Abstract

In this paper, a Polymer Electrolyte Membrane (PEM) fuel cell power system including burner, steam reformer, heat exchanger, and water heater has been considered. A PEM fuel cell system is designed to meet the electrical, domestic hot water, heating, and cooling loads of a residential building located in Tehran. Operating conditions of the system with consideration of the electricity cost has been studied. The cost includes social cost of the environmental pollutants (e.g. CO2, CO and NO). The results show that the maximum energy needs of the building can be met by 12 fuel cell stacks with nominal capacity of 8.5 kW. Annual average electricity cost of thissystem is equal to 0.39 US$/kWh and entropy generation of this system through a year is equal to 1004.54 GJ/K1. It is also concluded that increase in ambient temperature from 1 °C to 40 °C increases the entropy generation by 5.73%, carbon monoxide by 14.56%, and nitrogen monoxide by 8.9%, but decreases carbon dioxide by 0.47%.

Introduction

In the last decade, worldwide problems related to energy factors (oil crisis), ecological aspects (climatic change), electric demand (significant growth), and financial/regulatory restrictions of wholesale markets have rapidly increased. These difficulties, far from finding effective solutions, are continuously increasing, which suggests the need of technological alternatives to assure their solution. One of these technological alternatives is named distributed generation (DG), and consists of generating electricity as near to the consumption site as possible, similar to the early years of the electric industry, but now incorporating the advantages of the modern technology [1].

In addition to higher overall energy conversion efficiency and lower environmental pollutions, these technologies provide other advantages such as elimination of power distribution lines, lower overall system cost, and higher security. Natural and man-made causes like earthquakes, wars, or acts of terrorism may destroy central power plants and the distribution systems and cause large economic losses and bring discomfort to the people [1].

Distributed generation (DG) technologies are divided into two main objects: (1) renewable, and (2) non-renewable technologies. Among non-renewable technologies, cogeneration systems play an important role. Cogeneration systems are employed where both electricity and heat are required. These systems utilize the waste heat produced during electricity generation and allow more efficient fuel consumption. Thus, a more economical method is obtained compared to the systems where electricity and heat are separately produced [2]. Since combined heat and power (CHP) systems involve the production of both thermal energy, generally in the form of steam or hot water and electricity, the efficiency of energy production can be increased from current levels that vary from 35% to 55% in the conventional power plants to over 90% in the CHP systems [3]. Among cogeneration systems which are used in residential buildings, fuel cell systems play an important role because of their cost effectiveness and high efficiency [4]. The use of fuel cells, micro gas turbines and internal combustion engines for on-site combined heat and power production (OS-CHP) in a residential building, has been studied by several researchers [5–36].

The present research studies the design and operating conditions of a CHP fuel cell system by considering entropy production and energy costs including the social cost of the environmental pollutions of CO2, CO, and NO in order to meet the electrical, heating and cooling loads of residential building.

Social cost of air pollution is the charge based on negative effects of air pollution on the health of society and environment. The economic aspect of these effects is called externalized social cost of air pollution.

The system includes fuel cell stack, burner, steam reformer, heat exchanger, battery, and water heater to meet the electrical power of the building as well as part of the power required by heat pump and mechanical refrigerator needed for heating, cooling, and DHW systems. The remaining part of the power for heat pump and mechanical refrigerator is provided by the exhaust gases. The burner and reformer use natural gas as fuel. The followings points are considered in this work:

  • A new model is proposed to CHP fuel cell.

  • Thermodynamic modeling of fuel cell system for CHP application is employed.

  • Number of CHP fuel cell stacks is estimated due to electrical, heating, cooling, and domestic hot water needs of the building.

  • Social cost of air pollution is considered.

  • Exergy analysis of the system has been carried out.

Estimation of the Electrical, Heating, and Cooling Energy Needs of a Residential Building

The residential building considered in this study is located in Tehran and is a 10-story building containing 40 units, each with a floor area of 200 m2. The building has a height of 30 m, a length of 40 m (in the east and west directions), and a width of 20 m (in the north and south directions). The window areas are 30% of the areas of south and north walls and 20% of the areas of east and west walls of the building. The external and internal walls are 22 and 12 cm thick, respectively, all made of brick with gypsum plaster on the interior walls. The roof is also 22 cm thick, made of brick and roofing materials. No thermal insulation is employed in the walls or the roof of the building. To calculate the electrical, heating and cooling loads of this building, it was assumed that the 15th day of each month represents the whole days of that month. Figure 1 shows the ambient air temperatures for Tehran, during the months of January, April, and July [5]. Figures 2 and 3 show the total electrical power requirement of the building in a 24 h period on January 15, and July 15, respectively. It should be mentioned that these figures do not include the electrical power and energy needed to operate the electrical motors used for the central heating and cooling systems of the building [5]. Figure 4 shows the heating and cooling loads of the building on January 15, April 15, and July 15, respectively.

Fig. 1
Ambient air dry-bulb and wet-bulb temperatures for Tehran, during the months of January, April, and July
Fig. 1
Ambient air dry-bulb and wet-bulb temperatures for Tehran, during the months of January, April, and July
Close modal
Fig. 2
Total electrical power requirement of the residential building in a 24-h period, estimated for 15 January
Fig. 2
Total electrical power requirement of the residential building in a 24-h period, estimated for 15 January
Close modal
Fig. 3
Total electrical power requirement of the residential building in a 24-h period, estimated for 15 July
Fig. 3
Total electrical power requirement of the residential building in a 24-h period, estimated for 15 July
Close modal
Fig. 4
The heating and cooling loads of the building, estimated on January 15, April 15, and July 15
Fig. 4
The heating and cooling loads of the building, estimated on January 15, April 15, and July 15
Close modal

To determine the hourly energy needs for the domestic hot water, it is assumed that all units have the same hot water consumption rate, uniformly distributed between 5 a.m. to 11 p.m. Figure 5 shows the daily energy needs of the building for domestic hot water.

Fig. 5
Domestic hot water energy needs of the residential building
Fig. 5
Domestic hot water energy needs of the residential building
Close modal

Description of the System

The fuel cell stack has a nominal power of 8.4 kW and uses natural gas as fuel [37]. PEM is connected to a battery to produce electrical power. The configuration of this system is shown in Fig. 6. Natural gas is fed through line (1) to burner and reformer. In the burner, natural gas reacts with air (line 5), and generated heat is used to meet the energy needs of the reformer. In the reformer, natural gas (line 3) reacts with steam produced in the heater (line 10) and produces carbon dioxide (CO2) and hydrogen (H2). Carbon dioxide (CO2) is released to atmosphere through line (9) and hydrogen (H2) is fed to PEM fuel cell (line 11). This hydrogen reacts with air (line 7), to produce electrical power (line 13) and hot water (line 12). The excess air discharges to the atmosphere through line (14).

Fig. 6
Configuration of CHP fuel cell system
Fig. 6
Configuration of CHP fuel cell system
Close modal

Cooling water pumped to the fuel cell (line 16) is directed to the heat exchanger (line 17) and then is mixed with part of the hot water produced in PEM (line 19) and fed to storage tank through line (20). The remaining part of produced water by PEM fuel cell evaporates in the heater (line 18) and is used in the reformer (line 10).

