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Exergetic and thermoeconomic analysis of a 200-kW phosphoric acid fuel cell plant
Fuel 83 (2004) 2087–2094 www.fuelfirst.com
Exergetic and thermoeconomic analysis of a 200-kW phosphoric acid fuel cell plant Ho-Young Kwaka,*, Hyun-Soo Leea, Jung-Yeul Junga, Jin-Seok Jeonb, Dal-Ryung Parkb a
Mechanical Engineering Department, Chung-Ang University, 221, Huksuk-Dong, Dongjak-Ku, Seoul 156-756, South Korea b R&D Center, Korea Gas Corporation, Ansan 425-790, South Korea Received 9 February 2002; revised 9 February 2002; accepted 7 April 2004; available online 4 May 2004
Abstract Exergetic and thermoeconomic analysis were performed for a 200-kW phosphoric acid fuel cell plant which offers many advantages for co-generation in the aspect of high electrical efficiency and low emission. This analytical study was based on the data obtained by in-field measurement of PC25C fuel cell plant to find whether this system is viable economically. For 100% load condition, the electrical efficiency obtained, 43.7% turned out to be much better than that for the 1000-kW gas turbine co-generation plant. However, the calculated unit cost of electricity with the initial investment cost per power of fuel cell plant of 3000 $/kW, 0.068 $/kWh turned out to be 125% higher than the cost obtained for the 1000-kW gas turbine co-generation plant. This fuel cell system may be viable economically when the initial investment cost per power is reduced to the level of the gas turbine co-generation plant of 1500 $/kW. q 2004 Elsevier Ltd. All rights reserved. Keywords: Exergy analysis; Fuel cell plant; Modified Productive structure; Phosphoric acid fuel cell; Thermoeconomic analysis
1. Introduction Exergetic analysis permits to predict the performance of energy systems as well as the efficiency of each component of the systems. On the other hand, thermoeconomic analysis provides a tool to estimate the unit cost of products properly and the monetary loss associated with the entropy generation in the components of the system. One of the merits of the fuel cell system is that considerable entropy generation occurred during combustion process inevitably at gas burner can be saved by reformer where endothermic reaction takes place, even though only 40% of the chemical exergy of natural gas is utilized to produce electricity at fuel cell stack and the life time of the system is shorter [1]. In this study, exergetic and thermoeconomic analysis were performed for a 200-kW phosphoric acid fuel cell (PAFC) plants which offers many advantages for co-generation in the aspect of high electrical efficiency and low emissions [2] to find whether the system is viable economically. This system analysis based on the detailed conservation laws employed the data obtained by * Corresponding author. Tel.: þ 82-28205278; fax: þ 82-28267464. E-mail address: [email protected] (H.-Y. Kwak). 0016-2361/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.fuel.2004.04.002
the in-field measurement of PC25C fuel cell power plant (ONSI corporation), installed and operated at Korea Gas Corporation. The exergy-balance equation developed by Oh et al. [3] and the corresponding cost-balance equation by Kim et al. [4] were utilized in this analysis. Detail computational works on the estimation of property values were done by using the polynomial for gases [5] and the equations suggested by International Formulation Committee for water and steam [6]. For hydrocarbon fuels, Benedict – Webb –Rubin equation of state [7] was utilized. Rearrangement of the components depending on their function of the PAFC system was done to apply the developed cost-balance equation with integrated exergy stream [8] to the system concerned. The performance and the unit cost of products of the system were evaluated at various loads. For 100% load condition, the electrical efficiency of the PAFC system was about 43.7%, which turned out to be much better than that for the 1000-kW gas turbine cogeneration plant [4]. However, the calculated unit cost of electricity with the initial investment cost of fuel cell plant of 3000 $/kW, 0.068 $/kWh turned out to be 125% higher than the cost obtained for the gas turbine co-generation plant.
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2. Cost-balance equation based on modified productive structure analysis
the annualized cost by using the capital recovery factor CRFði; nÞ; i.e.
