Thermo-economic performance analysis of a gas turbine generator equipped with a pressurized and an atmospheric solid oxide fuel cell

Energy Conversion and Management 136 (2017) 249–261

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

Thermo-economic performance analysis of a gas turbine generator equipped with a pressurized and an atmospheric solid oxide fuel cell Jamasb Pirkandi ⇑, Mostafa Mahmoodi, Mohammad Ommian Department of Aerospace Engineering, Malek Ashtar University of Technology, Tehran, Iran

a r t i c l e

i n f o

Article history: Received 22 June 2016 Received in revised form 10 December 2016 Accepted 5 January 2017

Keywords: Gas turbine Pressurized fuel cell Atmospheric fuel cell Exergy efficiency Irreversibility Electricity price

a b s t r a c t The main objective of this research is to introduce and present two different configurations for hybrid gas turbine-fuel cell systems of direct type and to analyze these systems based on the thermodynamic and thermo-economic models. In the first proposed design, two fuel cells are situated at the upstream of turbine and operate at a specific pressure; while in the second design, one of the cells is transferred to the downstream of turbine, and it works under atmospheric pressure. Also, in the economic analyses performed in this research, a simple economic model and the Total Revenue Requirement model are employed to compute the electricity generation price and the other relevant expenses. The examination of the two proposed systems shows that the hybrid system with one pressurized and one atmospheric fuel cell (the second design) enjoys a higher efficiency and power generation capacity, but at the same time, it has greater exergy destruction and irreversibility rates. The results also indicate that this design generates more pollution compared to the first design. From an economical point of view, the generated electricity price and the purchase, installation and startup costs of both systems are almost the same, and have no significant difference. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction A solid oxide fuel cell is a type of cell with a high working temperature, and it can be used more fittingly in hybrid power generation systems. This cell always produces a substantial quantity of high-quality heat and energy. Many researchers have recently become interested in using this heat in the most effective way. A more common application for solid oxide fuel cells is to combine these cells with various types of turbines and micro gas turbines [1]. In this type of hybrid systems, the gas turbine cycle can be combined with the fuel cell directly (under pressure or at atmospheric pressure) or indirectly [2]. Replacing the gas turbine cycle’s combustion chamber by a high-temperature fuel cell (or a set of fuel cell and afterburner) or placing a fuel cell at the downstream or upstream of the combustions chamber forms a type of pressurized direct hybrid system; and placing a fuel cell at the downstream of a gas turbine forms a direct hybrid system operating under atmospheric pressure. In direct hybrid systems under pressure, the fuel cell is often subjected to a specific pressure; which increases its output power but, accordingly, creates more challenges in the design and control of the resulting hybrid system.

⇑ Corresponding author. E-mail address: [email protected] (J. Pirkandi). http://dx.doi.org/10.1016/j.enconman.2017.01.013 0196-8904/Ó 2017 Elsevier Ltd. All rights reserved.

Because of the high pressures produced in the fuel cell, its casing has to be properly and securely sealed. In this system, the fuel and the oxidizer that have not reacted in the cell, exit the cell at a high temperature, burn in an afterburner or a secondary combustion chamber, and provide the needed heat energy for the lower cycle. Another example of this type of direct hybrid system includes the direct combination of an atmospheric fuel cell with a gas turbine cycle. In this system, the air flowing into the fuel cell is extracted from the gas turbine’s exhaust gasses. Due to low pressure of the turbine’s exhaust gasses, medium-temperature solid oxide fuel cells or molten carbonate fuel cells are used in this type of hybrid systems. The gasses exiting the fuel cell then enter a combustion chamber and, after reacting, are used in the cycle’s heat exchangers. In this type of hybrid systems, the output power of the gas turbine is about 1/3 of the hybrid system’s total power. The indirect combination of the gas turbine cycle with fuel cell forms another type of hybrid systems. In this type of hybrid system, the fuel cell and the gas turbine cycle use separate systems for providing their needed air. In this type of systems, the fuel cell mostly operates under atmospheric pressure. Although in this case, the insulation requirement for the fuel cell becomes less, the major issue in these systems is the proper design of the heat exchanger. Because of the large differences between the temperatures and pressures of the hot and cold sections of the heat exchanger, these

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Nomenclature A C C˙ C_ P;tot C_ F;tot cP CCL cfuel E˙ E˙D E˙L FC 0 i _ fuel m n N PEC k r FC

cell area, m2 electricity price, $/kW h cost rate, $/h rate of total power generation cost, $/h rate of total fuel cost, $/h electricity generation cost, $/kW h investment cost, $ cost of fuel in the first operating year of the system cell voltage at standard conditions, V rate of exergy destruction, kW rate of exergy losses, kW annual cost of fuel in the first year of system operation, $ interest rate flow rate of consumed fuel, kmol/h number of years the equipment have been in operation total annual operating hours initial purchase cost of equipment, $ yearly escalation rate of fuel cost

sections must be made of special metals; which probably amounts to high costs. Because of the existing heat transfer and pressure losses inside the heat exchanger of indirect hybrid systems, they are expected to have a lower efficiency than the direct hybrid systems [2]. A review of the literature indicates that, in recent years, numerous research works have been conducted on hybrid power generation systems. In 2006, Araki et al. [3] explored a hybrid power generation system consisting of two high-temperature and lowtemperature solid oxide fuel cell stacks. In this analysis, a comparison was made between the efficiencies of a high-temperature and a low-temperature fuel cell, and the efficiency of these two cells connected in series. Their findings indicated the increased efficiency of the hybrid system consisting of two fuel cells connected in series. In 2008, Musa and Paepe [4] investigated the performances of hybrid cycles with two high-temperature and medium-temperature solid oxide fuel cells. They concluded that the efficiency of a hybrid cycle with two medium-temperature fuel cells is higher than that of a hybrid cycle with two hightemperature and medium-temperature cells and also a cycle consisting of a single fuel cell. In 2010, Cheddie [5] analyzed a 10 MW hybrid system of gas turbine and fuel cell. In this system, four heat exchangers had been used to recover the output heat of the turbine and fuel cell. In this investigation, he employed a thermo-economic model to optimize his hybrid system. In this study, the output power of the hybrid system including the heat exchangers, with 66.2% efficiency, was close to 4 times that of the initial hybrid system. Also, based on the presented model in this research, the capital investment return period was estimated to be less than 4 years. In 2010, Tarroja et al. [6] studied a hybrid system of gas turbine and solid oxide fuel cell, investigated the different methods of preheating the cathode’s inflowing air (e.g., using a blower or ejector), and compared the results with those of a system with a single heat exchanger. The effects of parameters such as pressure ratio, fuel utilization, oxygen consumption and current density were also analyzed in this research. The findings indicated that the hybrid system with a single heat exchanger has a better performance. In 2014, Facchinetti et al. [7] explored the design and optimization of a SOFC-GT hybrid cycle with a new configuration, which had been considered for use in residential buildings. The presented hybrid cycle included a 5 kW plate type solid oxide fuel cell unit and a micro gas turbine unit consist-