Theoretical Calculations

Equations of mass flow rates of the reformer can be evaluated as follow:
m·fuelin,r=W·net9.648FvufMfuel
(1)
m·streamin,r=m·H2Oout;he=W·net3.764FVMH2O
(2)
m·H2out,r=W·net2FvufMH2
(3)
m·co2out,r=W·net7.456FVMco2
(4)
where m·fuelin,r,m·streamin,r,m·H2out,r and m·CO2outr are mass flow rates of inlet fuel, steam to the reformer, outlet hydrogen and carbon dioxide respectively. In addition, F is the Farad number which is equal to 96.685. W·net, Uf and V are the net power of the system, percentage of the fuel consumption, and the voltage of fuel cell, respectively. In these Equations, Mfuel, MH2O, MH2 and Mco2 are molecular masses of fuel, water, hydrogen and carbon dioxide, respectively. Mass flow rates of inlet reactants and outlet products of fuel cell are determined from:
m·H2inf=W·net2FVUfMH2
(5)
m·airin,f=W·net4FVUaxo21xo2raMair
(6)
m·airout,f=W·net4FV1xo2(r2-1)Mair
(7)
m·n2oout,f=W·net2FVMH2O
(8)
m·N2in,f=W·net4FVUaxN2xo2r2MN2
(9)
m·N2out,f=W·net4FVUxN2xO2(r2-1)MN2
(10)
m·O2in,f=W·net4FVUar2Mo2
(11)
m·O2out,f=W·net4FVUa(ra-1)MO2
(12)

where m·H2in,f,m·airin,f,m·airout,f, m·H2Oout,f, m·N2in,f, m·N2out,f, m·O2in,f and m·O2out,f are mass flow rates of inlet hydrogen, inlet and outlet air, outlet water, inlet and outlet nitrogen, and inlet and outlet oxygen, respectively. In addition, xO2, xN2 and ra are mole fractions of oxygen and nitrogen in the air and stoichiometric air fuel ratio, respectively. Ua is the fraction of air which is reacted with fuel in the fuel cell.

Equation of burning process in burner is:
(0.81CH4+0.079C2H6+0.042C3H8+0.047C4H10+0.01N2+0.012CO2)+2.412ra(O2+3.76N2)a'CO2+b'H2O+c'O2+g'cO+d'N2+f'NO
(13)
With regard to the following equations:
2CO22CO+O2
(14)
N2+O22NO
(15)
Equilibrium coefficients are:
KCO=g2ea2(Pair,out,cPb)2+1-2
(16)
KNO=f2de(Pair,out,cPb)2-1-1
(17)
a=a'/r',b=b'/r',d=d'/r',e=e'/r',f=f/r',g=g'/r'
(18)
r'=a'+b'+d'+e'+f'+g'
(19)

where a, b, d, e, f, g, r, a′, b′, d′, e′, f′, g′ and r′ are equilibrium coefficients and KCO and KNO are the equilibrium coefficients of the carbon monoxide and nitrogen monoxide, respectively. Moreover, Pb is the pressure of the burner, nb and nair,out,c are the equilibrium coefficients of the burner and outlet air compressor, respectively.

The mass flow rate of inlet fuel into burner can be calculated by the following equation:
m·fuelin,b=Q·rqb
(20)
Also, Q·r,qb and Q·f can be calculated by the following equations:
Q·r=1.294m·co2out,r[h0fco2+Cpco2(Tr-To)]+4.824m·H2out,r×[CPH2(Tb-T0)]-2.564m·H2oin,r[h0fh2o+CPH2O(Tf-To)]-m·fuelin,r[h0ffuel]
(21)
qb=[h0ffuel+2h0fO2+7.52hfN2]-2[h0fhZo+CPH2O(Tb-T0)]-[h0fco2+Cpco2(Tb-T0)]-7.52[h0fN2(Tb-To)]
(22)
Q·f=m·H2in,f[CpH2(Tr-To)]+m·airin,f[Cpair(Tr-T0)]-m·airout,f[Cpair(Tf-T0)]-m·H2Oout,f[h0fh2O+CpH2O(Tf-To)]
(23)

where Q·r and Q·f are the heat rate of the reformer and heat generation in the fuel cell, respectively. qb is the heat rate of the burner and Tsat is equal to 373 K. Tr, T0, Tb, and Tf are the temperature of the reformer, standard temperature, temperature of the burner, and temperature of the fuel cell. hofH2O, hofo2, hofCO2, hofuel, and h0N2 are enthalpies of formation of water, oxygen, carbon dioxide, fuel, and nitrogen, respectively. In addition, CPH2O, CPair, CPH2, and CPCO2 are specific heat coefficient of water, air, hydrogen, and carbon dioxide, respectively.

Equations of mass flow rates of burner can be evaluated as follow:
m·airin,b=9.52MairMfuelm·fuelin.b
(24)
m·CO2out,b=MCO2Mfuelm·fuelin,b
(25)
I=112i(1+i)L(1+i)L-1
(26)
m·NOout,b=MNOMfuelm·fuelin,b
(27)
m·H2Ocot,b=2MH2OMfuel=m·fuelin,b
(28)
m·N2out,b=7.52MN2Mfuelm·fuelin,b
(29)

where m·airm,b, m·fuelm,b, m·CO2out,b, m·COout,b, m·NOoot,b, m·H2Oout,b and m·N2out,b are mass flow rates of inlet air, fuel, outlet carbon dioxide, carbon monoxide, water, and nitrogen to the burner, respectively. Also Mfuel, Mair, and MN2 are molecular masses of methane as fuel, air, and nitrogen, respectively.

Pressure of the burner can be calculated as follows:
Pb=Pair,out,crbrair,out,cTbTair,out,c
(30)
where Tair,out,c is the compressor outlet air temperature. Compressor input power and net power of system can be evaluated as follows:
W·c=mRTln(Pair,out,c101.3)
(31)
W·net=n.W·f-W·c-W·p
(32)

where W·f and W·c are the electrical power produced by each fuel cell stack and the power used by compressor in kW, respectively. W·p is power consumed by cooling pump and n is the number of identical fuel cell stacks employed.

For heat transfer in the cooling channels of the fuel cell and mass flow rate of cooling water we have:
Nuave=7.56have=Nuavekdh
(33)
TC,Wout=Tf-(Tf-TCWin)exp(-PcLhavem·C.WcPc.w)
(34)
m·c,w=Q·fCpc,w(Tc,wout-Tc.win)
(35)

where Nuave is the average Nusselt number in cooling channel, have is the average convection heat transfer coefficient, k is heat conduction coefficient, dh is hydraulic diameter of channel, m·c.w is mass flow rate of cooling water, Tc.win and Tc.wout are the temperatures of inlet and outlet cooling water of the fuel cell, L and pc are the length and perimeter around thecooling channel, and CPc.w is specific heat coefficient of the cooling water.

