cooling cogeneration system based on a solid oxide fuel cell

Energy 94 (2016) 64e77

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Energy and exergoeconomic evaluation of a new power/cooling cogeneration system based on a solid oxide fuel cell Leyla Khani a, S. Mohammad S. Mahmoudi a, *, Ata Chitsaz b, Marc A. Rosen c a

Faculty of Mechanical Engineering, University of Tabriz, Tabriz, 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, L1H 7K4, Canada b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 5 July 2015 Received in revised form 12 October 2015 Accepted 1 November 2015 Available online xxx

A new cogeneration system consisting of a hydrogen-fed SOFC (solid oxide fuel cell), a GT (gas turbine) and a GAX (generator-absorber-heat exchange) absorption refrigeration cycle is proposed and analyzed in detail. The electrochemical equations for the fuel cell and thermodynamic and exergoeconomic relations for the system components are solved simultaneously with EES (Engineering Equation Solver) software. Through a parametric study, the influences of such decision parameters as current density, fuel utilization factor, pressure ratio and air utilization factor on the performance of the system are studied. In addition, using a genetic algorithm, the system performance is optimized for maximum exergy efficiency or minimum SUCP (sum of the unit costs of products). The results show that, the exergy efficiency of the proposed system is 6.5% higher than that of the stand-alone SOFC. It is also observed that the fuel cell stack contributes most to the total irreversibility. The exergoeconomic factor, the capital cost rate and the exergy destruction cost rate for the overall system are observed to be 27.3%, 10.63 $/h and 28.3 $/h, respectively. It is observed that for each 6 $/GJ increase in the hydrogen unit cost, the optimum sum of the unit costs of products is increased by around 62.5 $/GJ. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Solid oxide fuel cell Cogeneration GAX Exergoeconomics Waste heat utilization Hydrogen Thermodynamic simulation

1. Introduction The negative effects such as depletion of energy resources, global warming and long-term increases in energy prices have spurred efforts to find new and more beneficial ways to convert the chemical energy of fuels to electricity, cooling and heating. Fuel cells can support such efforts because of their many advantages, which include high efficiency, low emissions, high power density, ability to produce energy locally, ease of installation and operation, and ability to use a variety of fuels [1]. It is also possible to combine high temperature fuel cells, such as the SOFC (solid oxide fuel cell) or the MCFC (molten carbonate fuel cell), with other power plants such as gas turbine or other bottoming cycles to obtain higher efficiencies. Such systems can achieve efficiencies of 70% or higher [2]. Many researchers have studied various combined systems based on fuel cells, especially SOFCs [3e13].

* Corresponding author. E-mail address: [email protected] (S.M.S. Mahmoudi). http://dx.doi.org/10.1016/j.energy.2015.11.001 0360-5442/© 2015 Elsevier Ltd. All rights reserved.

Bakalis et al. [14] analyzed three different SOFC hybrid power systems with zero-CO2 emission and reported that capturing the CO2 in these systems does not lower their efficiencies much. Using life cycle assessment method, Lee et al. [15] assessed the environmental impact of a SOFC-based CHP system and concluded that the manufacturing stage and disposal stage have small contributions to the total environmental impact. Costamagna et al. [16] analyzed the design and off-design performance of a hybrid system consisting of a recuperated micro gas turbine and a high temperature solid oxide fuel cell and reported thermal efficiencies over 60% at the design point and over 50% at part load conditions for the system. Granovskii et al. [17] thermodynamically compared using numerical approaches two combined SOFC-gas turbine systems, and concluded that, for the same SOFC stack, the scheme with recycling is more efficient but the scheme with steam generation generates more power. Using two-stage gasification, Bang-Møller et al. [18] evaluated the performance of a hybrid plant consisting of a solid oxide fuel cell and a micro gas turbine for producing heat and power. Under optimized conditions, the plant can produce 290 kW of electrical power with an efficiency of 58.2%. Using the Lagrange Multipliers method, Cheddie [19] developed a thermo-economic

L. Khani et al. / Energy 94 (2016) 64e77

65

model to simulate the performance of an indirectly coupled SOFCgas turbine hybrid power plant and reported, under optimized conditions, a breakeven unit energy cost of USD (2011) 4.54 ¢/kWh when the output power was 18.9 MW with an energy efficiency of 48.5%. Using two methods for hydrogen separation, Becker et al. [20] examined the design and performance of a combined heat, hydrogen and power production system incorporating a methanefueled, 1 MW SOFC, for steady state conditions. They reported that the expected cost of SOFC-based distributed hydrogen production is on par with other distributed hydrogen production technologies, such as natural gas reforming or electrolysis. Rokni [21] designed a hybrid SOFC-Stirling plant with a power capacity of up to 10 kW and an efficiency of 60%, for use with alternative fuels. Bellomare et al. [22] studied two configurations of municipal solid waste gasification plants integrated with a SOFC and a gas turbine, and showed that, under optimized conditions, they achieve a thermodynamic efficiency of approximately 52% for the plant with regenerative gas turbine. Chen et al. [23] investigated the economics of a cogeneration/trigeneration system comprised of a SOFC and an absorption cooling system for residential use in Hong Kong. Akikur et al. [24] modeled a cogeneration system using solar energy and SOFC technology, and reported the overall system efficiency for the solar-SOFC mode to be 23%. Sanaye et al. [25] performed a multi-objective optimization of a hybrid SOFC-micro gas turbine system using a genetic algorithm. It was observed that cell current density, among other system design parameters, plays an important role in balancing system cost and performance. Ranjbar et al. [26] studied a trigeneration system consisting of a SOFC, a GAX absorption refrigeration and a heat recovery steam generator, and showed that the energy efficiency of the trigeneration system is at least 33% higher than that of the SOFC and that the main exergy destructions occur in the air heat exchanger, the SOFC and the afterburner. 1.1. Configuration optimizing In optimizing the configuration for multi-generation system, especially when different cycles are combined, the temperature matching between the sub-systems plays an important role. As this temperature matching brings about less exergy destruction and consequently more efficient system. This point has been considered by the researchers in combining the SOFC with GT, as concluded from the above discussion. The exhaust gas from the gas turbine however, possesses a considerable amount of energy, so that it can be utilized to run another bottoming cycle to produce cooling. In this paper a new combined SOFC-GT-GAX system is introduced and investigated in detail from thermodynamic and exergoeconomic viewpoints. This plant produces electrical power and cooling as its main and secondary products, respectively, and can be useful in practical applications, since a considerable amount of cooling is produced from the SOFC-GT waste heat. The system performance is simulated and assessed by applying the conservation of mass and energy, exergy balances and exergoeconomic relations to each system component. A detailed electrochemical analysis is performed for the fuel cell to calculate its voltage and electrical power generation. In addition, a parametric study is carried out to investigate the effects on system performance of the main decision parameters. Finally the system performance is optimized for maximum exergy efficiency or minimum SUCP. 2. System description and assumptions A schematic of the proposed system is shown in Fig. 1. This system includes air and fuel compressors, heat exchangers, a solid

Fig. 1. Schematic diagram of the electrical power/cooling cogeneration system.