Z_ CI tot Z_ OM tot

initial capital investment cost, $/h operating and maintenance cost, $/h

Greek letters h efficiency Ur operating and maintenance cost Acronyms BL book life of the system CRF capital recovery factor LHV lower heating value of consumed fuel, kj/mol OMC operating and maintenance cost, $ SOFC Solid Oxide Fuel Cell TRR total revenue requirement cost, $ Subscripts ab afterburner is isentropic p polytropic

ing of two turbines and a radial compressor, whose thermodynamic performance was analyzed. The optimization results of this research showed a first law efficiency of 64% and an exergy efficiency of nearly 66% for the new hybrid system. In this research, the temperature of the turbine’s inflowing gasses was assumed to be 1573 K. Arsalis [8,9] investigated four different steam turbine cycles. The models have been developed to function both at design and off-design conditions. Cheddie and Murray [10–12] proposed direct, semi-direct and indirectly coupled of SOFC and a 10 MW power plant. Akikur et al. [13] presented performance assessment of a co-generation system to deliver electrical and thermal energy using the solar energy and the reversible solid oxide fuel cell. Lorenzo and Fragiacomo [14] formulated zero-dimensional and stationary simulation model of an SOFC system fed by syngas in cogenerate arrangement and implemented in the Matlab environment by which the SOFC system performances were evaluated. Ebrahimi and Moradpoor [15] proposed a novel cycle combining three technologies of solid oxide fuel cell, micro gas turbine, and organic Rankine cycle to produce power in micro scale. Zouhri and Lee [16] analyzed the effect of various materials parameters and environmental conditions on the performance of SOFC. These researchers have employed simple economic models in their investigations in order to determine the price of the generated electricity, and their considered hybrid systems have consisted of gas turbines and pressurized fuel cells. The main goal of this research is to introduce and present two different configurations for direct hybrid systems of gas turbine and fuel cell and to analyze these two structures based on their thermodynamic and thermo-economic models. In the economic analyses performed in this research, a simple economic model and the total revenue requirements (TTR) model have been used to calculate the price of the generated electricity and the other associated expenses. The TRR model is an accurate and complete model for economic analyses and it can calculate all the capital investment and current costs of a system [17].

2. The proposed hybrid systems In this section, the schematics of two types of gas turbine generators equipped with two fuel cells, which have been investigated in this research, are presented. The first proposed system consists

J. Pirkandi et al. / Energy Conversion and Management 136 (2017) 249–261

of two pressurized fuel cells which have been installed, in series formation, at the upstream of turbine. As is observed in Fig. 1, the air and fuel coming into the system, after being warmed up by the recuperators, enter the first fuel cell and after participating in electrochemical reactions and in the generation of power there enter the second fuel cell. Since a major portion of the inlet fuel (about 85%) is used up in the first cell, in order to provide the fuel needed by the second cell, a specific amount of extra fuel is injected at the anode inlet of the second fuel cell. The remaining air and fuel from the first cell, along with the added fuel, enter the second cell and generate more power there through a series of electrochemical reactions. The outflowing gasses from the second cell then enter an afterburner chamber and after participating in chemical reactions there enter the turbine to generate power. Eventually, for the purpose of heating the air, fuel and water needed by the system, the hot exhaust gasses from the turbine enter the heat exchangers and then are discharged into the surrounding environment. As is illustrated in Fig. 1, in the proposed system, a pump has been provided to supply the needed warm water. By using this pump, the considered system can be employed in combined heat and power generation applications. In the second proposed system, one pressurized and one atmospheric fuel cell has been used in the gas turbine cycle. As was mentioned in the previous sections, the fuel cell operating under pressure is situated at the upstream and the atmospheric fuel cell is at the downstream of turbine. According to Fig. 2, the air and fuel coming into the system, after being warmed up in the heat exchangers, enter the pressurized fuel cell and provide part of the power generated by the hybrid system. The remaining gasses from the pressurized fuel cell then enter the afterburner chamber and, there, all the leftover fuel is used up in a chemical reaction. The hot exhaust gasses from the afterburner chamber, on their way, enter the turbine and after generating electrical power there, enter the cathode of the atmospheric fuel cell. Then, along with the fuel injected into the anode section, these gasses provide another part of the power generated by the hybrid system. Similar to the pressurized fuel cell, the unused gasses in the atmospheric cell enter the second afterburner chamber and after participating in high-temperature chemical reactions, are conveyed towards the heat exchangers. For heating the air, fuel and water needed by the hybrid system, the hot exhaust gasses from the afterburner

251

chamber enter the heat exchangers and, after exchanging their heat, are discharged into the surrounding environment. Similar to the first system, a pump has been used in this design to supply the warm water needed. 3. Assumptions The following assumptions have been considered in the modeling and analysis of the introduced hybrid systems: – Gas leakage from inside the system to the outside has been disregarded. – A stable fluid flow has been considered in all the cycle components. – The fluctuations of kinetic and potential energies have been disregarded. – The behavior of all the gasses in the cycle has been assumed as that of an ideal gas. – The distribution of temperature, pressure and chemical components within the fuel cell has been disregarded. – A constant voltage has been considered for the cells of the fuel cell. – It has been assumed that the fuel inside the fuel cell converts to hydrogen through internal reforming.

4. Governing equations In this section, the governing equations of the problem, comprising the economic, thermodynamic and exergy and equations have been presented. 4.1. Economic equations For an economic optimization of energy systems, one needs to compare the annual expenses associated with capital investment, fuel costs and the operating and maintenance costs. For an ideal case, Eq. (1) expresses the relationship between the above parameters and provides a cost balance for the whole system [17].

_ OM C_ P;tot ¼ C_ F;tot þ Z_ CI tot þ Z tot

Fig. 1. The direct hybrid system with two pressurized fuel cells.

ð1Þ

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Fig. 2. The hybrid system with one pressurized and one atmospheric fuel cell.

The sum of the costs associated with the initial capital investment and the operating and maintenance expenses is introduced, accord_ [17]. ing to Eq. (2), as a single parameter called ‘Z’

_ OM Z_ ¼ Z_ CI tot þ Z tot

ð2Þ

Since in this research, the generated electricity and the natural gas have been considered as the product of the hybrid system and the fuel consumed in the system, respectively, Eq. (1) transforms into Eq. (3). This equation is the very objective function in the optimization, in which the electricity generation cost should be minimized.

_ net ¼ C_ F;tot þ Z_ CI þ Z_ OM cP W tot tot _ OM C_ F;tot þ Z_ CI tot þ Z tot cP ¼ _ net W

ð3Þ ð4Þ

4.1.1. Lazaretto’s simple economic model Being one of the simplest economic models, this model has been presented by professor Lazaretto of the University of Milan. In this model, the sum of the initial capital investment cost and the operating and maintenance expenses has been formulated according to Eq. (5) [17].

Z_ k ¼ CRF

simple economic model of Lazaretto and the total revenue requirement method have been employed for the economic analyses performed in this research. In simple economic models, the costs associated with the equipment and land purchase, and the design and construction expenses are considered as part of the investment-related expenses; and the operating costs are determined by applying some empirical factors to the equipment purchase cost. Contrary to the simple economic method, in the total revenue requirement approach, all the costs associated with establishing a power generation system are calculated separately, and with a high accuracy.

3600N

PEC k


 $ s

ð5Þ

In the above equation, Ur is the operating and maintenance cost (1.06–1.1), N is the total annual operating hours of the system under full load (85% of total work capacity, and equal to 7446 h). In thermo-economic analyses, the CRF is usually estimated to have a range of 0.147–0.18. In Eq. (6), the interest rate or the discount factor has been considered in the range of 0.1–0.12. [17] n

CRF ¼ Usually, in thermo-economic analysis, especially in large and complicated systems, the most difficult task concerns the economic modeling. The accuracy of a thermo-economic analysis greatly depends on the validity of the economic model considered in the computation of Z_ [17]. In view of the abovementioned items, the

Ur

ið1 þ iÞ n ð1 þ iÞ  1

ð6Þ

4.1.2. The economic model of total revenue requirements (TRR) The annual ‘total revenue requirements’ for a system refers to the revenues which should be earned in a year through the sale of the system’s products, so that this earning compensates all the system’s expenses during its operation in the same year and ensures a cost-effective performance for the system. Based on the TRR method, or the method of calculating the total product cost, the revenues earned from the sale of a system’s product within a specific year should compensate the total expenses incurred by operating that system in the mentioned year [17]. In the TRR method, the series of expenses and revenues specific to each operating year of a system is not uniform. The annual total revenue requirements in the jth year comprise a set of 8 components, and are determined according to Eq. (7) [17].