Pressure losses in cooling channel are then determined from:
ΔPl=f1dhρ2v2
(36)
ΔPk=ξρ2v2
(37)
ΔPs=0.106m·
(38)

In these equations, ΔPl,ΔPk and ΔPs are frictional pressure loss of direct part of channel, local pressure loss, and pressure loss in diffusion layer, ρ is the density of fluid and v is the velocity of fluid in the channel; ξ is the correctional coefficient which can be considered between 1 and 2 and depends on the shape of corners, f is the frictional coefficient, and m· is mass flow rate.

Conservation of energy in a heater can be considered in the form of:
m·out,bCpout,b(Tb-Tha)=m·out,beCPstream(Tr-Tsat)+hfgCPc.wout.f(Tsat-Tf)
(39)

where m·out,b and m·out.he are mass flow rates of the outlet exhaust gas of the burner and outlet steam of the heater, respectively; CPout,b, CPstream, and CPC.Wout,f are specific heat coefficients of the outlet exhaust gas of the burner, outlet steam of the heater, and outlet cooling water of the fuel cell respectively. The is heater outlet steam temperature.

Estimation of the Number of Fuel Cell Stacks

The theoretical model developed in fortran considers the fuel cell stack, burner, steam reformer, water heater, and heat exchangers. The fuel cell stack with a nominal power of 8.4 kW is employed by considering natural gas as fuel.

It can be seen from Figures 2–5 that the maximum electrical power requirement is 32.96 kW around 7 p.m. in July, where the maximum heating load is 1590 kW at 5 a.m. in January; the maximum cooling load is 2028 kW at 3 p.m. in July, and the maximum domestic hot water energy requirement is 0.926 kW in January. A method to meet the energy needs of the residential building under consideration is to employ a number of fuel cell stacks to produce electricity to meet the electrical energy needs of the building, and to meet part of the heating and cooling energy needs through a heat pump. The energy in the exhaust gases is to meet the rest of the heating and cooling energy needs. We can use the following equation to determine the number of fuel cell stacks needed during the heating season [5]:
(nW·f-W·n)βhp+nQ·ex.gα-Q·DHW=Qheattag
(40)
where n is the number of identical fuel cell stacks employed, W·f is the electrical power produced by each fuel cell stack, W·n is the electrical power need, βhp is the coefficient of performance (COP) of the heat pump employed. Q·ex.g is the energy in the exhaust gases, α is the effectiveness of the heat exchanger to utilize the energy to produce hot water or steam for heating, Q·DHW is the DHW energy needs, and Q·heatng is the heating energy needs of the building. For summer operation, or when cooling is needed the following equation can be used [5]:
(nW·p-W·n)βref+(nQ·ex.gα-Q·DHW)βabc=Q·cooling
(41)
where βref is the COP of the refrigerator, operating in the refrigeration mode, βabs is the COP of the employed absorption refrigerator to produce chilled water for cooling, and Q·cooling is the cooling load of the building in kW. To use Eqs. (39) and (40), we assume the following properties for the employed system:
βhp=3,βref=2.5,βabc=0.7,α=0.8
Equation (40) is used in order to find n for 15 January at 5 a.m. Referring to Figs. 1–5, the following values are obtained:
Ta=2.8°C,e'=2.05kW,Qh=1590kW,q'=0.926kW,e=8.5kW

thus, Eq. (40) provides n = 6.63 or n = 7 stacks.

For 15 July at hour 3 p.m. we have:
Ta=39°C,e'=2.83kW,Qc=2028kW,q'=0.285kW,e=8.5kW

From Eq. (41), the number of stacks n = 11.76 or n = 12 will be concluded. With a total of 12 fuel cell stacks selected, all the energy needs of the building can be met at different seasons of the year.

Depending on the energy needs throughout the year, the number of fuel cell stacks needed to meet both the electrical and thermal energy needs of the building is presented in Table 1.

Table 1

Number of fuel cell stacks which should be operated at different hours of the 15th each month

HourJanFebMarAprMayJunJulyAugSepOctNovDec
1663112222135
2764212222136
3774212221136
4774212221146
5774211221246
6774212221146
7774212221136
8663112332135
9652123443125
10441134553214
11331245775212
12321256996311
1321236810107421
1411237911118421
15112471012128321
1611236911118421
1721236810107421
18321356996322
19431246775313
20441235664213
21542134553214
22652123443224
23652123332125
24663112322125
HourJanFebMarAprMayJunJulyAugSepOctNovDec
1663112222135
2764212222136
3774212221136
4774212221146
5774211221246
6774212221146
7774212221136
8663112332135
9652123443125
10441134553214
11331245775212
12321256996311
1321236810107421
1411237911118421
15112471012128321
1611236911118421
1721236810107421
18321356996322
19431246775313
20441235664213
21542134553214
22652123443224
23652123332125
24663112322125

Exergy Analysis of Fuel Cell System

Exergy analysis is a method that uses the conservation of mass and energy as well as the second law of thermodynamics for the analysis, design, and improvement of the systems [38]. The exergy method is a useful tool for more efficient energy-resource use, by identifying the locations, types, and magnitudes of wastes and losses [39]. There has recently been a much stronger emphasis on exergy aspects of systems and processes, system analysis and thermodynamic optimization as well as emphasis on the mainstream of engineering, physics, biology, economics, and management. As a result of recent advances, exergy has gone beyond thermodynamics and has become a new distinct discipline mainly because of its interdisciplinary character as the confluence of energy, environment and sustainable development.

According to the literature, exergy can be divided into four distinct components. The two important ones are the physical exergy and chemical exergy. In this study, the two other components which are kinetic exergy and potential exergy are assumed to be negligible as the elevation and speed have negligible changes [38,39]. The physical exergy is defined as the maximum theoretical useful work obtained as a system interacts with an equilibrium state. The chemical exergy is associated with the departure of the chemical composition of a system from its chemical equilibrium. The chemical exergy is an important part of exergy in a combustion process.

Chemical and physical exergy relations are shown as follows [38]:
eph=cpT0[TT0-1-ln(TT0)]+RT0ln(PP0)
(42)
eoh=i-1Rxiech.i+RT0i-1nx1ln(x1)
(43)
And the total exergy will be [37]:
et=eph+ech
(44)

In these equations eph, ech, and et, are physical exergy, chemical exergy and total exergy, respectively. Furthermore, T is temperature, P is pressure, R is the gas constant, and xi is mole fraction of the mixture.

The total entropy generation rate of the whole system is [37]:
S·gen-1T0[inm·er-outm·er-w·ner]
(45)

Estimation of Electricity Cost Produced by the Fuel Cell Stack

The cost of electricity produced by power generation system is obtained by the following equation [40]:
CE=CI+CO+CS+CA
(46)

in which CE, CI, CO, CF, and CA are the cost of electricity, the cost associated with the initial investment (including the installation cost), the cost associated with the operation and maintenance, the cost associated with the fuel consumption and the externalized social cost of air pollution respectively.

For CI:
CI=CI8760Cf
(47)

where C is the total capital cost of the installed power generation system (US$/kW), I is the capital salvage factor to be paid on the unit of borrowed capital, and Cf is the capacity factor.

The capital salvage factor (I) can be calculated form the following relation [6]:
I=112I(1+I)LT(1|I)LT1
(48)

where L.T is the life time of the power generation system (in years), or the period at which the borrowed capital C has to be paid back which is assumed to be 20 years and i is the annual interest rate assumed to be constant during the lifetime of the system, or the period of the loan repayment.