oxide fuel cell stack, an inverter, an afterburner, a gas turbine and a GAX absorption refrigeration cycle. The inlet fuel and air are pressurized by the fuel and air compressors, respectively before entering the fuel cell. As indicated in Fig. 1, the pressurized fuel and air are heated separately, by means of the combustion gases exiting the gas turbine, before they enter the fuel cell stack. There, the electrochemical reaction between the hydrogen and oxygen generates electrical current (DC), which is converted to alternating current (AC) by the inverter. As the electrochemical reaction is exothermic, the stack temperature rises. A

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L. Khani et al. / Energy 94 (2016) 64e77

fraction of the inlet hydrogen leaves the stack unburned and enters the afterburner, where it is burned completely. The exhaust gases leaving the afterburner pass to the gas turbine to produce additional electrical power. After the gas turbine exhaust gases pass through the fuel and air heat exchangers, they enter the generator and drive the GAX cycle for producing cooling. Details of the GAX cycle have been explained previously by the authors [27,28]. The following assumptions are invoked in the system modeling [5,16,27e30]:












The system operates under steady state conditions. All SOFC-GT system components operate adiabatically. Working fluids in the SOFC-GT system behave like ideal gases. The same temperature exists at the anode and cathode outlets. The SOFC stack is in thermal equilibrium with the anode and cathode outlet streams. Air is composed of 79% N2 and 21% O2 and the fuel is composed of 89% H2 and 11% H2 O. Air and fuel enter the system at environmental conditions, i.e. P0 ¼ 1 bar and T0 ¼ 25  C. The refrigerant is saturated at the exits of the condenser and the evaporator. Pressure drops due to friction are neglected only in the GAX cycle. Solutions at the absorber and generator exits are at the corresponding device temperatures. The approach temperature at either end of the GAX heat exchanger is 0 K.

3. System modeling 3.1. SOFC electrochemical modeling The fuel cell considered here (made by Siemens Westinghouse Power Corporation) is a tubular solid oxide fuel cell with a length of

150 cm and an active diameter of 2.2 cm. The electrochemical reaction occurring in the fuel cell is H2 þ 1=2O2 /H2 O [31]. The electrical power produced by the SOFC stack can be written as:

_ W SOFC ¼ iAact Ncell Vcell

where i, Aact , Ncell and Vcell are the current density, the active surface area, the number of cells in the stack and the fuel cell voltage, respectively. The fuel cell voltage can be calculated using the Nernst voltage as well as the voltage loss which is the sum of the ohmic, the concentration and the activation overvoltages, as follows:

Vloss ¼ Vohm þ Vcon þ Vact

(2)

Vcell ¼ VN  Vloss

(3)

Expressions for the terms in Eqs. (2) and (3) are listed in Table 1 [1,32e37]. _ is The molar flow rate of hydrogen consumed in the reaction, z, related to the current density and is calculated using the Faraday's law:

z_ ¼

iAact Ncell ne F

Nernst voltage

Ohmic overvoltage

Concentration overvoltage




 n_ H2 consumed z_  uf ¼
¼ n_ H2 ;5 n_ H2 supplied

Equation qffiffiffiffiffiffiffiffi! PH2 PO2 RTcell þ ln VN ¼ ne F ne F PH2 O Dg0f

0 1 Dg0f ¼ g0H2 O  g0H2  g 0O2 ; g0 ¼ h  Tcell s0 2 Vohm ¼ iðra þ rc þ re þ rint Þ   1392 ; la ¼ 0:0001m ra ¼ 2:98  105 la exp Tcell   600 rc ¼ 8:11  105 lc exp ; lc ¼ 0:0022m Tcell   10350 re ¼ 2:94  105 le exp ; le ¼ 0:00004m Tcell   4690 rint ¼ 1:2  103 lint exp ; lint ¼ 0:000085m Tcell i 1 8 0 19 0 1 = iL;H2 A RT < 1 A Vcon ¼ cell ln@ þ ln@ ; i i ne F : 1þ 1 iL;H2 O iL;O2

iL;k ¼ Activation overvoltage

(4)

where ne is the number of electrons produced per hydrogen mole that reacts through electrochemical reaction and F is the Faraday constant (9.649  107 C/kmol). The inlet hydrogen and oxygen molar flow rates are calculated using fuel and air utilization factors, respectively [1]:

Table 1 The electrochemical equations for the solid oxide fuel cell. Voltage term

(1)

ne FDeff ;k RTcell lk

Pk

     2RTcell i i Vact ¼ þ sinh1 sinh1 2i0;a 2i0;c ne F !    PH2 O P 110000 i0;a ¼ 7  109 H2 exp P0 P0 RTcell !  0:25 P 155000 exp i0;c ¼ 7  109 O2 P0 RTcell

(5)

L. Khani et al. / Energy 94 (2016) 64e77






n_ O z_ 2 ua ¼
2 consumed ¼ n_ O2 ;6 n_ O2 supplied =

(6)

Considering the inlet fuel and air composition, the molar flow rate of the entering H2O and N2 can be determined using the Eqs. (7) and (8), respectively:

n_ H2 O;5 ¼ n_ N2 ;6 ¼

11 n_ 89 H2 ;5

(7)

79 n_ 21 O2 ;6

(8)

67

Finally E_ D;k denotes the rate of exergy destruction within the kth component. According to Eq. (16) the rate of exergy transfer into the component must exceed the rate of exergy transfer out of the component. The difference is the rate of exergy destruction within the component due to irreversibilities. Therefor unlike energy and mass, exergy is not conserved. In the absence of electrical, magnetic, nuclear and surface tension effects and neglecting the changes in kinetic and potential exergies, the total exergy rate of a stream is the sum of its physical and chemical exergy rates:

E_ ¼ E_ ph þ E_ ch

(17)

H2 and O2 are consumed and H2O is produced in the electrochemical reaction (N2 does not participate in the reaction), so the molar flow rates exiting the fuel cell are obtained by means of applying the mass balance:

The physical exergy is the maximum possible work when a system changes state from a specified initial condition to the limited dead state (environmental state) through a reversible process [38]:

n_ H2 ;7 ¼ n_ H2 ;5  z_

E_ ph ¼

(9)

n_ H2 O;7 ¼ n_ H2 O;5 þ z_ n_ O2 ;8 ¼ n_ O2 ;6 

(10)

z_ 2

(11) (12)

The rate of heat generated by the electrochemical reaction in the SOFC stack is determined using the following equation:

Q_ elec ¼ iAact Ncell ðVohm þ Vcon þ Vact Þ þ Tcell DSelec

(13)

where:

"

DSelec ¼ z_

s0H2 O  s0H2

1  s0O2 2



pffiffiffiffiffiffiffiffi!# PH2 PO2 þ Rln PH2 O

s is molar entropy and superscript 0 denotes the value of a property at the environmental conditions. As the fuel cell stack is well-insulated, this heat is used to increase the temperature of the SOFC anode and cathode outlets. 3.2. Energy, exergy and economic analyses Under steady state conditions and neglecting changes in kinetic and potential energies, energy and exergy balances can be expressed for the kth component, as a control volume, respectively as follows [38]:

_ ¼ Q_ k  W k

X

n_ e he 

e

E_ D;k ¼

X j

X

n_ i hi

(15)

i

!

