4 0 2.6 2.6 2.6 2.6 2.6

0 0 41.5 0 0 41.5 0 0 41.5 0 0 37.2 36.3 36.3 36.3 36.3 36.3

0 0 156.1 0 0 156.1 0 0 156.1 0 0 156.1 156.1 156.1 156.1 156.1 156.1

Table 17 Stream data for the bottoming KC-TEG-RO system at the optimal design point. State

Fluid

ṁ (kg.s−1)

T (K)

P (bar)

h (kJ.kg−1)

s (kJ.kg−1)

ex (kJ.kg−1)

Salinity (ppm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

96% NH3-4% H2O 96% NH3-4% H2O 82.3% NH3-17.7% H2O 82.3% NH3-17.7% H2O 82.3% NH3-17.7% H2O 82.3% NH3-17.7% H2O 82.3% NH3-17.7% H2O 82.3% NH3-17.7% H2O 82.3% NH3-17.7% H2O 54% NH3-46% H2O 54% NH3-46% H2O 54% NH3-46% H2O Water Water Saline water Saline water Saline water Saline water Saline water Saline water Fresh water Brine Brine

0.19 0.19 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.07 0.07 0.07 17.62 17.62 3.97 3.97 3.97 3.97 3.89 0.08 2.62 1.35 1.35

393 349 349 335 308 309 339 349 393 393 359 349 298 30.1 298 298 298 298 298 298 298 298 298

30.0 11.0 11.0 11.0 11.0 30.0 30.0 30.0 30.0 30.0 30.0 11.0 1.01 1.01 1.01 6.58 6.32 6.07 72.8 1.01 1.01 51.0 1.01

1841 1707 1322 1171 316 320 471 518 1466 475 304 304. 105 117 99.7 100 100 100 107 99.7 105 94.6 89.1

5.93 5.99 4.82 4.38 1.67 1.67 2.14 2.28 4.89 2.15 1.69 1.71 0.37 0.41 0.35 0.35 0.35 0.35 0.35 0.35 0.37 0.29 0.29

19,161 19,007 16,257 15,237 16,190 16,192 16,204 15,111 16,379 9030 8995 8999 0.00 0.06 0.00 0.57 0.55 0.52 7.40 0.00 2.63 8.82 3.37

– – – – – – – – – – – – – – 35,000 35,000 35,000 35,000 35,000 35,000 450 100,490 100,490

value. The best final result should be selected according to the previously mentioned decision making methods such as LINMAP and TOPSIS. The exergy efficiency and the obtained costs of both methods are found to be equal, at 53.7% and 36.8 $/hr, respectively. Numerical values of optimum design parameters at A and B (optimum points according to single-objective methods) as well as final points determined by the TOPSIS and LINMAP approaches, are listed in Table 14. Table 15 lists the costs for the parts of the hybrid system at the optimum points. As anticipated, the capital cost is higher for the SOFC stack than the other components of the system. The highest capital costs after fuel cell are for the RO desalination system and the Kalina lowtemperature power production system. Tables 16 and 17 present the thermodynamic values of the state points of the system at the optimal state.

of the overall system. Nonetheless, it is worth examining the contribution of each of component to the exergy destruction rate to improve the performance of the system. Fig. 11 presents the exergy destruction rate and exergy efficiency of various SOFC stack components. Due to the high-temperature difference across the air preheater, the greatest exergy destruction occurs in this component. As expected, the second and third greatest contributors are the afterburner, due to the irreversible nature of combustion, and the fuel cell, due to the irreversibility of the electrochemical and mixing processes.

7.4. Optimization results Fig. 12 shows the Pareto front obtained by multi-objective optimization of the hybrid system. As the figure suggests, the exergy efficiency and the total cost rate are in contradiction with each other. The exergy efficiency takes on its highest value at point A while the economic performance is the worst value at this point. Conversely, at point B, the lowest cost is obtained while the exergy efficiency takes on its worst

8. Conclusion In this study, an SOFC system is integrated with a KC-TEG to recover the dissipated heat of the SOFC stack and to produce fresh water by RO 309

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desalination. To provide thermodynamic and economic insights, exergy and economic aspects are explored. The effects are examined of key design parameters on the system performance (in terms of net power production, fresh water production rate, energy and exergy efficiencies and total cost). The exergy analysis of the integrated system shows that the highest exergy destruction rates are attributable to the air preheater, afterburner and fuel cell. The system is optimized using a genetic algorithm to maximize system exergy efficiency and minimize system cost. The results show that the energy and exergy efficiencies are 58% and 54% at the optimum state, respectively. The costs of the system at this optimal point is 36.8 $/h. The RO unit produces 226 m3/ day of fresh water. In the parametric study, the effects of some of the design parameters such as current density, input temperature to the SOFC, fuel utilization factor, pressure input to the Kalina turbine and ammonia mass fraction on the performance of the system have been studied. The results of these studies are as follows:

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• By increasing the current density, the molar fuel flow rate into the • • • •

fuel cell increases linearly, which increases the amount of electricity and fresh water production, while the energy and exergy efficiencies yields the lowest current density. Increasing the inlet temperature causes an increase in the amount of fresh water produced, but the amount of power generation increases first, then decreases with a maximum capacity at 956 K. The energy and exergy efficiency variations are similar to those for the produced power. Increasing the fuel utilization factor has an adverse effect on the net power and fresh water production, while the energy and exergy efficiencies exhibit a peak at fuel utilization factor of 0.85. The minimum total cost rate of the hybrid system occurs at the lowest current density and the lowest input temperature to the SOFC and the highest fuel utilization factor. The power produced by the KC-TEG system and the amount of fresh water produced in RO increases with increasing pressure in the Kalina turbine, which increases the energy and exergy efficiencies of the system. Also, increasing the mass fraction of ammonia increases the electricity generation and production of fresh water.

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