Cf is calculated by the following equation:
Cf=W·n,anW·f
(49)

where W·n,a is an annual and average consumption of electrical power by the building and W·f is the fuel cell stack nominal power.

For fuel consumption cost (CF), the following equation can be applied [6]:
Cf=Fuelcost(SkWh)η1
(50)
where η1 is efficiency of the first law. The social cost of air pollution CA can be obtained as the following equation:
CA=[m·NO(CA,NO)+m·CO(CA,CO)+m·CO2(CA,CO2)]13600W·f
(51)

where m·NO,m·CO,andm·CO2 are the exhaust mass flow rates of nitrogen monoxide, carbon monoxide, and carbon dioxide in kg/s and CA,NO,CA,CO,andCA,CO2 are the externalized social cost of air pollution for nitrogen monoxide, carbon monoxide, and carbon dioxide, respectively, in US$/kW. For a simple fuel cell, the cost of installation is estimated to be about 6000 US$/kW, and the cost of operation and maintenance about 0.03 US$/kW [41]. For a CHP fuel cell, the cost of installation is estimated about 8400 US$/kW, and the cost of operation and maintenance about 0.05 US$/kW [41].

External social costs of nitrogen monoxide, carbon monoxide and carbon dioxide are considered to be 8.175, 6.424 and 0.024 US$/kg, respectively [37]. In this analysis, other pollution sources such as water, soil, etc., are produced by an operational power generating system are ignored.

Results and Discussions

With increasing of ambient air temperature, the temperature of burner increases and thus leads to reduction of heat rate of burner (Eq. (22)). According to Eq. (21), this reduction causes an increase in mass flow rate of fuel and it can be concluded from Eq. (45) that with an increase in inlet mass to the system, entropy generation increases. Figure 7 shows the variation of entropy generation with ambient air temperature for one unit of CHP fuel cell stack. It can be observed that when the ambient air temperature increases from 1 °C to 40 °C, the system entropy generation increases from 1.36 (kW/K) to 1.438 (kW/K).

Fig. 7
Variation of total entropy generation in one fuel cell stack with ambient air temperature
Fig. 7
Variation of total entropy generation in one fuel cell stack with ambient air temperature
Close modal

Entropy generation for fuel cell stacks operating in the residential building to meet the electrical, heating, and cooling loads during the hours of each month is shown in Table 2. It can be seen from this table that when the maximum number of fuel stacks (12) operate, the maximum entropy is generated at 3 p.m. on 15 June and 15 July and it is equal to 12,624 (kW/K). At this point, the air temperature is equal to 39 °C. Furthermore, the minimum entropy generation is at 12 h on 15 December, when one fuel cell stack operates, and it is equal to 1.001 (kW/K).

Table 2

Entropy generation from fuel cell stacks which operate in the residential building in kW/K

HourJanFebMarAprMayJunJulyAugSepOctNovDec
15.9885.9883.0061.0151.0192.0612.0612.0532.0441.0083.0074.993
26.9795.9874.0072.031.0182.0592.0592.0512.0451.0073.0075.984
36.9796.9834.0062.0271.0172.0572.0572.051.0091.0073.0095.989
46.9836.9834.0052.0271.0162.0552.0552.0481.0071.0074.0085.984
56.9796.9834.0032.0271.0162.0532.0532.0461.0062.0144.0065.983
66.9836.9834.0032.0261.0162.0542.0542.0451.0051.0074.0095.981
76.9836.9844.0032.0281.0172.0582.0582.051.0061.0073.0065.979
85.9885.9883.0031.0161.023.0953.0953.0832.0461.0083.0084.995
95.9884.9912.0031.0192.044.1324.1324.1163.0831.0092.0024.997
104.0014.0011.0031.0233.075.1885.1885.1653.0832.0281.0054.556
113.0063.0061.0032.0554.1087.37.37.2635.1592.0371.0042.003
123.0062.0041.0032.0624.1559.4089.4089.366.2043.0571.0031.001
132.011.0052.0273.16.19810.48710.48710.4217.2564.1072.0291.003
141.0051.0052.0283.1027.23311.56711.56711.5038.3054.112.031.007
151.0051.0052.0284.1447.22912.62412.62412.5528.3133.0832.0311.007
161.0051.0052.0283.1046.17911.5611.5611.4948.2934.112.0311.006
172.0091.0042.0263.1036.18810.49110.49110.4327.2564.1032.0221.003
183.0082.0051.0033.1025.1279.4249.4249.3736.2123.0622.0232.007
194.0093.0071.0032.0564.2237.3097.3097.2725.1513.0581.0073.005
204.0054.0051.0032.053.0716.2446.2446.2144.122.0331.0063.003
215.0014.0012.0031.0243.0685.1865.1865.1633.0822.0261.0053.997
225.994.9922.0031.022.0424.1374.1374.1213.0752.0182.0043.992
235.9894.9912.0031.0182.0233.0993.0993.0852.0481.0082.0034.986
245.9885.9883.0031.01531.0193.0923.0922.0532.0451.00824.984
HourJanFebMarAprMayJunJulyAugSepOctNovDec
15.9885.9883.0061.0151.0192.0612.0612.0532.0441.0083.0074.993
26.9795.9874.0072.031.0182.0592.0592.0512.0451.0073.0075.984
36.9796.9834.0062.0271.0172.0572.0572.051.0091.0073.0095.989
46.9836.9834.0052.0271.0162.0552.0552.0481.0071.0074.0085.984
56.9796.9834.0032.0271.0162.0532.0532.0461.0062.0144.0065.983
66.9836.9834.0032.0261.0162.0542.0542.0451.0051.0074.0095.981
76.9836.9844.0032.0281.0172.0582.0582.051.0061.0073.0065.979
85.9885.9883.0031.0161.023.0953.0953.0832.0461.0083.0084.995
95.9884.9912.0031.0192.044.1324.1324.1163.0831.0092.0024.997
104.0014.0011.0031.0233.075.1885.1885.1653.0832.0281.0054.556
113.0063.0061.0032.0554.1087.37.37.2635.1592.0371.0042.003
123.0062.0041.0032.0624.1559.4089.4089.366.2043.0571.0031.001
132.011.0052.0273.16.19810.48710.48710.4217.2564.1072.0291.003
141.0051.0052.0283.1027.23311.56711.56711.5038.3054.112.031.007
151.0051.0052.0284.1447.22912.62412.62412.5528.3133.0832.0311.007
161.0051.0052.0283.1046.17911.5611.5611.4948.2934.112.0311.006
172.0091.0042.0263.1036.18810.49110.49110.4327.2564.1032.0221.003
183.0082.0051.0033.1025.1279.4249.4249.3736.2123.0622.0232.007
194.0093.0071.0032.0564.2237.3097.3097.2725.1513.0581.0073.005
204.0054.0051.0032.053.0716.2446.2446.2144.122.0331.0063.003
215.0014.0012.0031.0243.0685.1865.1865.1633.0822.0261.0053.997
225.994.9922.0031.022.0424.1374.1374.1213.0752.0182.0043.992
235.9894.9912.0031.0182.0233.0993.0993.0852.0481.0082.0034.986
245.9885.9883.0031.01531.0193.0923.0922.0532.0451.00824.984

As explained, increasing the ambient air temperature leads to reduction in burner heat rate and increase in fuel mass flow rate. It can be seen from Eq. (26) that an increase in mass flow rate of the fuel increases the outlet mass flow rate of carbon monoxide from the burner. Variation of carbon monoxide and nitrogen monoxide production with the ambient air temperature can be seen in Fig. 8. As seen from this figure, when the ambient air temperature increases from 1 °C to 40 °C, carbon monoxide production by each fuel cell stack increases from 0.0277(kg/s) to 0.0316(kg/s). Carbon monoxide production from fuel cell stacks is shown in Table 3. The maximum carbon monoxide production is at 3 p.m. on 15 July and is equal to 0.378 (kg/s).