1

X X T0 _ _ cv þ Qj  W E_ i  E_ e Tj e i

X

(16)

where the subscripts i and e indicate inlet and exit, respectively. In _ and h denote heat transfer, work transfer rate and Eq. (15) Q_ , W molar enthalpy, respectively. This equation, also known as the first law of thermodynamics, states that the total rate of energy entering a control volume must be equal to the total rate of energy exiting it. In Eq. (16), Tj is the local temperature on the boundary of control volume where the heat Q_ j is transferred, and the associated exergy transfer is given by ð1  T0 =Tj ÞQ_ j. The terms E_ i and E_ e indicate the rate of exergy transfer at the control volume inlets and outlets.

h



i 0 hi  hi  T0 si  s0i

(18)

n_ i ech i þ RT0

X

n_ i ln yi

(19)

where ech i is the standard chemical exergy of species, as given by Szargut [39], yi is the mole fraction of the gas i in the mixture and R is the universal gas constant (8.314 kJ/kmol.K). The chemical exergy for the ammoniaewater solution in the GAX cycle is [40]:

E_ ch ¼ m_ (14)

n_ i

The chemical exergy is the maximum work obtained when the state of the system changes from the limited dead state to the real dead state. The chemical exergy rate for an ideal gas mixture is [38]:

E_ ch ¼

n_ N2 ;8 ¼ n_ N2 ;6

X





x

Mammonia

 ech ammonia þ

 1x ech water Mwater

(20)

where x is the mass concentration of ammonia in NH3eH2O solution. Mammonia and Mwater are the molecular weights of ammonia and water, respectively. Exergoeconomics combines exergy analysis and economic principles to provide information not available through conventional energy analysis or economic evaluation. The objectives of exergoeconomic analysis are to calculate the costs of each product generated by the system having more than one product, to understand the cost formation process and the flow of costs in the system and also to optimize the single components or the overall system [38]. To calculate the exergy unit cost of each stream, the cost balance equation along with the required auxiliary equations are applied to each system component. For a system component receiving heat and producing power, the cost balance is written as:

X

C_ e;k þ C_ w;k ¼

C_ ¼ cE_

X

C_ i;k þ C_ q;k þ Z_ k

(21) (22)

where c is the cost per unit exergy of each stream. Eq. (21) states that the sum of the cost rates associated with exiting exergy streams equals the sum of the cost rates of all entering exergy streams plus the total expenditure rate needed to accomplish the process. The term Z_ k in Eq. (21) is the total cost rate associated with capital investment and operating and maintenance for the kth component and can be calculated as [41]:

Z CRF4 Z_ k ¼ k N

(23)

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L. Khani et al. / Energy 94 (2016) 64e77

Here, 4 is the maintenance factor (1.1), N is the number of system operating hours in a year (7446 h) and CRF is the capital recovery factor, which can be written as:

CRF ¼

ir ð1 þ ir Þn ð1 þ ir Þn  1

3.3. Performance criteria The net electrical power, cooling capacity and the exergy efficiency can be written as:

(24)

Also, ir is the interest rate (12%) and n is the system life (20 years). The cost balance and auxiliary equations as well as the purchased equipment cost for each system component are outlined in Table 2 [12,28,38,40,42].

_ _ _ _ _ _ net ¼ W _ W SOFC hinv þ W GT  W AC  W FC  W P  W ASP

(25)



Q_ evap ¼ n_ 23 h24  h23

(26)

Table 2 Cost balance relations, auxiliary equations and purchased equipment cost for each component. Component

Cost balance relation

Auxiliary equation

Purchased costa

Fuel compressor

C_ 1 þ C_ 39 þ Z_ FC þ Z_ M ¼ C_ 3

71:1m1 rp lnðrp Þ ZFC ¼ 0:9h

Air compressor

C_ 2 þ C_ 40 þ Z_ AC þ Z_ M ¼ C_ 4

Fuel heat exchanger

C_ 3 þ C_ 10 þ Z_ FHE ¼ C_ 5 þ C_ 11

c39 ¼ c42 c1 ¼ 15$=GJ c40 ¼ c42 c2 ¼ 0 c10 ¼ c11

Air heat exchanger

C_ 4 þ C_ 11 þ Z_ AHE ¼ C_ 6 þ C_ 12

c11 ¼ c12

SOFC

C_ 5 þ C_ 6 þ Z_ SOFC ¼ C_ 7 þ C_ 8 þ C_ 41

Inverter

C_ 41 þ Z_ Inv ¼ C_ 42

c7 ¼ c41 c8 ¼ c41 e

Afterburner

C_ 7 þ C_ 8 þ Z_ AB ¼ C_ 9

e

Gas turbine

C_ 9 þ Z_ GT ¼ C_ 10 þ C_ 43

c9 ¼ c10

Desorber

C_ 12 þ C_ 15 þ C_ 19 þ C_ Q_

GAXD

GAXA

AC

 ZFHE ¼ 130

AFHE 0:093

0:78

 ZAHE ¼ 130

AAHE 0:093

0:78

ZSOFC ¼ Aact Ncell ð2:96Tcell  1907Þ

ZAB ¼

W_ SOFC 500

!0:7

46:08m_ 8 P 0:995P9

ð1 þ expð0:018T9  26:4ÞÞ   m_ 9 P9 ¼ 479:34 1 þ expð0:036T9  54:4ÞÞ 0:92h ln P10 8

GAXD

þ Z_ Des ¼ C_ 13 þ C_ 16 þ C_ 18

C_ 18  C_ 15 C_ 16  C_ 15 ¼ E_ 18  E_ 15 E_ 16  E_ 15 C_ 18  ðC_ 15 þ C_ 19 þ C_ 28v þ C_ rq Þ E_  ðE_ þ E_ þ E_ þ E_ rq Þ

GAXA

C_ 17 þ C_ 27v þ Z_ GAXA ¼ C_ 27l þ C_ av

C_ 18 þ C_ 31 þ Z_ Rec ¼ C_ 19 þ C_ 20 þ C_ 32

GT



c12 ¼ c13

C_ 15 þ C_ 19 þ C_ 28v þ C_ rq þ Z_ GAXD ¼ C_ 18 þ C_ 28l

C_ 17 þ C_ 25 þ C_ 26 þ C_ 37 þ Z_ Abs ¼ C_ 14 þ C_ 15 þ C_ 38 þ C_ Q_

ZGT

15

19

28v

C_  ðC_ 15 þ C_ 19 þ C_ 28v þ C_ rq Þ ¼ 28l E_ 28l  ðE_ 15 þ E_ 19 þ E_ 28v þ E_ rq Þ c15 ¼ cav C_ 17 þ C_ 26 C_ 15 ¼ E_ 17 þ E_ 26 E_ 15 C_ 17 þ C_ 25 C_ 14 ¼ E_ 17 þ E_ 25 E_ 14 C_ av  ðC_ 17 þ C_ 27v Þ E_ av  ðE_ þ E_ Þ 17