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TRRj ¼ TCRj þ ROIj;ce þ ROIj;ps þ ROIj;d þ ITX j þ OTXIj þ FC j þ OMC j

ð7Þ

The above equation is considered as the main equation in the TRR method. The procedure for calculating each constitutive component has been presented in [17]. In this section, the TRR method has also been used for the economic analysis of the system. In this approach, based on the economic assumptions used, the cost of purchased equipment, land purchase cost, costs of engineering services, construction expenses, fuel cost, operating and maintenance costs, etc. are computed and annually levelized for the operating period of the system [17]. In this model, the total expenses related to the initial capital investment and maintenance costs are determined according to Eq. (8) [17].

CC L þ OMC L PEC k Z_ k ¼ P s k PEC k

ð8Þ

CC L ¼ TRRL  FC L  OMC L

ð9Þ

In the above equations, FCL is the levelized fuel cost, OMCL is the levelized operating and maintenance cost, and TRRL is the levelized total revenue requirements cost. The cost of fuel is considered as one of the effective parameters in economic analysis. The series of annual expenses paid for fuel remains uniform during the operating period, and includes only one escalation [17]. j1

FC j ¼ FC 0 ð1 þ r FC Þ

j ¼ 2; . . . ; BL

_ OM CC L þ OMC L Z_ tot ¼ Z_ CI tot þ Z tot ¼

ð18Þ

CC L þ OMC L þ FC L TRRL ¼ C_ p;tot ¼

ð19Þ

s

s

cp ¼

ð11Þ ð12Þ ð13Þ

s

TRRL

ð20Þ

s  W_ tot

cpp ¼

PEC tot þ 0:46PEC tot _ tot W

ð21Þ

4.1.3. Cost of purchased equipment The purchase cost of the proposed system’s equipment will be obtained by using Eqs. (22)–(31). The prices presented in Eqs. (22)–(26) are based on the equations of the year 1994, and an index diagram is employed to update these prices [17]. – Prices of air and fuel compressors [17]

 PEC ca ¼

_ ca 71:1m 0:9  gsc

    Pe Pe ln ð$Þ Pi Pi

ð22Þ

– Price of afterburner ! chamber [17]

_ ab 46:08m ½1 þ expð0:018T e  26:4Þ ð$Þ 0:995  PPe

PEC ab ¼

ð10Þ

In the above equation, rFC is the yearly nominal escalation rate of fuel cost; which is considered as 0.06 [17]. BL is the book life of the system (considered as 20 years in this research), and FC 0 is the annual cost of fuel in the first year of system operation (in $), which is obtained through Eq. (11).

_ fuel  LHV  s  3600 ½$ FC 0 ¼ cfuel  m  n  kFC 1  kFC FC L ¼ FC 0   CRF ð1  kFC Þ 1 þ r FC kFC ¼ 1þi

In the above equation, detailed information regarding its computation has been given in [17].

ð23Þ

i

– Price of turbine [17]   

PEC gt ¼

_g 479:34m Pi ln ½1 þ expð0:036T i  54:4Þð$Þ 0:92  gst Pe

ð24Þ

– Price of recuperators [17]

  _ g ðhi;g  he;g Þ 0:6 m 18  DT lm;APH  T e;a Þ  ðT e;g  T i;a Þ

PEC APH ¼ 4122  ðT i;g

DT lm;APH ¼

T

T

e;a ln T i;g e;g T

ð25Þ ð26Þ

i;a

In the above equations, i is the average annual effective discount factor (assumed as 0.12 in this research) and n indicates the total number of years the equipment are operated (considered as 20 years in this research). Similar to the fuel cost, the annual operating and maintenance costs can also be computed. These costs for each year of operation are computed by Eq. (14) [17].

PEC sofc ¼ Asofc ½2:96T cell  1907 !0:7 _ 5 ðW DCtot Þsofc PEC inv erter ¼ 10 500

ð27Þ

OMC j ¼ OMC 0 ð1 þ r OMC Þj1

PEC sofc;aux ¼ 0:1PEC sofc

ð29Þ

j ¼ 2; . . . ; BL

ð14Þ

In the above equation, r OMC is the nominal escalation rate of operating and maintenance costs (except the fuel cost); which is considered equal to 0.05 [17]. The levelized annual operating and maintenance cost can be computed, according to the above method, by means of Eq. (15) [17].

  n kOMC 1  kOMC OMC L ¼ OMC 0   CRF ð1  kOMC Þ 1 þ rOMC kOMC ¼ 1þi

ð15Þ ð16Þ

The levelized annual total revenue requirement (TRRL) is determined by applying the capital recovery factor and the discount factor, according to Eq. (17) [17]:

TRRL ¼ CRF

n X TRRj j¼1

ð1 þ iÞ

j

ð17Þ

– Prices of fuel cell, inverter, and supplementary cell equipment [10–12]

ð28Þ

– Price of pump [8,9]

_ wp Þ 1:41f PEC wp ¼ 442ðW g ! 1  0:8 fg ¼ 1 þ 1  gwp 0:71

ð30Þ ð31Þ

The total purchase price of system equipment is equal to the sum of the prices of every single component and is obtained from Eq. (32).

PEC tot ¼

X PEC i

ð32Þ

i

4.2. Thermodynamic and exergy equations In this part, the governing equations of the problem, comprising thermodynamic and energy have been presented.

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4.2.1. Air compressor By assuming an adiabatic compression process and knowing the pressure ratio (rp;ca ), compressor’s isentropic efficiency (gis;ca ), air specific heat ratio (ka ) and the flow rate of air passing through the compressor (nca ), the temperature of the compressor’s exhaust _ ca ) can gasses, and the actual work required by the compressor (W be determined [18]. It should be mentioned that due to the dependency of isentropic efficiency on the compressor’s pressure ratio and because of the fluctuations of this efficiency with pressure changes, polytropic efficiency (gp;ca ) has been employed in analyzing the system instead of isentropic efficiency. Eq. (33) has been used to calculate the polytropic efficiency.

gis;ca ¼

ðr p;ca Þ

ka 1 ka

1

ka 1

ðrp;ca Þka :gp;ca  1

T out;ca ¼ ðr p;ca Þ T in;ca    _ ca ¼ n_ ca : h W out;ca  hin;ca ka 1 ka :gp;ca

E_ out;ca  E_ in;ca wca ¼ _ ca W

ð33Þ ð34Þ ð35Þ

ð36Þ ð37Þ

4.2.3. Afterburner chamber Since only a portion of the fuel and air that enter the system are used up in the fuel cell, an afterburner chamber is necessary for the cycle. The exhaust gasses from the fuel cell, including water vapor, carbon dioxide, hydrogen, methane and carbon monoxide at the anode section and unused oxygen and nitrogen at the cathode section, react with each other in the afterburner chamber. All the above reactions are exothermic, and they raise the temperature of the gasses that exit the afterburner chamber. By writing the energy conservation equation and considering the chamber efficiency, the temperature of exhaust gasses can be computed by means of Eq. (39).