Fig. 8
Variation of total carbon monoxide production in one fuel cell stack with ambient temperature
Fig. 8
Variation of total carbon monoxide production in one fuel cell stack with ambient temperature
Close modal
Table 3

Monoxide carbon mass production from fuel cell stacks which operate in the residential building in kg/s

HourJanFebMarAprMayJunJulyAugSepOctNovDec
10.16860.16860.08490.02920.02940.05960.06040.05980.05940.02870.08520.1405
20.1960.1680.11320.05840.02940.05960.06020.05980.05940.02870.08490.168
30.1960.1960.11320.05820.02930.05940.06020.05960.02960.02870.08520.168
40.1960.1960.11320.05820.02930.05940.060.05960.02950.02870.11320.168
50.1960.1960.11320.05820.02930.02960.060.05940.02950.05740.11320.168
60.1960.1960.11320.05820.02930.05940.060.05940.02950.02870.11320.1674
70.1960.1960.11320.05820.02940.05960.06020.05960.02960.02870.08490.168
80.16860.1680.08490.02920.02950.05980.09090.090.05940.02870.08520.1405
90.16860.14050.05660.02950.0590.090.12120.12040.08940.02870.0570.1405
100.11280.11280.02860.02970.08910.12080.1530.15150.090.05820.02860.1128
110.08490.08490.02870.060.120.15250.21560.21420.15150.05880.02870.0566
120.08520.05660.02870.06040.1510.18360.27990.27630.18240.08850.02870.0283
130.0570.02850.05820.09090.18180.24560.3130.3080.21350.11960.05840.0284
140.02860.02850.05820.09120.21280.27720.34540.34210.24560.120.05840.0287
150.02860.02860.05820.1220.21210.310.3780.37320.24560.090.05840.0287
160.02860.02850.05820.09120.18120.27720.34540.34210.24480.120.05840.0286
170.0570.02850.05820.09120.18120.24640.3130.310.21420.11960.05820.0284
180.08520.05680.02880.09120.150.18420.28080.27720.1830.08850.0580.0568
190.11360.08490.02870.060.11960.18360.2170.21490.15150.08850.02870.0849
200.11320.11320.02870.05960.08940.1520.18480.1830.12040.05860.02870.0846
210.1410.11280.0570.02970.08880.12080.1530.15150.090.05820.02860.1124
220.16860.14050.05680.02950.05920.090.12160.12040.08940.05760.0570.112
230.16860.14050.05660.02940.05880.090.09090.090.05960.02870.05680.14
240.1680.1680.08490.02920.02940.05960.09060.060.05940.02870.05680.1395
HourJanFebMarAprMayJunJulyAugSepOctNovDec
10.16860.16860.08490.02920.02940.05960.06040.05980.05940.02870.08520.1405
20.1960.1680.11320.05840.02940.05960.06020.05980.05940.02870.08490.168
30.1960.1960.11320.05820.02930.05940.06020.05960.02960.02870.08520.168
40.1960.1960.11320.05820.02930.05940.060.05960.02950.02870.11320.168
50.1960.1960.11320.05820.02930.02960.060.05940.02950.05740.11320.168
60.1960.1960.11320.05820.02930.05940.060.05940.02950.02870.11320.1674
70.1960.1960.11320.05820.02940.05960.06020.05960.02960.02870.08490.168
80.16860.1680.08490.02920.02950.05980.09090.090.05940.02870.08520.1405
90.16860.14050.05660.02950.0590.090.12120.12040.08940.02870.0570.1405
100.11280.11280.02860.02970.08910.12080.1530.15150.090.05820.02860.1128
110.08490.08490.02870.060.120.15250.21560.21420.15150.05880.02870.0566
120.08520.05660.02870.06040.1510.18360.27990.27630.18240.08850.02870.0283
130.0570.02850.05820.09090.18180.24560.3130.3080.21350.11960.05840.0284
140.02860.02850.05820.09120.21280.27720.34540.34210.24560.120.05840.0287
150.02860.02860.05820.1220.21210.310.3780.37320.24560.090.05840.0287
160.02860.02850.05820.09120.18120.27720.34540.34210.24480.120.05840.0286
170.0570.02850.05820.09120.18120.24640.3130.310.21420.11960.05820.0284
180.08520.05680.02880.09120.150.18420.28080.27720.1830.08850.0580.0568
190.11360.08490.02870.060.11960.18360.2170.21490.15150.08850.02870.0849
200.11320.11320.02870.05960.08940.1520.18480.1830.12040.05860.02870.0846
210.1410.11280.0570.02970.08880.12080.1530.15150.090.05820.02860.1124
220.16860.14050.05680.02950.05920.090.12160.12040.08940.05760.0570.112
230.16860.14050.05660.02940.05880.090.09090.090.05960.02870.05680.14
240.1680.1680.08490.02920.02940.05960.09060.060.05940.02870.05680.1395

Similar to that of carbon monoxide, when the ambient air temperature increases from 1 °C to 40 °C, the nitrogen monoxide production increases from 0.0518(kg/s) to 0.0557 (kg/s). Increasing the ambient air temperature leads to reduction in burner heat rate and an increase in mass flow rate of fuel; as a result, the burner outlet mass flow rate of nitrogen monoxide increases (see Eq. (27)). Figure 9 shows variation of nitrogen monoxide production in one fuel cell stack with ambient temperature. When the ambient temperature increases from 1 °C to 40 °C, nitrogen monoxide mass production by each fuel cell stack increases from 0.0518(kg/s) to 0.0557(kg/s). Table 4 shows nitrogen monoxide production from fuel cell stacks. The maximum production is at 3 p.m. on 15 July when the ambient air temperature is high and the maximum number of fuel cell stacks operate. The production rate is equal to 0.6672 (kg/s).

