Exergy, Economic, and Environmental Analysis of a PEM Fuel Cell Power System to Meet Electrical and Thermal Energy Needs of Residential Buildings

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.

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.

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.

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).

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).

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 r_a are mole fractions of oxygen and nitrogen in the air and stoichiometric air fuel ratio, respectively. U_a is the fraction of air which is reacted with fuel in the fuel cell.

where a, b, d, e, f, g, r, a′, b′, d′, e′, f′, g′ and r′ are equilibrium coefficients and K_CO and K_NO are the equilibrium coefficients of the carbon monoxide and nitrogen monoxide, respectively. Moreover, P_b is the pressure of the burner, n_b and n_air,out,c are the equilibrium coefficients of the burner and outlet air compressor, respectively.

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 T_sat is equal to 373 K. T_r, T₀, T_b, and T_f 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.

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 M_fuel, M_air, and $MN2$ are molecular masses of methane as fuel, air, and nitrogen, respectively.

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.

where Nu_ave is the average Nusselt number in cooling channel, h_ave is the average convection heat transfer coefficient, k is heat conduction coefficient, d_h 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 p_c are the length and perimeter around thecooling channel, and $CPc.w$ is specific heat coefficient of the cooling water.

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.

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.

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.

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

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.

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.

In these equations e_ph, e_ch, and e_t, are physical exergy, chemical exergy and total exergy, respectively. Furthermore, T is temperature, P is pressure, R is the gas constant, and x_i is mole fraction of the mixture.

in which C_E, C_I, C_O, C_F, and C_A 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.

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 C_f is the capacity factor.

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.

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.

where $m·NO,m·CO, and m·CO2$ are the exhaust mass flow rates of nitrogen monoxide, carbon monoxide, and carbon dioxide in kg/s and $CA,NO,CA,CO, and CA,CO2$ 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.

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).

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).

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).

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).

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.

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 (C_F) and the externalized social cost of air pollution (C_A) increase. Table 6 shows the cost of electricity of fuel cell stacks through a year in US$/kWh.

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.

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

C =

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

C_A =

social cost of air pollution (US$/kW)

C_E =

total cost of electricity (US$/kW)

C_f =

capacity factor

C_F =

fuel consumption cost (US$/kW)

C_I =

initial investment cost (US$/kW)

C_o =

operation and maintenance cost (US$/kW)

C_P =

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)

P_c =

ambient around (m)

q =

heat rate (kJ/kg)

$Q·$ =

heat rate (kW)

r_a =

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)

U_a =

fraction of air which is reacted with fuel

U_f =

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

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

$βabs$ =

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 (%)