ð39Þ

In the above equation, Q_ Loss;ab is the heat losses of the afterburner chamber and its value depends on the chamber’s efficiency (gab ) and the heating value of fuel (LHV) [18]. The amount of heat loss in the afterburner chamber is obtained from Eq. (40).

Q_ Loss;ab ¼ n_ f ;ab  ð1  gab Þ  LHV

gab

f ¼ theoretical f actual

ð40Þ ð41Þ

The rate of entropy generation, rate of exergy destruction, and the exergy efficiency of the afterburner chamber are obtained from Eq. (42) [19,20].

Q_ loss;ab S_ gen;ab ¼ n_ out;absout;ab  n_ in;absin;ab þ T surr E_ ab ¼ E_ in;ab  E_ out;ab  E_ Q ;ab E_ out;ab wab ¼ E_ in;ab



1 r p;gt



gp;gt ðkg 1Þ kg

1

ð45Þ

kg 1 kg

r p;gt

gp;gt ðkg 1Þ

T in:gt k ¼ r p;gt g T out;gt    _ gt ¼ n_ gt h W in;gt  hout;gt

ð46Þ ð47Þ

The rate of entropy generation, rate of exergy destruction, and the exergy efficiency in the turbine’s expansion process are obtained according to Eq. (48) [19,20].

  S_ gen;gt ¼ n_ gt sout;gt  sin;gt  _ gt E_ D;gt ¼ E_ in;gt  E_ out;gt  W _ gt W wgt ¼ _Ein;gt  E_ out;gt

ð48Þ ð49Þ ð50Þ

ð38Þ

4.2.2. Fuel compressor The computations related to the fuel compressor are similar to those of the air compressor.

  _ _ out;ab h n_ in;ab h in:ab  n out;ab  Q loss;ab ¼ 0

gis;gt ¼

1

1

The rate of entropy generation, rate of exergy destruction, and the exergy efficiency of the air compressor have been computed by means of Eqs. (36)–(38), respectively [19,20].

  S_ gen;ca ¼ n_ ca : sout;ca  sin;ca  _ ca  E_ out;ca  E_ in;ca E_ D;ca ¼ W

4.2.4. Turbine The hot gasses exiting the afterburner (or combustion) chamber, on their way, enter the turbine to generate electrical current. Part of this generated electrical power is consumed by the air and fuel compressors and also the pump, and the remaining power is utilized as the net power output of the turbine. By computing the turbine’s ideal work and considering its isentropic efficiency, the amount of work produced by the turbine and its output temperature can be determined by Eqs. (45)–(47).

ð42Þ ð43Þ ð44Þ

4.2.5. Fuel cell The general solutions for the conservation of mass and energy equations of the fuel cell require the evaluation of the voltage and current generated in the cell. The reversible voltage of the fuel cell is defined by the Nernst equation, and according to Eq. (51) [14,21,22].

PH2 P 0:5 Ru T O2 E¼E þ ln ne F P H2 O

!



ð51Þ

In the above equation, E is the cell voltage under standard conditions, Ru is the general gas constant, T is the temperature of the cell pile (stack), F is the Faraday’s constant and ne is the number of electrons flowing in the circuit for each water molecule formed. To determine the real voltage of the fuel cell, the losses associated with the cell including the activation voltage loss (V act ), ohmic voltage loss (V ohm ) and the concentration voltage loss (V conc ) should be calculated. Ultimately, the real cell voltage (V cell ) is obtained from Eq. (52) [14,16].

V cell ¼ E  ðV act þ V ohm þ V conc Þ

ð52Þ

The procedures for determining the cell voltage loss have been thoroughly covered in [21,22]. After computing the real cell voltage, each cell’s generated current and the total power produced by the cell stack are obtained according to the following equations:

Icell ¼ iAcell

ð53Þ

ðW DCtot Þsofc ¼ nV cell Icell

ð54Þ

ðW ACtot Þsofc ¼ ðW DCtot Þsofc  ginv ;fc

ð55Þ

In Eq. (55), ginv ;fc is the direct-to-alternating current conversion factor. In this paper, a fuel cell with direct internal reforming has been used, in which the heat released during the electrochemical reactions of electrodes is utilized to carry out the endothermic reforming reaction. In computing the temperature of the exhaust gasses from the fuel cell stack, the three heat sources in the cell should be taken into consideration. The amounts of heat resulting from

J. Pirkandi et al. / Energy Conversion and Management 136 (2017) 249–261

the reforming, shifting and electrochemical reactions are respectively obtained through Eqs. (56)–(58) [23].

     Q_ r ¼ x h CO þ 3hH2  hCH4  hH2 O      Q_ sh ¼ y h CO2 þ hH2  hCO  hH2 O Q_ elec ¼ zT DS  IDV loss

ð56Þ ð57Þ ð58Þ

The residual net heat remaining from the reactions in the fuel cell is obtained according to Eq. (59).

Q_ net ¼ Q_ elec þ Q_ sh  Q_ r

ð59Þ

In view of Eq. (59), a portion of this residual net heat is spent to raise the temperature of the cell’s internal and outflowing gassesðQ_ 0 Þ; and another portion enters the surrounding environment ðQ_ surr Þ .

Q_ net ¼ Q_ 0 þ Q_ surr

ð60Þ

In a real situation, the processes implemented in a fuel cell cannot be considered as adiabatic at all; and always there is some heat loss to the surrounding atmosphere. By considering this problem as an ideal case, it is assumed that the fuel cell is internally adiabatic and that the net residual heat is used to raise the temperature of the cell’s internal and outflowing gasses ðQ_ 00 Þ. In this case, by considering the same temperature for the gasses exiting from the anode and cathode, Eq. (61) will be obtained. In this equation, Dha;in and Dhc:in denote the enthalpy changes of reactants, and Dha;out and Dhc;out indicate the enthalpy changes of products at the anode and cathode, respectively.

Q_ 00 ¼ Dhc;in þ Dhc;out þ Dha;in þ Dha;out

ð61Þ

To compute the temperature of the fuel cell’s exhaust gasses, an iteration algorithm has been employed; and the convergence criterion has been considered as Eq. (62).

Q error



Q_ 00  Q_ 0



¼

< 0:01

Q_ 0

ð62Þ

After computing the output temperature, the heat losses in the fuel cell can be calculated by means of Eq. (63).

 þ n_ h  c;out þ n_ a;out h a;out þ Q_ surr þ W _ sofc _ c;out h n_ c;in h c;in a;in a;in ¼ n

ð63Þ

The rate of entropy generation, rate of exergy destruction, and the exergy efficiency of the chemical processes within the fuel cell are obtained according to Eq. (64) [19].

s_ gen;sofc ¼ ðn_ c;out sc;out þ n_ a;out sa;out Þ  ðn_ c;insc;in þ n_ a;insa;in Þ þ _ sofc E_ D;sofc ¼ E_ c;in þ E_ a;in  E_ c;out  E_ a;out  E_ Q  W _ sofc W wsofc ¼ _ _ ðEc;in þ Ea;in Þ  ðE_ c;out þ E_ a;out Þ

Q_ surr T surr

ð64Þ ð65Þ

ereg

T c:out  T c:in ¼ T h;in  T c;in

By using Eq. (69), the amount of warm water needed for the heating units in the cogeneration system (n_ w ) can be determined. In this research, the temperature of the warm water coming out of the recuperator has been considered as 90 °C. The amount of heat obtained from the last recuperator is used to calculate the total thermal efficiency of the system. The rate of entropy generation, rate of exergy destruction, and the exergy efficiency of the first recuperator are obtained according to Eq. (70) [19].