Rectifier

FC

_

71:1m2 rp lnðrp Þ ZAC ¼ 0:9h

ZInv ¼ 105

18

Absorber

_

ADes 100

ZDes ¼ 17500

 0:6 GAXD ZGAXD ¼ 17500 A100

 AAbs 100

ZAbs ¼ 16500

27v

 ARec 100

ZRec ¼ 17000

0:6

AGAXA 100

27v

17

0:6

 ZGAXA ¼ 16500

C27l  ðC_ 17 þ C_ 27v Þ ¼ E27l  ðE_ þ E_ Þ c31 ¼ c32

0:6

0:6

Condenser

C_ 20 þ C_ 33 þ Z_ Cond ¼ C_ 21 þ C_ 34

C_ 20  C_ 18 C_ 19  C_ 18 ¼ E_ 20  E_ 18 E_ 19  E_ 18 c33 ¼ c34

Pre-cooler

C_ 21 þ C_ 24 þ Z_ Prec ¼ C_ 22 þ C_ 25

c24 ¼ c25

Evaporator

C_ 23 þ C_ 35 þ Z_ Evap ¼ C_ 24 þC_ 36

c23 ¼ c24

 0:6 AEvap ZEvap ¼ 16000 100

EV1

C_ 16 þ Z_ EV 1 ¼ C_ 17 C_ 22 þ Z_ EV 2 ¼ C_ 23 C_ 14 þ C_ 44 þ Z_ P þ Z_ M ¼ C_ 26

e

ZEV 1 ¼ 0

e c44 ¼ c42

ZEV 2 ¼ 0

C_ 29 þ C_ 45 þ Z_ ASP þ Z_ M ¼ C_ 30

c45 ¼ c42

e

e

EV2 Pump

ASP

Motor

a

These costs are updated to the 2014 using Chemical Engineering Cost Index.

 ACond 100

ZCond ¼ 8000

0:6

 ZPrec ¼ 12000

ZP ¼ 800

W_ P 10

ZASP ¼ 800 ZM ¼ 150

APrec 100

!0:26 

1hP hP

W_ ASP 10 W_ 10

0:6

0:5

!0:26 

!0:67 

1hASP hASP

1hM hM



0:5

L. Khani et al. / Energy 94 (2016) 64e77



j¼

T0 _ net þ Q_ W evap 1  Tb

n_ f ef

 (27)

where Tb , n_ f and ef represent the thermodynamic mean temperature of the low temperature heat source associated with the evaporator, inlet fuel molar flow rate and chemical exergy of fuel, respectively. The total irreversibility rate of the system is the sum of the exergy destruction rate in the system components plus the exergy loss rate associated with stream 13. That is:

E_ D;tot ¼

X

E_ D;k þ E_ 13

(28)

k

The exergy destruction ratio for components can be compared to determine most irreversible parts, where the exergy destruction ratio is expressed as:

YD;k ¼

E_ D;k _ ED;tot

As different parts of the developed model are validated separately, it can be concluded that the model developed for the entire system is validated. 4. Results and discussion

C_ F;k E_

(30)

C_ P;k E_

(31)

F;k

cP;k ¼

Westinghouse (see Fig. 2) [2,31]. The figure shows a good agreement between the two results. The maximum relative difference between the two results is less than 2.67%.
In order to validate the developed thermodynamic model, the data for hydrogen-fed solid oxide fuel cell system reported by Akkaya et al. [30] is used. The comparison is shown in Table 3 indicating a maximum relative difference of 3.75% between the total irreversibility obtained from the two works.
The performance of GAX cycle has been validated previously by the authors [27]. However, additional validation is carried out using the available data in Ref. [29]. Fig. 3 compares the obtained results in this paper with those reported by Ref. [29]. Referring to Fig. 3, there is a good agreement between these two (the error is less than 4%). Hence it can be concluded that the present model for GAX cycle is reliable and correct.

(29)

The exergoeconomic assessment of the proposed system is performed using thermoeconomic variables, namely, the unit cost of the fuel ðcF;k Þ, the unit cost of the product ðcP;k Þ, the cost rate of exergy destruction ðC_ D;k Þ, the cost rate of exergy loss ðC_ L;k Þ, the exergoeconomic factor ðfk Þ and the relative cost difference ðrk Þ. The exergoeconomic factor expresses the relative importance of the non-exergy-related cost rate to the total cost rate, and the relative cost difference indicates the relative increase in the exergy unit cost rate between fuel and product of a component. The increase in the unit exergy cost is due to the exergy destruction and the investment cost for the component. These parameters are calculated using the following relations [38]:

cF;k ¼

69

P;k

C_ D;k ¼ cF;k E_ D;k

(32)

C_ L;k ¼ cF;k E_ L;k

(33)

The input data for the simulations are listed in Table 4. Hydrogen is an energy carrier that can be obtained from various energy forms: fossil fuels (natural gas reforming, coal gasification); renewable and nuclear energy (biomass processes, photo-electrolysis, biological production, high temperature water splitting); and electricity (water electrolysis). At present, hydrogen is produced largely from fossil fuels without carbon capture and storage (48% from natural gas, 30% from refinery/chemical off-gases, 18% from coal), and the rest is mainly produced via water electrolysis. Hydrogen costs are highly sensitive to coal, gas, biomass and electricity prices. The unit cost of hydrogen as the fuel entering the SOFC is an important factor in determining the cost of the products which are electrical power and cooling capacity. For the base case and parametric studies, a value of 15 $/GJ is assumed for hydrogen cost [43e46]. Table 5 shows the calculated thermodynamic properties along with the exergy unit costs for the state points of the system. Table 5 indicates that the exergy unit cost of produced electrical power by the fuel cell and gas turbine as well as that of the produced cooling are 27.4 $/GJ, 27.9 $/GJ and 164.6 $/GJ, respectively.

0.8 Pcell = 1 bar

0.75

rk ¼

Z_ k _ _ Z k þ C D;k þ C_ L;k

(34)

cP;k  cF;k cF;k

(35)

3.4. Validation

Tcell = 1273.15 K

Cell voltage, Vcell [V]

fk ¼

0.7


To validate the fuel cell electrochemical modeling, the obtained results in the form of a voltageecurrent density plot are compared with the experimental data provided by Siemens

u f = 0.85

0.65 0.6 0.55

The verification of the developed model for the system in the EES (Engineering Equation Solver) software is done in three sections, i.e., for the electrochemical behavior of the SOFC, hydrogenfed SOFC system and the GAX cycle.

u a = 0.167

0.5 1500

Present work Refs. [2, 31]

2500 3500 4500 2 Current density, i [A/m ]

5500

Fig. 2. Comparison of the results obtained in the present work with experimental data reported for the SOFC electrochemical behavior [2,31] (Pcell ¼ 1 bar, Tcell ¼ 1273 K, ua ¼ 0.167, uf ¼ 0.85).