Fig. 9
Variation of total nitrogen monoxide production in one fuel cell stack with ambient temperature
Fig. 9
Variation of total nitrogen monoxide production in one fuel cell stack with ambient temperature
Close modal
Table 4

Monoxide nitrogen mass production from fuel cell stacks which operate in the residential building in kg/s

HourJanFebMarAprMayJunJulyAugSepOctNovDec
10.31320.31320.15750.05330.05360.1080.10860.10820.10740.05290.15750.2615
20.36540.31320.20960.10660.05350.10760.10860.1080.10740.05280.15750.3132
30.36540.36050.20960.10640.05350.10740.10840.1080.05360.05280.15750.3132
40.36540.36050.20960.10640.05340.10740.10840.10760.05360.05280.210.3132
50.36540.36470.20960.10640.05340.05370.10840.10740.05360.10560.20960.3132
60.36540.36470.20960.10640.05340.10740.10840.10740.05360.05280.210.3132
70.36540.36470.20960.10640.05350.10760.10860.1080.05370.05280.15750.3132
80.31320.31320.15720.05340.05360.1080.16320.16260.10740.05290.15750.2615
90.31380.2620.10540.05360.10720.16260.2180.21760.16140.05290.10480.262
100.20960.210.05270.05370.16110.21720.27350.2730.16260.10640.05280.2096
110.15750.15750.05290.10840.21680.27250.3850.38290.27150.10660.0530.105
120.15780.10520.05290.10860.27150.32820.49680.49410.32640.16050.05290.0525
130.10540.05270.10640.16350.32640.43760.5540.5470.38080.2160.10660.0525
140.05270.05270.10640.16350.38150.49230.61160.60280.43520.21640.10660.0528
150.05270.05270.10640.21840.38080.5480.66720.65760.4360.16260.10660.0528
160.05270.05270.10640.16350.32580.49320.61050.60280.4360.21680.10660.0528
170.10520.05260.10620.16350.32580.43760.5540.5470.38220.2160.10660.0526
180.15750.1050.05290.16350.2710.32820.49590.49410.32760.16080.10620.1052
190.210.15750.0530.10840.2160.32820.38430.38290.27250.16080.05280.1575
200.20960.20960.05280.1080.16140.27250.32880.32760.21720.10680.05270.1572
210.26150.20920.10520.05380.16110.21720.27350.27250.16260.10680.05290.2092
220.31320.2610.1050.05360.10720.16260.2180.21720.1620.10580.10520.2092
230.31320.2610.1050.05350.1070.16260.16320.16290.10760.05290.1050.261
240.31320.31320.15750.05330.05360.1080.16290.10840.10740.05290.1050.261
HourJanFebMarAprMayJunJulyAugSepOctNovDec
10.31320.31320.15750.05330.05360.1080.10860.10820.10740.05290.15750.2615
20.36540.31320.20960.10660.05350.10760.10860.1080.10740.05280.15750.3132
30.36540.36050.20960.10640.05350.10740.10840.1080.05360.05280.15750.3132
40.36540.36050.20960.10640.05340.10740.10840.10760.05360.05280.210.3132
50.36540.36470.20960.10640.05340.05370.10840.10740.05360.10560.20960.3132
60.36540.36470.20960.10640.05340.10740.10840.10740.05360.05280.210.3132
70.36540.36470.20960.10640.05350.10760.10860.1080.05370.05280.15750.3132
80.31320.31320.15720.05340.05360.1080.16320.16260.10740.05290.15750.2615
90.31380.2620.10540.05360.10720.16260.2180.21760.16140.05290.10480.262
100.20960.210.05270.05370.16110.21720.27350.2730.16260.10640.05280.2096
110.15750.15750.05290.10840.21680.27250.3850.38290.27150.10660.0530.105
120.15780.10520.05290.10860.27150.32820.49680.49410.32640.16050.05290.0525
130.10540.05270.10640.16350.32640.43760.5540.5470.38080.2160.10660.0525
140.05270.05270.10640.16350.38150.49230.61160.60280.43520.21640.10660.0528
150.05270.05270.10640.21840.38080.5480.66720.65760.4360.16260.10660.0528
160.05270.05270.10640.16350.32580.49320.61050.60280.4360.21680.10660.0528
170.10520.05260.10620.16350.32580.43760.5540.5470.38220.2160.10660.0526
180.15750.1050.05290.16350.2710.32820.49590.49410.32760.16080.10620.1052
190.210.15750.0530.10840.2160.32820.38430.38290.27250.16080.05280.1575
200.20960.20960.05280.1080.16140.27250.32880.32760.21720.10680.05270.1572
210.26150.20920.10520.05380.16110.21720.27350.27250.16260.10680.05290.2092
220.31320.2610.1050.05360.10720.16260.2180.21720.1620.10580.10520.2092
230.31320.2610.1050.05350.1070.16260.16320.16290.10760.05290.1050.261
240.31320.31320.15750.05330.05360.1080.16290.10840.10740.05290.1050.261

Figure 10 shows the variation of carbon dioxide production in one fuel cell stack with ambient air temperature. It can be concluded that unlike nitrogen monoxide and carbon monoxide, the mass flow rate of carbon dioxide decreases from 0.802 (kg/s) to 0.79843 (kg/s) when the inlet air temperature increases from 1 °C to 40 °C. In fact, an increase in the ambient air temperature leads to reduction in the burner heat rate and an increase in the mass flow rate of fuel. As such, mass production of carbon dioxide by the burner increases (see Eq. (25)). On the other hand, with increasing ambient air temperature, outlet pressure and power of compressor increase (see Eq. (36) and Eq. (37)). Thus, the net power of the system decreases and the reformer outlet carbon dioxide decreases. Increase in mass production of carbon dioxide by the burner is less than the decrease in mass production of carbon dioxide by the reformer. As such, the total mass production of the carbon dioxide by the system decreases with the increase in ambient air temperature. This variation is shown in Fig. 10. Moreover, carbon dioxide production from fuel cell stacks is shown in Table 5.

Fig. 10
Variation of carbon dioxide production in one fuel cell stack with ambient air temperature
Fig. 10
Variation of carbon dioxide production in one fuel cell stack with ambient air temperature
Close modal
Table 5

Dioxide carbon mass production from fuel cell stacks which operate in the residential building in kg/s