    S_ gen;reg;a ¼ n_ a se;a  si;a  n_ g si:g  se;g   E_ D;APH ¼ E_ in;g  E_ out;g  E_ out;a  E_ in;a wAPH

E_ out;a  E_ in;a ¼ E_ in;g  E_ out;g

ð67Þ

_ wp ¼ n_ w v w ðPout;w  Pin;w Þ W

   Q_ reg;w ¼ ereg;w n_ g h in;reg  hout;reg    p T out;w  T in;w Q_ reg;w ¼ n_ w C

ð68Þ ð69Þ

ð71Þ ð72Þ

ð73Þ

In the above relation, mw is the specific volume of water flowing into the pump. After exchanging its heat in the heating units, the outflowing warm water from the pump is returned to the power generation system for reheating. The rate of entropy generation, rate of exergy destruction, and the exergy efficiency of the pump is obtained according to Eq. (74).

  S_ gen;wp ¼ n_ w sout;w  sin;w  _ wp  E_ out;wp  E_ in;wp E_ D;wp ¼ W wwp

E_ out;wp  E_ in;wp ¼ _ wp W

ð74Þ ð75Þ ð76Þ

4.2.8. Hybrid system In this section, by considering the whole hybrid system as a control volume, its electrical, thermal, total, and exergy efficiencies will be obtained by means of Eqs. (77)–(79).

_ W

gele ¼ _ net nf LHV Q_

gth ¼ _ reg;w nf LHV gtot ¼ wsys ¼

_ net þ Q_ reg;w W n_ f LHV _ net þ E_ out;wp W

E_ in;a þ E_ in;f þ Ein:wp

ð77Þ ð78Þ ð79Þ ð80Þ

In the above equations, the net power output of the system is equal to the sum of the net power outputs of fuel cell and turbine, and also the energy input of the system is equal to the sum of the energies released by the utilization of fuel in the cell and afterburner chamber.

_ net ¼ ðW _ ACtot Þ þ ðW _ ACnet Þ W sofc gt _ _ _ wp  W _ ca  W _ cf ðW ACnet Þgt ¼ ðW DCnet Þgt  ginv ;gen  W _ gt _ DCnet Þ ¼ W ðW gt

Eqs. (68) and (69) have been used to compute the useful heating load in the last recuperator, by considering the efficiency of this recuperator.

ð70Þ

4.2.7. Pump The required work of the pump will be obtained through Eq. (73).

ð66Þ

4.2.6. Recuperator The temperatures of the gasses exiting from the first three recuperators are calculated based on their coefficient of performance (ereg ), and according to Eq. (67) [19].

255

ð81Þ ð82Þ ð83Þ

In Eq. (82), ginv ;gen is the direct-to-alternating current conversion factor in the micro turbine generator. Also, the rate of entropy generation in the whole system is obtained from Eq. (84).

S_ sys gen ¼

X S_ gen;i i

ð84Þ

256

J. Pirkandi et al. / Energy Conversion and Management 136 (2017) 249–261

Considering the mentioned equations, the rate of exergy destruction, rate of exergy loss, and the rate of irreversibility in the whole proposed system are obtained from Eqs. (85)–(87), respectively.

_ net  E_ out;wp  E_ out;g E_ D;sys ¼ E_ in;a þ E_ in;f þ Ein:wp  W E_ L;sys ¼ E_ out;g

ð85Þ

I_tot ¼ E_ D;sys þ E_ L;sys

ð87Þ

ð86Þ

5. The solution method In view of the equations mentioned in the previous sections, a computer program has been written for analyzing the problem. The first part of this computer code contains the hybrid system’s input information including its working pressure and the flow rates of air and fuel entering the system (or the temperature of the turbine’s inflowing gasses). At this point, because of the cell’s working temperature not being constant, an arbitrary cell temperature is initially guessed. Using this guesstimated cell temperature, in the next step, the nonlinear reforming and electrochemical equations as well as the cell’s thermal equations are solved simultaneously, and the desired outcomes including the composition of produced chemical components and the values of temperature, voltage loss, real voltage, electrical current, power, efficiency, and other considered parameters in the fuel cell are obtained. The equations of the other system components are also analyzed along with the solutions of fuel cell equations. After analyzing the whole system, the new cell temperature is determined by considering the given conditions. In case the convergence condition of the cycle is not fulfilled, the analysis will be repeated with a new temperature. Following the thermodynamic analyses, economic analyses are also carried out for the system in the final section. 6. Validation In order to validate the prepared computer code, it is necessary to compare the results obtained from this code for a specific sample with the existing empirical and numerical results. Considering the shortage of empirical results regarding hybrid systems, in this research, the system introduced by Chan et al. [23] has been modeled, and the results obtained from the present computer program have been compared with their findings. The close agreement between these results in Table 1 validates the present method and the developed code. The reason for the slight difference between the results of the written code and the results of Chan is the way the concentration voltage loss of the fuel cell has been computed. In calculating this voltage loss, Chan et al. had assumed a constant limit current density; while in the present research, the limit current density value was calculated. 7. Results In this section, the results related to the thermo-economic performance analysis of two gas turbine generators equipped with two solid oxide fuel cells have been presented. In the performed analyses, the effects of the number of cells in each fuel cell and the manner of fuel injection into the system, as two effective parameters, on the efficiency of the two introduced cycles have been investigated and the relevant results have been presented. The price of generated electricity and the expenses associated with the purchase and installation of system-related equipment are two important parameters which have been examined in these analyses. The fuel cells used in this research are of the tubular solid oxide type, and they are similar to the model manufactured by the Siemens-Westinghouse Company [24]. Also, the constant

Table 1 Comparing the results of the present computer code with the numerical results of Chan. Investigated parameters

Results obtained by Chan et al. [23]

Results obtained by the written computer code

System’s electrical efficiency Total efficiency of the system Recovered heat (kW) Power output of the system (kW) Cell voltage (v)

62.2 83.8 731 381

60.52 80.62 722.3 374.45

0.738

0.71

Table 2 Assumed parameter values of the hybrid system [23,24]. Parameter

Assumed value

Length of each cell Diameter of each cell Fuel utilization factor Pressure loss of fuel cell Inverter’s efficiency Pressure loss of recuperators Pressure loss of afterburner Compressors’ isentropic efficiency Efficiency of the air-gas recuperators Efficiency of the water-gas recuperator Pump’s efficiency Afterburner chamber’s efficiency Microturbine’s isentropic efficiency Generator’s efficiency

150 cm 2.2 cm 0.85 4% 89% 4% 5% 81% 80% 85% 85% 95% 84% 95%

parameters used for the equipment of the hybrid system have been listed in Table 2. In the first proposed design (Fig. 1), two fuel cells under pressure have been used at the upstream of turbine. In this system, due to the utilization of a large portion of inlet fuel in the first fuel cell, some additional fuel must be injected into the system for the second cell. Another issue is the utilization of a portion of the system’s inlet air. For this reason, the injection of extra fuel into the system should be proportional to the remaining volume of air, so that the temperature of the cell and its exhaust gasses are not raised. The last issue involves the selection of the number of cells for the two fuel cells used in the proposed system. The selected number of cells should be such that the current density of both fuel cells is within the same recommended range. The performances of this hybrid system at different operating conditions have been summarized in Table 3. In this table, the amount of fuel supplied to the system has been investigated in three different cases, and the obtained results have been compared. According to this table, the obtained results are almost similar. Because the amount of injected fuel divides between the two fuel cells, the current density of both cells diminishes. The electrical and the overall efficiency of the system is about 54% and 67%, respectively. Also, the price of generated electricity in this design is estimated at about 23 cents/kW h. In view of the amount of fuel injected into the system, it is recommended to use an inlet air-tofuel ratio of about 15.8 in this type of hybrid system, and also to consider the amount of compensatory fuel to be about 60–90% of the amount of fuel coming into the first fuel cell. The major problem with this design is the high price of generated electricity and the high purchase and installation costs associated with the system. Since the number of cells and their surface areas are effective factors in determining the price of a fuel cell and its supplementary equipment, and since the current density in both fuel cells is low, the abovementioned concerns can be explored by altering the number of cells and their surface areas. In continuation, by changing the number of cells, the impact of this parameter on system performance will be investigated.