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L. Khani et al. / Energy 94 (2016) 64e77

Table 3 Comparison between the results of this work and those of Ref. [30] for hydrogen fed SOFC system ðrp ¼ 1:11; Tcell ¼ 930 C; uf ¼ 0:8; ua ¼ 0:15Þ. Current density ðA=m2 Þ

_ net ðkWÞ W Present work

Ref. [27]

Present work

Ref. [27]

Present work

Ref. [27]

1000 2000 3000 4000

109.3 193.7 260.5 312

107 190 260 305

46.92 41.57 37.26 33.47

46 42 38 34

115.5 257 417.6 593.9

120 252 410 615

The results obtained for the proposed system are compared with those calculated for the stand-alone fuel cell system in Table 6, and demonstrate the benefits from combining the SOFC-GT system with the GAX cycle. The exergy efficiency of the proposed system (SOFCGT-GAX) is shown in Table 6. It is 6.5% higher than that of the standalone SOFC-GT system. This is due to the fact that a significant amount of cooling is produced in the GAX absorption refrigeration cycle at the expense of a negligible electrical power loss. Fig. 4 shows the produced and consumed electrical powers in the system components. The gas turbine is observed to make the greatest contribution to the total electrical power production, while the air compressor has the highest electrical power consumption, mainly because of its high molar flow rate. The pumps in the GAX cycle have the lowest electrical power consumptions, as expected. Fig. 5 presents the irreversibility ratios for the system components. Referring to Fig. 5, the highest exergy destruction occurs in the fuel cell (as expected), and this is mainly attributable to the three sources of irreversibility in this component, i.e. the electrochemical reaction, temperature differences, and mixing. The second highest exergy destruction belongs to the afterburner, similarly because of the irreversible nature of combustion and the other two sources of irreversibility. The exergoeconomic results for the system components are presented in Table 7. The afterburner and fuel heat exchanger are observed to have the lowest fk values, respectively, indicating that the costs associated with the exergy destruction in these components are very high. This suggests an improvement is merited in the exergy efficiencies of these components. The highest value of fk however, is associated with the inverter, suggesting a lower investment cost is appropriate for this component at the expense of its exergy efficiency. It is also observed that the exergoeconomic

Coefficient of performance, COP

1.4 Present work

1.3

4.1. Parametric study 4.1.1. The effect of current density and fuel utilization factor The effects on system performance of varying current density and fuel utilization factor are shown in Figs. 6e9. Fig. 6 shows the effects on fuel cell voltage of varying current density and fuel utilization factor. An increase in the current density is observed to result in a decrease in the cell voltage, primarily because a higher current density raises both the hydrogen consumption rate and the stack temperature, since the reaction is exothermic. The simultaneous increase in current density and fuel cell temperature results in a reduced Nernst voltage and an increased voltage loss so that the fuel cell output voltage is reduced. It can also be seen in Fig. 6 that, for a given value of current density, an increase in fuel utilization factor has a negative effect on fuel cell voltage. When the fuel utilization factor increases, the entering fuel molar flow rate and also the exiting hydrogen molar flow rate decrease (the hydrogen consumption rate is constant). These variations cause a reduction in the afterburner outlet and stack temperatures. Consequently, the Nernst voltage decreases, the voltage loss increases and the fuel cell voltage decreases as fuel utilization factor rises. In fact as uf increases, VN decreases despite the reduction in stack temperature. This is because a rise in uf leads to

Table 4 Input parameters used in the system modeling.

1.1

Parameter

Value

rp ðÞ

6.5 0.0834

Aact ðm2 Þ Ncell

1 0.9

0.7 292.5

factor for the GAX cycle is relatively low. This indicates that it is better to use more effective components in the GAX cycle in spite of their higher costs. As indicated in Table 7, values of the parameter rk are highest for the generator/absorber assembly and the evaporator. The value of this parameter is lowest for the rectifier. The overall system exergoeconomic factor is determined to be 27.3%, meaning that 72.7% of the total system cost is associated with the exergy destruction and loss. Therefore, an increase in the components' capital costs may improve the exergoeconomic performance of the system.

Ref [29]

1.2

0.8

E_ D;tot ðkWÞ

h ð%Þ

T16 = 150 C, T14 = 40 C, T24 = 5 C

297

301.5

306 T21 [K]

310.5

315

Fig. 3. Comparison of the results obtained in this work with that of Ref. [29] for the GAX cycle.

i ðA=m2 Þ uf ðÞ ua ðÞ hInv ð%Þ hAB ð%Þ hP ð%Þ εPrec ð%Þ Dx ¼ X14  X16 DPðforSOFCÞð%Þ DPðforFHE; AHE; ABÞð%Þ EffectivenessðforFHEandAHEÞð%Þ IsentropicefficiencyðforFC; AC; GTÞð%Þ

1798 5000 0.85 0.15 95 98 50 80 0.3 2 3 85 85

L. Khani et al. / Energy 94 (2016) 64e77

71

Table 5 Thermodynamic properties, mass flow rates and cost of the streams. State no.

T ð CÞ

P ðbarÞ

m_ ðkg=sÞ

E_ ðkWÞ

c ð$=GJÞ

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 27l 27v 28l 28v 31 32 33 34 35 36 37 38 39

25 25 266.95 268.15 485.55 472.15 783.85 783.85 856.85 523.5 507.25 316.85 140 42.75 80.95 150 115.95 80.95 80.95 60.15 30 6.15 1.85 0 19.25 43 80.95 80.95 115.95 115.95 25 60.95 25 40.15 25 3.15 25 60.95

1 1 6.5 6.5 6.3 6.3 6.18 6.18 6 1.08 1.05 1.02 1 3.98 11.61 11.61 3.98 11.61 11.61 11.61 11.61 11.61 3.98 3.98 3.98 11.61 3.98 3.98 11.61 11.61 1 1 1 1 1 1 1 1

0.0194 1.78 0.0194 1.78 0.0194 1.78 0.082 1.72 1.8 1.8 1.8 1.8 1.8 0.9343 0.9343 0.6073 0.6073 0.3366 0.00958 0.327 0.327 0.327 0.327 0.327 0.327 0.9343 0.705 0.0978 0.743 0.1357 0.2421 0.2421 6.425 6.425 4.168 4.168 1.9 1.9

e

e

e

1076 3.73 1110 409.9 1127 612.2 290.7 991.8 1196 428.8 402.8 179.7 37.94 8100 8119 1712 1708 6634 83.21 6545 6534 6535 6535 6499 6497 8101 3424 1774 4069 2426 0 2.03 0 10 0 14.71 0 15.98 36.89

15 0 15.49 31.01 15.48 30.44 24.11 24.11 25.87 25.87 25.87 25.87 25.87 66.66 66.62 66.24 66.39 66.59 40.92 66.59 66.71 66.73 66.74 66.74 66.74 66.66 81.76 96.56 66.61 66.32 0 0 0 0 0 164.6 0 88.22 27.37

40

e

e

e

444.2

27.37

41

e

e

e

292.4

24.11 27.37

42

e

e

e

277.8

43

e

e

e

718

44

e

e

e

1.71

27.9 27.37

an increase in PH2 O and a reduction in PH2 at the stack outlet, even though PO2 is constant at this location. Fig. 7 shows the variations in net electrical output power and cooling capacity with current density for two values of fuel utilization factor. The figure indicates that the net electrical output power increases as the current density increases. In fact the fuel cell output power increases with increasing current density in spite of the voltage reduction. The inlet fuel and air molar flow rates are both functions of the fuel consumed in the electrochemical reaction _ (see Eqs. (5) and (6)); therefore, the electrical power (z)

Table 6 Performance parameters for the SOFC-GT-GAX and the SOFC-GT systems (see Table 4 for working conditions). Parameter

SOFC-GT-GAX

SOFC-GT

Vcell ðVÞ _ net ðkWÞ W

0.39 512.9

0.39 514.8

381.4

e 47.87 564.7

Q_ evap ðkWÞ j ð%Þ E_ D;tot ðkWÞ

50.99 523.8

Fig. 4. The amount of electrical power produced/consumed in the system components (see Table 4 for working conditions).