HourJanFebMarAprMayJunJulyAugSepOctNovDec
14.80964.80962.40420.80050.80031.59981.5991.59961.60.80092.40394.008
25.61194.81023.20561.6010.80031.59981.59921.59961.60.8012.40424.8102
35.61195.61193.20561.60120.80041.61.59921.59980.80010.8012.40394.8102
45.61195.61193.20561.60120.80041.61.59941.59980.80020.8013.20564.8102
55.61195.61193.20561.60120.80040.80011.59941.60.80021.6023.20564.8102
65.61195.61193.20561.60120.80041.61.59941.60.80020.8013.20564.8102
75.61195.61193.20561.60120.80031.59981.59921.59980.80010.8012.40424.8108
84.80964.81022.40420.80050.80021.59962.39822.39911.60.80092.40394.008
94.80964.0081.60280.80021.60042.39913.19763.19842.39970.80091.60244.008
103.2063.2060.80110.82.43.1983.99553.9972.39911.60120.80113.206
112.40422.40420.8011.59943.19883.9965.59165.59373.9971.60060.8011.6028
122.40391.60280.8011.5993.99754.79467.18747.19014.79582.40090.8010.8014
131.60240.80121.60122.39824.79646.39127.9847.9885.59443.19921.6010.8013
140.80110.80121.60122.39795.59517.18928.78138.78466.3923.19881.6010.8009
150.80110.80111.60123.19685.59587.9879.57849.58326.39122.39911.6010.8009
160.80110.80121.60122.39794.7977.18928.78138.78466.39283.19881.6010.8011
171.60240.80121.60122.39794.7976.39127.9847.9875.59373.19921.60120.8013
182.40391.60260.80082.39793.99854.7947.18657.18924.79522.40061.60141.6026
193.20522.40420.80091.59943.19924.79465.59095.5933.9972.40060.8012.4042
203.20563.20560.8011.59982.39973.99654.79344.79523.19841.60080.8012.4045
214.00753.2061.60240.82.40033.1983.99553.9972.39911.60120.80113.2064
224.80964.0081.60260.80021.60022.39913.19723.19842.39971.60181.60243.2068
234.80964.0081.60280.80031.60062.39912.39822.39911.59980.8011.60264.0085
244.80964.81022.40420.80050.80031.59982.39851.59941.60.8011.60264.009
HourJanFebMarAprMayJunJulyAugSepOctNovDec
14.80964.80962.40420.80050.80031.59981.5991.59961.60.80092.40394.008
25.61194.81023.20561.6010.80031.59981.59921.59961.60.8012.40424.8102
35.61195.61193.20561.60120.80041.61.59921.59980.80010.8012.40394.8102
45.61195.61193.20561.60120.80041.61.59941.59980.80020.8013.20564.8102
55.61195.61193.20561.60120.80040.80011.59941.60.80021.6023.20564.8102
65.61195.61193.20561.60120.80041.61.59941.60.80020.8013.20564.8102
75.61195.61193.20561.60120.80031.59981.59921.59980.80010.8012.40424.8108
84.80964.81022.40420.80050.80021.59962.39822.39911.60.80092.40394.008
94.80964.0081.60280.80021.60042.39913.19763.19842.39970.80091.60244.008
103.2063.2060.80110.82.43.1983.99553.9972.39911.60120.80113.206
112.40422.40420.8011.59943.19883.9965.59165.59373.9971.60060.8011.6028
122.40391.60280.8011.5993.99754.79467.18747.19014.79582.40090.8010.8014
131.60240.80121.60122.39824.79646.39127.9847.9885.59443.19921.6010.8013
140.80110.80121.60122.39795.59517.18928.78138.78466.3923.19881.6010.8009
150.80110.80111.60123.19685.59587.9879.57849.58326.39122.39911.6010.8009
160.80110.80121.60122.39794.7977.18928.78138.78466.39283.19881.6010.8011
171.60240.80121.60122.39794.7976.39127.9847.9875.59373.19921.60120.8013
182.40391.60260.80082.39793.99854.7947.18657.18924.79522.40061.60141.6026
193.20522.40420.80091.59943.19924.79465.59095.5933.9972.40060.8012.4042
203.20563.20560.8011.59982.39973.99654.79344.79523.19841.60080.8012.4045
214.00753.2061.60240.82.40033.1983.99553.9972.39911.60120.80113.2064
224.80964.0081.60260.80021.60022.39913.19723.19842.39971.60181.60243.2068
234.80964.0081.60280.80031.60062.39912.39822.39911.59980.8011.60264.0085
244.80964.81022.40420.80050.80031.59982.39851.59941.60.8011.60264.009
Table 6

Cost of electricity of fuel cell stacks which operate in the residential building in US$/kWh

HourJanFebMarAprMayJunJulyAugSepOctNovDec
18.798.7844.411.4871.49233.0143.0042.9941.4784.417.325
210.2488.7845.8762.9741.4912.9963.013.0022.9941.4774.418.778
310.24810.2485.8762.971.492.9963.0131.4951.4774.4138.79
410.24810.2485.8762.971.4892.9943.0062.9981.4941.4775.888.778
510.24810.2485.8762.971.4891.4963.0042.9981.4932.9525.8768.778
610.24810.2485.8762.971.4892.9923.0062.9961.4931.4775.888.778
710.24810.2485.8762.9721.492.9963.0131.4951.4774.418.772
88.798.7844.411.4881.4933.0024.5274.5092.9961.4784.4137.33
98.797.3252.9381.4932.9884.5096.046.024.4971.4792.9467.33
105.8725.8681.4751.4984.4946.0287.5757.5354.5092.9721.4765.868
114.414.411.4793.0066.0087.56510.65410.6127.522.9841.482.938
124.412.941.4793.0147.5359.0913.72513.6719.0664.4761.4791.469
132.9481.4742.974.5219.04212.15215.2915.2210.5986.0082.9741.471
141.4751.4742.9724.53310.54913.69816.84116.77512.1366.0122.9741.478
151.4751.4742.9726.05610.56315.2218.37218.31212.1364.5092.9761.477
161.4751.4742.9724.5369.03613.68916.84116.76412.1286.0122.9761.475
172.9481.4732.9684.5369.04812.15215.2915.2210.5986.0042.9721.471
184.4132.9421.484.5337.529.10213.74313.689.0784.4822.9662.944
195.8844.411.4793.0086.0049.0910.66810.6197.554.4791.4774.407
205.8765.8761.47734.4977.5359.1149.0786.0242.9781.4794.404
217.3355.8682.9481.4994.4916.0287.5757.5454.5092.971.4755.864
228.797.3252.9421.4942.994.5126.0486.0244.52.9582.9465.856
238.797.322.941.4912.9824.5064.5214.5122.9981.4782.9427.315
248.798.7844.411.4871.49234.5213.0042.9941.4782.9427.315
HourJanFebMarAprMayJunJulyAugSepOctNovDec
18.798.7844.411.4871.49233.0143.0042.9941.4784.417.325
210.2488.7845.8762.9741.4912.9963.013.0022.9941.4774.418.778
310.24810.2485.8762.971.492.9963.0131.4951.4774.4138.79
410.24810.2485.8762.971.4892.9943.0062.9981.4941.4775.888.778
510.24810.2485.8762.971.4891.4963.0042.9981.4932.9525.8768.778
610.24810.2485.8762.971.4892.9923.0062.9961.4931.4775.888.778
710.24810.2485.8762.9721.492.9963.0131.4951.4774.418.772
88.798.7844.411.4881.4933.0024.5274.5092.9961.4784.4137.33
98.797.3252.9381.4932.9884.5096.046.024.4971.4792.9467.33
105.8725.8681.4751.4984.4946.0287.5757.5354.5092.9721.4765.868
114.414.411.4793.0066.0087.56510.65410.6127.522.9841.482.938
124.412.941.4793.0147.5359.0913.72513.6719.0664.4761.4791.469
132.9481.4742.974.5219.04212.15215.2915.2210.5986.0082.9741.471
141.4751.4742.9724.53310.54913.69816.84116.77512.1366.0122.9741.478
151.4751.4742.9726.05610.56315.2218.37218.31212.1364.5092.9761.477
161.4751.4742.9724.5369.03613.68916.84116.76412.1286.0122.9761.475
172.9481.4732.9684.5369.04812.15215.2915.2210.5986.0042.9721.471
184.4132.9421.484.5337.529.10213.74313.689.0784.4822.9662.944
195.8844.411.4793.0086.0049.0910.66810.6197.554.4791.4774.407
205.8765.8761.47734.4977.5359.1149.0786.0242.9781.4794.404
217.3355.8682.9481.4994.4916.0287.5757.5454.5092.971.4755.864
228.797.3252.9421.4942.994.5126.0486.0244.52.9582.9465.856
238.797.322.941.4912.9824.5064.5214.5122.9981.4782.9427.315
248.798.7844.411.4871.49234.5213.0042.9941.4782.9427.315
Table 7