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J. Pirkandi et al. / Energy Conversion and Management 136 (2017) 249–261 Table 3 Performance parameters of the first design in three optimal cases with 5133 cells used in the fuel cells.

Table 4 Performance parameters of the first design in three optimal cases with 3850 cells used in the fuel cells.

Parameter

First case

Second case

Third case

Parameter

First case

Second case

Third case

Inlet air flow rate (kmol/h) Inlet fuel flow rate (kmol/h) Flow rate of added fuel (kmol/h) First cell’s temperature (°C) Second cell’s temperature (°C) Temperature inlet turbine (°C) Electrical efficiency (%) Exergy efficiency (%) Total efficiency (%) Net generated power (kW) Power generated by first cell (kW) Power generated by second cell (kW) Power generated by gas turbine Generated entropy (kW/K) Destroyed exergy (kW) Irreversibility (kW) CO2 emission (kmol/h) Equipment purchase cost ($) Price of generated electricity ($/kW h) Electricity price based on the simple model ($/kW h) Price of electricity in the first year ($/kW h) Purchase, installation and startup cost of the system ($/kW)

150 4.97 4.5 838 866 1200 54.41 53.23 67.13 1114 488.5 458.6 398.1 2.311 720.7 1001 9.328 1,949,000 0.2291 0.1228

150 5.48 4.0 844 866 1200 54.4 53.22 67.12 1115 531.9 416.1 398.3 2.312 721.7 1002 9.338 1,959,000 0.2297 0.123

150 5.96 3.5 849 866 1200 54.3 53.13 67.02 1110 571.6 372.1 398 2.312 721.4 1002 9.318 1,967,000 0.231 0.1234

150 4.62 4.5 841 875 1200 52.86 51.78 65.92 1042 435.7 440.3 397.1 2.332 709.1 993.7 8.983 1,537,000 0.2091 0.1202

150 5.13 4.0 848 875 1200 52.9 51.81 65.95 1044 477 400.6 397.3 2.33 710 994.1 8.993 1,546,000 0.2095 0.1202

150 5.63 3.5 855 875 1200 52.85 51.77 65.90 1043 517.4 359.3 397.3 2.331 710.5 995.1 8.993 1,555,000 0.2104 0.1205

0.2416

0.2424

0.244

0.2146

0.2152

0.2162

2555

2566

2586

Inlet air flow rate (kmol/h) Inlet fuel flow rate (kmol/h) Flow rate of added fuel (kmol/h) First cell’s temperature (°C) Second cell’s temperature (°C) Temperature Inlet Turbine (°C) Electrical efficiency (%) Exergy efficiency (%) Total efficiency (%) Net generated power (kW) Power generated by first cell (kW) Power generated by second cell (kW) Power generated by gas turbine Generated entropy (kW/K) Destroyed exergy (kW) Irreversibility (kW) CO2 emission (kmol/h) Equipment purchase cost ($) Price of generated electricity ($/kW h) Electricity price based on the simple model ($/kW h) Price of electricity in the first year ($/kW h) Purchase, installation and startup cost of the system ($/kW)

2153

2163

2176

As was mentioned in the previous section, by using two fuel cells and dividing the inlet fuel into two portions, the price of generated electricity in this system will go up. In this section, the effect of reducing the number of cells in the two fuel cells has been investigated for different cases. In Table 4, the optimal performances of the system with 3850 cells, in three different cases, have been compared. As is observed, the electrical efficiency and the overall efficiency of the system is about 52% and 65%, respectively. Also, as was expected, the price of the generated electricity in this system, with a reduction of 2 cents per kW h, is about 21 cents/ kW h. The results in this table indicate that, with a 25% reduction in the number of cells, the optimal state of the system occurs at the air-to-fuel ratio of 16.5, and the amount of added fuel is about 65–95% of the fuel flowing into the first fuel cell. Subsequently, by further reducing the number of cells in the fuel cells used (25% further reduction relative to the previous case), the performance of the system has been analyzed and the obtained results have been presented in Table 5. As is observed, the further reduction in the number of cells has reduced the price of generated electricity to 19 cents/kW h. With the reduction in the number of cells, the electrical efficiency and the total efficiency of the system has diminished to 50% and 64%, respectively. In this case, it is recommended to keep the inlet air-to-fuel ratio at about 17.3 and the amount of compensatory fuel at about 80–95% of the fuel flowing into the first fuel cell. The results indicate that at a constant air flow rate and at the same temperature of turbine’s inlet gasses, the reduction in the number of cells used in the fuel cells causes the following changes: – Increase in the current density and the working temperature of fuel cells, – Reduction in the power generation capacity and the efficiency of the system, – Reduction in the power generation capacity of the fuel cells, – Reduction in the exergy destruction and the irreversibility of the system, – Reduction of system pollution, – Reduction in the price of generated electricity and the purchase, installation and startup costs of the system.

Table 5 Performance parameters of the first design in three optimal cases with 2567 cells used in the fuel cells. Parameter

First case

Second case

Third case

Inlet air flow rate (kmol/h) Inlet fuel flow rate (kmol/h) Flow rate of added fuel (kmol/h) First cell’s temperature (°C) Second cell’s temperature (°C) Temperature inlet turbine (°C) Electrical efficiency (%) Exergy efficiency (%) Total efficiency (%) Net generated power (kW) Power generated by first cell (kW) Power generated by second cell (kW) Power generated by gas turbine Generated entropy (kW/K) Destroyed exergy (kW) Irreversibility (kW) CO2 emission (kmol/h) Equipment purchase cost ($) Price of generated electricity ($/kW h) Electricity price based on the simple model ($/kW h) Price of electricity in the first year ($/kW h) Purchase, installation and startup cost of the system ($/kW)

150 4.5 4.15 851 888 1200 50.51 49.57 64.07 944.5 392 386.7 396 2.363 694.1 985.8 8.52 1,120,000 0.1895 0.1189

150 5.0 3.64 859 888 1200 50.54 49.6 64.11 944 428.8 349.5 395.9 2.356 693.9 984.1 8.51 1,126,000 0.19 0.119

150 4.64 4.0 853 888 1200 50.53 49.59 64.1 943.8 402.1 375.9 395.9 2.358 693.6 984.3 8.51 1,121,000 0.1896 0.119

0.1871

0.1879

0.1874

1731

1742

1735

The summary of results related to the reduction of the number of cells in the fuel cells used in this hybrid system has been presented in Table 6. As is observed, the reduction of the number of cells severely affects the price of the generated electricity and the purchase and installation expenses of the hybrid system. These results indicate that by reducing the number and area of cells by 50%, savings of almost 32% and 17% can be achieved in the system’s purchase and installations costs and in the generated electricity price, respectively. In spite of these cost reductions, the point to emphasize is the 15% reduction in the power generation capacity and 7% reduction in the efficiency of the system.

J. Pirkandi et al. / Energy Conversion and Management 136 (2017) 249–261 0.24

Table 6 Comparing the effects of changing the number of cells in the two fuel cells on the performance of the hybrid system in the first design.