consumption rates of air and fuel compressors increase as current density rises. On the other hand, the molar flow rate and the inlet temperature of the gas turbine increase, allowing it to produce more electrical power. However, the increase in the produced electrical power due to the increase in current density is much higher than the corresponding increase in the consumed electrical power; therefore, an increase in current density increases the net electrical output power. Fig. 7 also indicates a higher value of cooling capacity at a higher current density, mainly because an increase in current density leads to a higher molar flow rate and temperature at the fuel cell exit, as mentioned earlier, so that the GAX cycle input energy and the amount of produced cooling are increased. It can also be observed from Fig. 7 that lower electrical output power and cooling capacity are resulted from a higher fuel utilization factor. The lower value of fuel cell electrical output power is attributed to the lower fuel cell voltage. In fact, a higher fuel utilization factor lowers the flow rate of fuel entering the fuel _ , while W _ compressor and consequently reduces W FC AC is constant. But a higher uf value leads to a lower turbine inlet temperature, and the simultaneous reduction in gas turbine inlet molar flow rate and _ . These changes result a lower W _ net for a temperature reducesW GT higher fuel utilization factor. Increasing the fuel utilization factor also causes a reduction in the cooling capacity, because it reduces the molar flow rate and temperature exiting the air heat exchanger. The variations in exergy efficiency with current density and fuel utilization factor are shown in Fig. 8. An increase in the current density is observed to lower the exergy efficiency. As explained earlier, an increase in current density leads to a simultaneous increase in the net electrical output power, the cooling capacity and the entering fuel molar flow rate (the system's entering exergy rate). However the rate of increase in the output exergy is less than that in the input exergy, so that the exergy efficiency decreases with increasing current density. Referring to Fig. 8, an increase in the fuel utilization factor brings about a decrease in the exergy efficiency for a constant current density. Although a higher fuel utilization factor leads to a lower value of n_ f , the reduction in system output exergy dominates the reduction in n_ f . Thus for a constant value of current density, the exergy efficiency decreases as the fuel utilization factor increases.

72

L. Khani et al. / Energy 94 (2016) 64e77

Fig. 5. Breakdown of exergy destructions and exergy losses in the system components (see Table 4 for working conditions).

The influence of current density and fuel utilization factor on the total irreversibility rate and SUCP is presented in Fig. 9. The total irreversibility rate is observed to increase with increasing current density, mainly because of the increase in the molar flow rate of all streams in the system. In addition the total irreversibility rate is lower for a higher fuel utilization factor mainly because of the reduced value of the molar flow rate of all system streams. When current density increases, the SUCP decreases. This is due to the fact that increasing current density leads to an increase in output cooling and in gas turbine and fuel cell electrical power production. But at constant current density, higher fuel utilization factor results in a higher SUCP, due to the decrease in the net electrical output power and cooling capacity. 4.1.2. The effect of pressure ratio and air utilization factor Figs. 10e13 illustrate the effects on system performance of varying pressure ratio and air utilization factor.

The variations in fuel cell voltage with pressure ratio are shown in Fig. 10 for two values of air utilization factor. An increase in the pressure ratio is seen to cause the fuel cell voltage to decrease. As the pressure ratio increases, the temperatures at the exits of the compressors increase. However, an increase in pressure ratio leads to a reduction in the turbine exit temperature and, since the turbine exit stream is used to preheat the air and fuel entering the fuel cell, the stack temperature decreases. The decrease in stack temperature raises the Nernst voltage and the voltage loss simultaneously. The increase in the Nernst voltage is, however, less than that in the voltage loss, so that the fuel cell voltage decreases as the pressure ratio increases. Fig. 10 also indicates that a higher fuel cell voltage is obtained with a higher air utilization factor. In fact, a higher air utilization factor causes a reduced inlet air molar flow rate and consequently a higher stack temperature (where air can be treated as a cooling medium for the fuel cell stack). Therefore, the Nernst voltage and voltage loss decrease, but

Table 7 Exergoeconomic results for the SOFC-GT-GAX system components. Component

cF ð$=GJÞ

cP ð$=GJÞ

C_ D þ C_ L ð$=hÞ

Z_ ð$=hÞ

f ð%Þ

rð%Þ

Fuel compressor Air compressor Fuel heat exchanger Air heat exchanger SOFC Inverter Afterburner Gas turbine GEN&ABS Rectifier Condenser Pre-cooler Evaporator Pump Overall system

27.37 27.37 25.87 25.87 12.19 24.11 24.11 25.87 25.87 66.59 66.59 66.71 66.74 27.37 15

31.02 31.29 37.94 29.28 24.11 27.37 25.87 27.66 66.59 66.59 66.71 66.73 40.55 60.71 219.87

0.3115 3.741 0.7584 1.946 7.224 1.269 7.493 4.595 7.931 1.2674 2.602 0.3545 4.972 0.08 28.3

0.01023 0.9383 0.01451 0.5354 5.319 1.994 0.09669 0.6417 0.5444 0.04742 0.192 0.06573 0.2118 0.01455 10.63

3.179 20.05 1.877 21.58 42.4 61.11 1.274 12.25 6.423 3.607 6.872 15.64 4.086 15.33 27.3

13.32 14.33 46.64 13.17 97.71 13.53 7.311 7.831 157.4 0.002 0.1784 0.0268 146.7 121.8 13.658

L. Khani et al. / Energy 94 (2016) 64e77

73

1

0.8

Vn (u f = 0.75)

Voltages, V [V]

Vloss (u f = 0.75) Vcell (u f = 0.75)

0.6

Vn (u f = 0.95) Vloss (u f = 0.95) Vcell (u f = 0.95)

0.4

2000

3500 5000 6500 2 Current density, i [A/m ]

8000

9500

Fig. 6. Variations in the voltages with current density and fuel utilization factor ðrp ¼ 6:5; ua ¼ 0:15Þ.

the decrease in the voltage loss is more significant than the decrease in the Nernst voltage so the fuel cell output voltage increases with increasing ua . Fig. 11 shows the influence of pressure ratio on the net electrical output power and the cooling capacity for two values of the air utilization factor. As pressure ratio increases, the net electrical output power is seen to decrease and the cooling capacity to increase. Actually, as the pressure ratio increases, the fuel cell electrical output power decreases due to a reduction in its voltage as current density is kept constant, but the energy interactions associated with the compressors and gas turbine increase. But the net electrical output power decreases with increasing pressure ratio because the increase in consumed electrical power exceeds significantly the rise in produced electrical power. As mentioned earlier, the increase in pressure ratio also causes an increase in the outlet temperatures of the compressors and a reduction in the gas turbine outlet temperature. Therefore, the amount of heat exchanged in the FHE and AHE is reduced and consequently the GAX cycle generator inlet temperature and input energy increase. Thus, the cooling capacity increases with increasing pressure ratio,

1000

as depicted in Fig. 11. Fig. 11 also indicates that a higher air utilization factor results in a higher net electrical output power but a lower cooling capacity. This can be explained by considering that when the air utilization factor increases the fuel cell electrical power production increases because of the voltage increase. The increase in the air utilization factor, however, considerably reduces the air compressor electrical power consumption because of the decrease in the inlet air flow rate. But the increase in air utilization factor has no effect on the inlet fuel flow rate and hence on the fuel compressor power consumption. Nonetheless, an increase in air utilization factor reduces the gas turbine power production despite the increase in gas turbine inlet temperature, due to the lower molar flow rate through the turbine. Finally, the above mentioned variations in the consumed and produced powers resulting from the variations in the air utilization factor are such that the net electrical output power increases with increasing air utilization factor. The increase in air utilization factor reduces the cooling capacity because of the reduction in the molar flow rate of exhaust gases through the GAX cycle generator, which leaves less heat available for the refrigeration system.