Product electrical energy, entropy generation, mass production of nitrogen monoxide, carbon monoxide and carbon dioxide and average cost of electricity in a year

Produced electrical energy957.075 (GJ/year)
Entropy generation1004.54 (GJ/K.year)
Total mass production NO1609.056 (kg/year)
Total mass production CO226107.23 (kg/year)
Total mass production CO1272.621 (kg/year)
Average cost of electricity in a year5.41 (US$/kWh)
Produced electrical energy957.075 (GJ/year)
Entropy generation1004.54 (GJ/K.year)
Total mass production NO1609.056 (kg/year)
Total mass production CO226107.23 (kg/year)
Total mass production CO1272.621 (kg/year)
Average cost of electricity in a year5.41 (US$/kWh)

It can be concluded that by increasing the ambient air temperature from 1 °C to 40 °C, the production of nitrogen monoxide and carbon monoxide increases by 8.9% and 14.56%, respectively, and production of carbon dioxide decreases by 0.47%. As such, we can conclude that with increasing ambient air temperature the total mass of air pollution increases.

Variation of cost of electricity with ambient air temperature is shown in Fig. 11. As we explained before, with increasing ambient air temperature, inlet fuel to burner and air pollutant increase. Thus, the cost associated with the fuel consumption (CF) and the externalized social cost of air pollution (CA) increase. Table 6 shows the cost of electricity of fuel cell stacks through a year in US$/kWh.

Fig. 11
Variation of cost of electricity for one fuel cell stack with ambient air temperature
Fig. 11
Variation of cost of electricity for one fuel cell stack with ambient air temperature
Close modal

The average cost of electricity in a year is equal to 5.41 (US$/kWh). Table 7 shows the annual average of electrical energy, entropy generation, mass production of nitrogen monoxide, carbon monoxide, carbon dioxide, and average electricity cost for fuel cell stacks.

Conclusion

In this paper, a polymer electrolyte membrane (PEM) fuel cell power system including burner, steam reformer, heat exchanger, and water heater for domestic application has been considered to meet the electrical, domestic hot water, heating, and cooling loads of a residential building located in Tehran. The peak demands of electricity, DHW, heating and cooling are 32.96 kW, 0.926 kW, 1590 kW and 2028 kW, respectively. With these measures, 12 CHP fuel cell units with 8.5 kW nominal power could meet all the electrical, DHW, heating, and cooling needs of the building. Exergy and environmental analysis of this CHP system shows that by increasing the ambient air temperature from 1 °C to 40 °C, entropy generation and production of nitrogen monoxide and carbon monoxide increases by 5.73%, 8.9%, and 14.56%, respectively, but production of carbon dioxide decreases by 0.47%. Economic analysis show that the average electricity cost in a year is equal to 5.41 (US$/kWh).

Nomenclature

    Nomenclature
     
  • C =

    total capital cost of installed system (US$/kW)

  •  
  • CA =

    social cost of air pollution (US$/kW)

  •  
  • CE =

    total cost of electricity (US$/kW)

  •  
  • Cf =

    capacity factor

  •  
  • CF =

    fuel consumption cost (US$/kW)

  •  
  • CI =

    initial investment cost (US$/kW)

  •  
  • Co =

    operation and maintenance cost (US$/kW)

  •  
  • CP =

    specific heat coefficient (kJ/kg.K)

  •  
  • COP =

    coefficient of performance

  •  
  • d =

    diameter (m)

  •  
  • e =

    exergy (kJ/kg)

  •  
  • f =

    frictional coefficient

  •  
  • F =

    Faraday constant

  •  
  • h =

    convection heat transfer coefficient (W/m2.K)

  •  
  • hio =

    enthalpy formation (kJ/kg)

  •  
  • i =

    annual interest rate

  •  
  • I =

    capital salvage factor

  •  
  • k =

    heat transfer coefficient (W/m.K)

  •  
  • K =

    equilibrium coefficient

  •  
  • L =

    length (m)

  •  
  • L.T =

    life time

  •  
  • m· =

    mass flow rate (kg/s)

  •  
  • M =

    molecular mass (kg/kmole)

  •  
  • n =

    number of fuel cell stacks

  •  
  • Nu =

    Nusselt number

  •  
  • P =

    pressure (kPa)

  •  
  • P0 =

    standard pressure (kPa)

  •  
  • Pc =

    ambient around (m)

  •  
  • q =

    heat rate (kJ/kg)

  •  
  • Q· =

    heat rate (kW)

  •  
  • ra =

    Stoichiometric air fuel ratio

  •  
  • R =

    gas constant (kJ/kg.K)

  •  
  • S·gen =

    total entropy generation rate (kW/K)

  •  
  • T =

    temperature (K)

  •  
  • T0 =

    standard temperature (K)

  •  
  • Ua =

    fraction of air which is reacted with fuel

  •  
  • Uf =

    percentage consumption of fuel

  •  
  • v =

    velocity of fluid (m/s)

  •  
  • V =

    voltage of fuel cell (V)

  •  
  • W· =

    power (kW)

  •  
  • W·n =

    electrical power need (kW)

  •  
  • W·p =

    electrical power consumed by pump(kW)

  •  
  • x =

    mole fraction

  •  
  • ΔP =

    pressure loss (kPa)

Subscripts

    Subscripts
     
  • a =

    annual

  •  
  • air =

    air

  •  
  • ave =

    average

  •  
  • b =

    burner

  •  
  • c =

    compressor

  •  
  • C.W =

    cooling water

  •  
  • ch =

    chemical

  •  
  • CO =

    monoxide carbon

  •  
  • CO2 =

    dioxide carbon

  •  
  • cooling =

    Cooling

  •  
  • DHW =

    domestic hot water

  •  
  • ex =

    heat exchanger

  •  
  • ex.g =

    exhaust gas

  •  
  • f =

    fuel cell

  •  
  • fuel =

    Fuel

  •  
  • h =

    hydraulic

  •  
  • H2 =

    hydrogen

  •  
  • H2O =

    water

  •  
  • he =

    heater

  •  
  • heating =

    heating

  •  
  • in =

    inlet

  •  
  • N2 =

    nitrogen

  •  
  • NO =

    monoxide nitrogen

  •  
  • O2 =

    oxygen

  •  
  • out =

    outlet

  •  
  • ph =

    physical

  •  
  • r =

    reformer

  •  
  • sat =

    saturation

  •  
  • steam =

    steam

  •  
  • t =

    total

Greek Symbols

    Greek Symbols
     
  • βabs =

    COP of the absorption refrigerator

  •  
  • βhp =

    COP of the heat pump

  •  
  • βref =

    COP of the heat pump operating in refrigeration mode

  •  
  • ξ =

    correctional coefficient

  •  
  • ρ =

    density (kg/m3)

  •  
  • α =

    effectiveness of heat exchanger

  •  
  • ηi =

    thermal efficiency (%)

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