25 2.75 1.74 6.36 1.62 0.78 3.69 8.79 15.70

50 7.11 4.49 15.35 3.89 1.76 8.86 17.45 32.38

Electricity Cost [$/kWh]

the number of cells (%) electrical efficiency (%) overall efficiency (%) total net power output (%) exergy destruction (%) irreversibility (%) pollution (%) the generated electricity price (%) the purchase, installation and startup

Third case

0.24

0.22 1050 0.21 1000 0.2 950

0.19

2900

3400

3900

4400

4900

900 5400

0.22

53

0.21

52

0.2

51

0.19

50

2900

3400

3900

4400

4900

Electrical efficiency (%)

54

0.24

1010

cp

1005

Electricity Cost [$/kWh]

0.23

1000 0.22

995

0.21

990 985

0.2

980 0.19 0.18 2400

Irreversibility [kW]

Irr

975 2900

3400

3900

4400

4900

970 5400

ncell Fig. 5. Effect of the number of cells used in the hybrid system on its irreversibility and the price of generated electricity (first design).

0.24

10

co2 emission

9.75

0.23

9.5 0.22

9.25

0.21

9 8.75

0.2

8.5 0.19

co2 emission [kmol/h]

cp

8.25 2900

3400

3900

4400

4900

8 5400

ncell

cp

0.23

Fig. 4. Effect of the number of cells used in the hybrid system on its power output and the price of generated electricity (first design).

0.18 2400

55

ηele

Electricity Cost [$/kWh]

1100

ncell

In order to select the proper number of cells used in this hybrid system, the values of different parameters can be extracted based on the curves presented in Figs. 3–6. In the second design, as was previously pointed out, one pressurized fuel cell and one atmospheric fuel cell have been used. Similar to the first case, in this design also, because of the utilization of a major portion of inlet fuel in the first fuel cell, some additional fuel must be injected into the system for the second fuel cell. Another issue is the utilization of a portion of air that comes into the system and also the entering of the combustion products to the cathode section of the atmospheric fuel cell. With the combustion produced gasses entering the cathode of the second fuel cell, the efficiency of this type of hybrid system is expected to diminish. Similar to the previous designs, in this hybrid system also, it is recommended to use a lower working pressure and an air-to-fuel ratio which is proportionate to this lower pressure. In this design also, the compensatory fuel should be injected in proportion to the remaining air so that the temperatures of the fuel cell and its exhaust gasses are not raised. Selecting the right number of cells in the fuel cells used is also an important issue; which has been addressed in the following sections. The performances of this hybrid system at different working conditions have been summarized in Table 7. In this table, the amount of fuel supplied to the system has been investigated for three different cases, and the results have been compared with each other. According to this table, the obtained results are almost similar. The electrical efficiency and the overall efficiency of the system is about 55% and 69%, respectively. The price of the generated electricity in this design is also estimated at about 23 cents/ kW h. With regards to the amount of fuel injected into the system, it is recommended to use an inlet air-to-fuel ratio of about 13.7 in this type of hybrid system, and to consider the amount of added

0.18 2400

cp

0.23

0.18 2400

Electricity Cost [$/kWh]

Reduction of Reduction of Reduction of Reduction of Reduction of Reduction of Reduction of Reduction of Reduction of cost (%)

Second case

1150

Power

SOFC-GT Power output [kW]

258

49 5400

ncell Fig. 3. Effect of the number of cells used in the hybrid system on its efficiency and the price of generated electricity (first design).

Fig. 6. Effect of the number of cells used in the hybrid system on its pollution level and the price of generated electricity (first design).

fuel to be about 60–80% of the amount of fuel that enters the first fuel cell. Similar to the first design, the main problem of this system is also the high price of generated electricity and the high purchase and installation costs of the system. In the following, by changing the number of cells, the effect of this parameter on system performance is investigated. The system performances obtained by changing the number of cells have been shown in Tables 8 and 9. In Table 8, the optimal performances of the system with 3850 cells, in three different cases, have been compared. As is observed, the electrical efficiency of the system is about 53% and its total

259

J. Pirkandi et al. / Energy Conversion and Management 136 (2017) 249–261 Table 7 Performance parameters of the second design in three optimal cases with 5133 cells used in the fuel cells.

Table 9 Performance parameters of the second design in three optimal cases with 2567 cells used in the fuel cells.

Parameter

First case

Second case

Third case

Parameter

First case

Second case

Third case

Inlet air flow rate (kmol/h) Inlet fuel flow rate (kmol/h) Flow rate of added fuel (kmol/h) First cell’s temperature (°C) Second cell’s temperature (°C) Temperature inlet turbine (°C) Electrical efficiency (%) Exergy efficiency (%) Total efficiency (%) Net generated power (kW) Power generated by first cell (kW) Power generated by second cell (kW) Power generated by gas turbine (kW) Generated entropy (kW/K) Destroyed exergy (kW) Irreversibility (kW) CO2 emission (kmol/h) Equipment purchase cost ($) Price of generated electricity ($/kW h) Electricity price based on the simple model ($/kW h) Price of electricity in the first year ($/kW h) Purchase, installation and startup cost of the system ($/kW)

150 6.77 4 942 957 1200 55.05 54.01 69.36 1282 714.8 421.4 374.2 2.56 818.4 1119 10.61 2,317,000 0.2328 0.1229

150 6.44 4.5 952 960 1200 55.16 54.14 69.68 1305 691.2 468.5 373.3 2.586 832.3 1133 10.78 2,344,000 0.2317 0.1225

150 6.1 5 962 962 1200 55.13 54.13 69.85 1323 664.3 514.5 372.2 2.622 845.9 1150 10.93 2,368,000 0.2312 0.1224

150 6.04 4 964 966 1200 51.72 50.89 66.95 1122 589.7 388.3 372.1 2.635 799.1 1114 9.889 1,319,000 0.1864 0.1165

150 5.73 4.5 974 971 1200 51.82 51.01 67.27 1146 572.5 429.4 371.3 2.673 814.8 1132 10.08 1,337,000 0.1855 0.1162

150 5.4 5 985 976 1200 51.82 51.04 67.51 1165 551.7 469.8 370.4 2.713 829.9 1150 10.24 1,355,000 0.1852 0.1161

0.2469

0.2456

0.245

0.1844

0.1834

0.183

2639

2623

2614

Inlet air flow rate (kmol/h) Inlet fuel flow rate (kmol/h) Flow rate of added fuel (kmol/h) First cell’s temperature (°C) Second cell’s temperature (°C) Temperature inlet turbine (°C) Electrical efficiency (%) Exergy efficiency (%) Total efficiency (%) Net generated power (kW) Power generated by first cell (kW) Power generated by second cell (kW) Power generated by gas turbine (kW) Generated entropy (kW/K) Destroyed exergy (kW) Irreversibility (kW) CO2 emission (kmol/h) Equipment purchase cost ($) Price of generated electricity ($/kW h) Electricity price based on the simple model ($/kW h) Price of electricity in the first year ($/kW h) Purchase, installation and startup cost of the system ($/kW)

1716

1703

1698

Table 8 Performance parameters of the second design in three optimal cases with 3850 cells used in the fuel cells. Parameter