1100

800

Qevap (u f = 0.75)

800 600 600 400 400 W net (u f = 0.95)

200

200

Total irreversibility, ED,tot [kW]

W net (u f = 0.75)

1000

Cooling capacity, Qevap [kW]

Net electrical outpet power, Wnet [kW]

1200

Fig. 8. Variations in the exergy efficiency with current density and fuel utilization factor ðrp ¼ 6:5; ua ¼ 0:15Þ.

880

350 ED,tot (u f = 0.75)

ED,tot (u f = 0.95)

SUCP (u f = 0.75)

SUCP (u f = 0.95)

320

660

290

440

260

220

230

SUCP [$/GJ]

0.2 500

Qevap (u f = 0.95)

0 500

2000

3500 5000 6500 2 Current density, i [A/m ]

8000

0 9500

Fig. 7. Variations in the net electrical power and cooling capacity with current density and fuel utilization factor ðrp ¼ 6:5; ua ¼ 0:15Þ.

0 500

2000

3500 5000 6500 2 Current density, i [A/m ]

8000

200 9500

Fig. 9. Variations in the total irreversibility and SUCP with current density and fuel utilization factor ðrp ¼ 6:5; ua ¼ 0:15Þ:

74

L. Khani et al. / Energy 94 (2016) 64e77

1

Voltages, V [V]

0.8 Vn (u a = 0.2) Vloss (u a = 0.2)

0.6

Vcell (u a = 0.2)

0.4

Vn (u a = 0.12)

0.2

Vloss (u a = 0.12)

0 3

Vcell (u a = 0.12)

4

5

6 7 Pressure ratio, rp

8

9

10

Fig. 10. The influence of pressure ratio and air utilization factor on the voltages ði ¼ 5000 A=m2 ; uf ¼ 0:85Þ.

Fig. 12. The influence of pressure ratio and air utilization factor on the exergy efficiency ði ¼ 5000 A=m2 ; uf ¼ 0:85Þ.

The variations in exergy efficiency with pressure ratio are shown in Fig. 12 for two values of air utilization factor. It is observed that the exergy efficiency decreases as pressure ratio increases. Note that, although the cooling capacity increases with increasing pressure ratio, the exergy efficiency is more dependent on the net electrical output power. Thus, the reduction in net electrical output power with increasing pressure ratio (see Fig. 11) explains the decrease of exergy efficiency (pressure ratio has no effect on molar flow rate of inlet fuel and consequently on the system's exergy input). Fig. 12 also demonstrates that higher exergy efficiency is obtained with a higher air utilization factor. This is due to the fact that the air utilization factor has a greater influence on the net electrical output power than on the cooling capacity. Fig. 13 shows the variations in total irreversibility and SUPC with pressure ratio and air utilization factor. The total irreversibility is seen to increase as pressure ratio increases. Although the exergy destruction in the air and fuel heat exchangers decreases with increasing pressure ratio (due to a lower temperature difference between the hot and cold streams), the exergy destructions of the other components increase with increasing pressure ratio. As the

latter effect is more dominant, a higher total irreversibility results from higher pressure ratios. Fig. 13 also shows that the total irreversibility decreases as air utilization factor increases, mainly because of the reduction in the molar flow rate in the system. Finally, the influence of the pressure ratio and air utilization factor on the SUPC is also seen in Fig. 13, where SUPC is observed to increase as pressure ratio increases, but to decrease as air utilization factor increases.

725

600

280 ED,tot (u a = 0.12)

500

475

400

375

275 3

300 W net (u a = 0.12)

W net (u a = 0.2)

Qevap (u a = 0.12)

Qevap (u a = 0.2)

4

5

6 7 Pressure ratio, rp

8

9

200 10

Fig. 11. The influence of pressure ratio and air utilization factor on the net electrical power and cooling capacity ði ¼ 5000 A=m2 ; uf ¼ 0:85Þ.

SUCP (u a = 0.12)

260

625 575 ED,tot (u a = 0.2)

525

240

SUCP (u a = 0.2)

475

SUCP [$/GJ]

575

Total irreversibility, ED,tot [kW]

675 Cooling capacity, Qevap [kW]

Net electrical output power, Wnet [kW]

675

4.1.3. The effect of heat losses in the SOFC stack and afterburner Although in most research works associated with the SOFC in literature, the stack and the afterburner have been assumed as adiabatic components, there are some heat losses from these components to the environment under real conditions. In this section this effect is studied. It is assumed that 1.7% of the power produced in the fuel cell [31] and 2% of the entering fuel lower heating value in the afterburner [38] are lost. The effect of these losses on the performance parameters of the proposed system are indicated in Table 8. Referring to Table 8, not much difference is

220

425 375 3

4

5

6 7 Pressure ratio, rp

8

9

200 10

Fig. 13. The influence of pressure ratio and air utilization factor on the total irreversibility and SUCP ði ¼ 5000 A=m2 ; uf ¼ 0:85Þ.

L. Khani et al. / Energy 94 (2016) 64e77 Table 8 The effect of heat losses in the SOFC stack and afterburner on the performance parameters. Parameter

Without heat loss

With heat loss

Vcell ðVÞ _ net ðkWÞ W

0.39 512.9

0.385 506.3

381.4

380

50.99 523.8

50.36 530.5

219.9

221.6

Q_ evap ðkWÞ jð%Þ E_ D;tot ðkWÞ SUCP ð$=GJÞ

75

Table 9 Optimum values of the decision variables and objective functions. Variable

Base case

2

observed for each parameter when the heat losses are taken into account.

i ðA=m Þ rp ðÞ T16 ð CÞ T21 ð CÞ ua ðÞ uf ðÞ jð%Þ _ net ðkWÞ W

Q_ evap ðkWÞ E_ D;tot ðkWÞ SUCP ð$=GJÞ

Optimal case EEOD

COD

5000

520.5

7978

6.5 150 30 0.15 0.85 50.99 512.9

3.213 150.6 33.8 0.2 0.8357 66.96 74.23

4.66 183.1 48.2 0.2 0.7509 61.05 1154

318.4

21.75

343.5

523.8

37.17

715.5

219.9

331.8

182.5

4.2. Optimization Considering the thermodynamic and economic viewpoints, it is normally desired to maximize exergy efficiency and to minimize SUCP. A genetic algorithm, since it is the most robust (although slowest) of available methods in EES, is applied to optimize the performance of the proposed system. The genetic algorithm method, unlike the direct search and variable metric methods, is not affected by the guess values of the independent variables [47]. After several test runs, the number of generations, number of individuals and maximum mutation rate are selected to be 32, 64 and 0.35 respectively. Considering six decision variables and their restrictions, the objective function in the optimization procedure is selected as either maximizing the exergy efficiency or minimizing the SUPC as follows:

Optimize j or SUCP i; rp ; uf ; ua ; T16 ; T21

(36)

Subject to:

500  i  9500 A=m2

(37)

3  rp  10

(38)

0:75  uf  0:95

(39)

0:1  ua  0:2

(40)

110  T16  210 C

(41)

25  T21  55 C

(42)

that the net electrical output power and cooling capacity in the COD case are much higher than the corresponding values in the EEOD case, since the current density is much higher in the COD case than in the EEOD case. Note also that, considering that the exergy efficiency for the COD case is only 8.8% lower than that for the EEOD case, the COD case is the more promising. As mentioned before, the unit cost of hydrogen may vary over a wide range. Therefore, four cost values are considered for the COD case. The results are shown in Table 10, where each 6 $/GJ increase in hydrogen unit cost leads approximately to a 62.5 $/GJ increase in the SUCP. This is due to the increase of 17 $/GJ and 45.5 $/GJ in the net electrical output power and cooling capacity unit exergy costs, respectively. Despite the increase in the hydrogen unit cost, it is desirable to have a high current density and a fairly low pressure ratio to obtain a COD plant. The ratio of cost of unit exergy of cooling capacity to that of unit electrical power decreases from 2.89 to 2.75 as the hydrogen unit cost increases from 6 $/GJ to 24 $/GJ. It is also observed in Table 10 that the exergy efficiency of the COD case decreases 4.53% due to an 18 $/GJ increase in the hydrogen cost. 5. Conclusions

Table 9 lists values of the decision variables and objective functions for the exergy efficiency optimal design (EEOD) and cost optimal design (COD), as well as values for the base case. For the case of EEOD, the optimum values of current density and pressure ratio are seen in Table 9 to be the lowest, but the fuel utilization factor is seen to be the highest. Also for the case of EEOD, the SUCP is 50.9%and 81.8% higher than the corresponding values for the base case and COD, respectively. This high value of SUCP is due to very low values of the net electrical output power and cooling capacity in the EEOD case. The highest generator and condenser temperatures and current density are obtained for the COD case (33.1  C, 18.2  C and 2978 A=m2 higher than the base case, respectively). The exergy efficiency is 31.3% higher for the EEOD case than the base case, while the SUCP is 20.5% lower for the COD case than the base case. Table 9 also demonstrates that the two optimized designs operate with approximately constant air utilization factors. Note

A new power/cooling cogeneration system is proposed and assessed. Energy, exergy and exergoeconomic balances are solved (with EES software) and the effects on system performance are investigated of various decision parameters. The main conclusions that can be drawn from the principal findings of the present work are as follows:

Table 10 Cost optimization results for the SOFC-GT-GAX system for several hydrogen unit costs. Variable

2

i ðA=m Þ rp ðÞ T16 ð CÞ T21 ð CÞ ua ðÞ uf ðÞ jð%Þ _ net ðkWÞ W

Hydrogen unit cost ($/GJ) 6

12

18

24

9459

8044

8822

9097

4.799 181.2 48.4 0.2 0.7631 60.44 1331

4.523 187 49.7 0.1922 0.771 60.03 1115

3.847 183.6 48.9 0.1797 0.7712 58.84 1196

5.193 191.5 50 0.1928 0.8499 57.82 1102

Q_ evap ðkWÞ E_ D;tot ðkWÞ cpower ð$=GJÞ ccooling ð$=GJÞ

416.5

318.9

367.8

321

849

719.3

816.9

777.1

22.68 65.51

39.53 111.5

56.43 157.3

73.6 202.7

SUCP ð$=GJÞ

88.19

151.1

213.7

276.3

76

L. Khani et al. / Energy 94 (2016) 64e77


At a specific condition, the exergy efficiency of the proposed system is 6.5% higher than that of the stand-alone solid oxide fuel cell-gas turbine system, because of the cooling production by the GAX absorption refrigeration cycle.
The largest contributions to the total system irreversibility are made, in order, by the fuel cell stack, the afterburner and the generator/absorber assembly.
The afterburner and the fuel heat exchanger have the lowest exergoeconomic factors, based on the exergoeconomic analysis, suggesting that their exergy efficiencies should be increased.
The optimization demonstrates that the cost optimal design is more promising than the exergy efficiency optimal design, as for the former case the sum of the unit costs of products is very low and the net electrical output power as well as cooling capacity is high compared to those parameters for the exergy efficiency optimal design case.
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Nomenclature A: Heat transfer area ðm2 Þ Aact : Cell active area ðm2 Þ

L. Khani et al. / Energy 94 (2016) 64e77 c: Cost per exergy unit ð$=GJÞ _ Cost rate ð$=hÞ C: CRF: Capital recovery factor Deff : Effective gas diffusion factor ðm2 =sÞ Dx : Degassing range Dg0f : Change in molar Gibbs free energy ðkJ=kmolÞ _ Exergy rate (kW) E: E_ D : Exergy destruction rate (kW) ech : Standard chemical exergy of species ðkJ=kmolÞ ef : Specific chemical exergy of fuel ðkJ=kmolÞ f: Exergoeconomic factor F: Faraday constant ðC=kmolÞ h: Molar enthalpy ðkJ=kmolÞ i: Current density ðA=m2 Þ i0 : Exchange current density ðA=m2 Þ iL : Limiting current density ðA=m2 Þ ir : Interest rate l: Current flow length (m) M: Molecular weight _ Mass flow rate ðkg=sÞ m: n: System lifetime (year) N: Number of system operating hours (hour) _ Molar flow rate ðkmol=sÞ n: Ncell : Number of cells in a stack ne : Number of electrons P: Pressure (bar) Q_ : Heat transfer rate (kW) r: Ohmic resistance; relative cost difference R: Universal gas constant ðkJ=kmol KÞ rp : Pressure ratio s: Molar entropy ðkJ=kmol KÞ SUCP: Sum of the unit costs of products ð$=GJÞ T: Temperature (K) Tb : Mean temperature of low temperature heat source (K) ua : Air utilization factor uf : Fuel utilization factor V: Voltage (V) _ Electrical power (kW) W: x: Mass concentration of ammonia in NH3eH2O solution y: Mole fraction of each gas in a gaseous mixture YD : Exergy destruction ratio (%) Z: Capital cost of a component ($) _ Reacted hydrogen molar follow rate ðkmol=sÞ z: _ Capital cost rate ð$=hÞ Z: Greek symbols h: Efficiency 4: Maintenance factor

ε: Effectiveness j: Exergy efficiency Subscripts 0: Environmental condition 1, 2, …: System state points a: Anode AB: Afterburner Abs: Absorber AC: Air compressor act: Activation AHE: Air heat exchanger ASP: Additional solution pump av: Available c: Cathode cell: Fuel cell ch: Chemical con: Concentration Cond: Condenser D: Destruction e: Electrode elec: Electrochemical reaction EV: Expansion valve evap: Evaporator f: Fuel FC: Fuel compressor FHE: Fuel heat exchanger GAXA: GAX-absorber GAXD: GAX-desorber Gen: Generator GT: Gas turbine H2 : Hydrogen H2 O: Steam int: Interconnection inv: DC to AC inverter loss: loss M: Motor N 2 : Nitrogen N: Nernst net: Net O2 : Oxygen ohm: Ohmic p: Pump; product ph: Physical Prec: Pre-cooler Rec: Rectifier SOFC: Solid oxide fuel cell tot: Total

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