First case

Second case

Third case

Inlet air flow rate (kmol/h) Inlet fuel flow rate (kmol/h) Flow rate of added fuel (kmol/h) First cell’s temperature (°C) Second cell’s temperature (°C) Temperature inlet turbine (°C) Electrical efficiency (%) Exergy efficiency (%) Total efficiency (%) Net generated power (kW) Power generated by first cell (kW) Power generated by second cell (kW) Power generated by gas turbine (kW) Generated entropy (kW/K) Destroyed exergy (kW) Irreversibility (kW) CO2 emission (kmol/h) Equipment purchase cost ($) Price of generated electricity ($/kW h) Electricity price based on the simple model ($/kW h) Price of electricity in the first year ($/kW h) Purchase, installation and startup cost of the system ($/kW)

150 6.47 4 951 961 1200 53.79 52.84 68.47 1217 663 409.4 373.3 2.586 810.5 1115 10.31 1,824,000 0.2094 0.119

150 6.15 4.5 961 964 1200 53.89 52.95 68.77 1241 642.2 454 372.5 2.617 824.9 1132 10.49 1,845,000 0.2083 0.1187

150 5.82 5 971 967 1200 53.86 52.94 68.94 1260 618.2 497.7 371.5 2.659 839.4 1150 10.66 1,866,000 0.2079 0.1186

0.2159

0.2146

0.214

2187

2172

2163

efficiency is 68%. Also, as was expected, the price of the generated electricity in this system is about 20 cents/kW h. The results of this table indicate that, with a 25% reduction in the number of cells, the optimal state of the system occurs at the air-to-fuel ratio of 14, and the amount of added fuel is about 60–90% of the amount of fuel entering the first fuel cell. In the next step, by further reducing the number of cells in the fuel cells used (25% further reduction relative to the previous case), the performance of the system has been evaluated and its results have been presented in Table 9. As is observed, the further reduction in the number of cells reduces the price of generated electric-

ity to 18 cents/kW h. Reducing the number of cells leads to a drop in the price of generated electricity and the purchase and installation costs of the hybrid system. On the other hand, with the reduction in the number of cells, the electrical and the overall efficiency of the hybrid system diminish to 51% and 67%, respectively. In this case, it is recommended to keep the inlet air-to-fuel ratio at about 14.5 and the amount of compensatory fuel at about 65–90% of the fuel flowing into the first fuel cell. The comparison of results indicates that at a constant air flow rate and at the same temperature of turbine’s inlet gasses, the reduction in the number of cells used in the fuel cells causes the following changes: – Increase in the current density and the working temperature of fuel cells, – Reduction in the power generation capacity and the efficiency of the system, – Reduction in the power generation capacity of the fuel cells, – Reduction in the exergy destruction and the irreversibility of the system, – Reduction of system pollution, – Reduction in the price of generated electricity and the purchase, installation and startup costs of the system. The results of reducing the number of cells in this hybrid system have been presented in Table 10. As is observed, similar to the previous case, the reduction of the number of cells severely affects the price of the generated electricity and the purchase and installation expenses of the hybrid system. These results indicate that by reducing the number and surface area of cells by 50%, savings of about 34% and 19% can be achieved in the system’s purchase and installations costs and in the generated electricity price, respectively. Despite these cost reductions, the power generation capacity and the efficiency of the system are reduced by 12% and 6%, respectively. Similar to the previous case, in order to select the right number of cells used in this hybrid system, the values of various parameters can be extracted based on the curves presented in Figs. 7–10.

J. Pirkandi et al. / Energy Conversion and Management 136 (2017) 249–261 0.25

Table 10 Comparing the effects of changing the number of cells in the two fuel cells on the performance of the hybrid system in the second design.

25 2.28 1.28 5.07 0.96 0.35 2.82 10.5 17.12

50 6.04 3.47 12.48 2.35 0.44 6.79 19.93 34.97

Electricity Cost [$/kWh]

co2 emission 10.6

0.23 10.4

0.22 0.21

10.2

0.2

10

0.19 9.8

0.18 0.17 2400

56

2900

3400

3900

4400

4900

9.6 5400

Fig. 10. Effect of the number of cells used in the hybrid system on its pollution level and the price of generated electricity (second design).

cp

ηele

55

0.23 54

0.22 0.21

53

0.2

52

0.19 51

0.18 0.17 2400

10.8

cp

ncell

0.25 0.24

Electricity Cost [$/kWh]

the number of cells (%) electrical efficiency (%) overall efficiency (%) total net power output (%) exergy destruction (%) irreversibility (%) pollution (%) the generated electricity price (%) the purchase, installation and startup

Third case

Electrical efficiency (%)

Reduction of Reduction of Reduction of Reduction of Reduction of Reduction of Reduction of Reduction of Reduction of cost (%)

Second case

0.24

co2 emission [kmol/h]

260

2900

3400

3900

4400

4900

The final analysis of the two proposed hybrid systems indicates that the hybrid system with one pressurized and one atmospheric fuel cells (second design) enjoys a greater efficiency and power generation capacity and, at the same time, a higher rate of exergy destruction and irreversibility. 8. Conclusion With regards to the hybrid systems introduced and discussed in this paper, the following conclusions can be presented:

50 5400

ncell Fig. 7. Effect of the number of cells used in the hybrid system on its efficiency and the price of generated electricity (second design).

Electricity Cost [$/kWh]

0.24

1300

Power

cp

1275

0.23

1250

0.22

1225

0.21

1200

0.2

1175

0.19

1150

0.18

1125

0.17 2400

2900

3400

3900

4400

4900

SOFC-GT Power output [kW]

0.25

1100 5400

ncell Fig. 8. Effect of the number of cells used in the hybrid system on its power output and the price of generated electricity (second design). 0.25

cp 1120

0.23 1118

0.22 0.21

1116

0.2

1114

0.19 1112

0.18 0.17 2400

Irreversibility [kW]

Electricity Cost [$/kWh]

0.24

1122

Irr

2900

3400

3900

4400

4900

1110 5400

ncell Fig. 9. Effect of the number of cells used in the hybrid system on its irreversibility and the price of generated electricity (second design).

 In hybrid systems with two pressurized fuel cells, the electrical, exergy, and total efficiencies of the system are about 54, 53 and 67%, respectively. The economic analyses of this type of hybrid system indicate that the electricity generation price of this design is about 23 cents/kW h and the total purchase, installation and startup cost of this system is about $2500/kW of generated electricity.  In hybrid systems with two pressurized fuel cells, it is recommended to use an inlet air-to-fuel ratio of about 15.8 and to limit the amount of compensatory fuel to 60–90% of the amount of fuel flowing into the first fuel cell.  The investigations indicate that in hybrid systems with two pressurized fuel cells, a reduction in the number cells leads to an increase in the current density and working temperature of fuel cells and a reduction in the power generation capacity and efficiency of the system, reduction in the power generation capacity of fuel cells, reduction in the exergy destruction and irreversibility of the system, reduction in system pollution and a reduction in the electricity generation price and the purchase and installation costs of the system.  In hybrid systems with one pressurized fuel cell and one atmospheric fuel cell, the electrical, exergy, and total efficiencies of the system are estimated at about 55, 54 and 69%, respectively. The economic analyze of this type of hybrid system show that the electricity generation price of this design is about 23 cents/kW h, and the total purchase, installation and startup cost of this system is about $2600/kW of generated electricity.  The final analysis of the two proposed hybrid systems indicates that the hybrid system with one pressurized and one atmospheric fuel cells (second design) has a greater efficiency and power generation capacity and, at the same time, a higher rate of exergy destruction and irreversibility. The findings also indicate that this design has a higher pollution level relative to the first design. From an economic standpoint, the price of generated electricity and the costs associated with equipment purchase, installation and startup are almost the same in both systems, and there is no significant difference between them.

J. Pirkandi et al. / Energy Conversion and Management 136 (2017) 249–261

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