A general exergy-balance equation that is applicable to any component of thermal system may be formulated by utilizing the first and second law of thermodynamics [3]. With some modification on the exergy-balance equation for the non-adiabatic components to account the exergy losses due to heat transfer, the general exergy-balance equation may be written as with integrated exergy stream 0 1 ! X X X X BQ BQ A @ _ECHE _ _ _ _ þ Ex;i 2 Ex;j þ Ex;i 2 Ex;j x
C_ ð$=yearÞ ¼ PW £ CRFði; nÞ
output
input
X
þ To
S_ i 2
inlet
X
inlet
outlet
!
_ CV =T ¼ E_ W S_ j þ Q
ð1Þ
output
input
þTo
inlet
S_ i 2
Dividing the levelized cost by 8000 annual operating hours, we obtain the following capital cost for the kth component of the plant. Z_ k ¼ fk C_ k =ð3600 £ 8000Þ
ð5Þ
The maintenance cost is taken into consideration through the factor of fk ¼ 1:06 for each plant component whose expected life is assumed to be 15 years.
outlet
where E_ and S_ denote the flow rate of exergy and entropy, _ CV in the fifth term denotes the heat respectively, and Q transfer interaction between a component and environment. The superscripts CHE, BQ and W denote chemical exergy, steam and work (or electricity), respectively. Assigning a unit exergy cost to each decomposed exergy system, the cost-balance equation corresponding to the exergy-balance equation given in Eq. (1) may be written as 0 1 ! X BQ X BQ X X CHE E_ x Co þ@ E_ x;i 2 E_ x;j ACBQ þ E_ x;i 2 E_ x;j CE X
ð4Þ
X
!
inlet
outlet
_ CV =To CS þZ_ ½k ¼ E_ W CW S_ j 2Q
ð2Þ
outlet
where Co ;CBQ ;CE ;CS and CW are the unit cost of fuel, steam, gas exergy and negentropy, and electricity, respectively. The term Z_ ½k includes all financial charges associated with owning and operating the kth plant component. Eqs. (1) and (2) are two basic equations used in this analysis. We call the exergy-costing method based on these equations as modified productive structure analysis (MOPSA) one in the sense that the cost-balance equation given in Eq. (2) yields the productive structure of thermal system at hand [4], which has been suggested and developed by Lozano and Valero [9] and Torres et al. [10].
3. Cost equation for plant component All costs due to owing and operating a plant depend on the type of financing, required capital, expected life of a component, etc. The annualized (levelized) cost method of Moran [11] was employed in this study. The amortization cost for a particular plant component may be written as present worth (PW) PW ¼ Ci 2 Sn PWFði; nÞ
ð3Þ
where Ci is initial investment cost and PWFði; nÞ is the PW factor. The PW of the component may be converted to
4. System descrition for 200-kW phosphoric acid fuel cell plant A schematic of a 200-kW phosphoric acid fuel cell (PAFC) is given in Fig. 1, and shows every state point which we accounted for in this analysis. Every state in the plant is described by three digits. The first digit indicates a specific fluid stream (0 for natural gas, 1 for air, 2 for hydrogen-rich gas, 3 for steam, 4 for water and 5 for flue gas), and the second digit indicates each component in the plant (1 for the first heat exchanger [HTX1], 2 for CO shift converter [COSC], 3 for reformer [RFM], 4 for gas burner [GASB], 5 for the air preheater [HTX2], 6 for fuel cell stack [FCS], 7 for the third heat exchanger [HTX3], 8 for steam/water separator [SWS] and 9 for the fourth heat exchanger [HTX4]). The final digit indicates the inlet (1) and outlet (2) stream of working fluids at each component. The fuel cell plant consists of fuel process system ([HTX1], [COSC], [RFM], and [GASB]) which converts natural gas into hydrogen-rich gas, power system ([FCS]) which converts chemical exergy of gas into electricity by electrochemical process and thermal management system ([SWS], [HTX4], and water treatment system [WTS]). At full load condition, the air to [GASB] and the fuel flow rate to the system are approximately 248 and 35 kg/h, respectively. The air flow rate to the cathode in [FCS] at the full load is about 678 kg/h. Part load condition can be achieved by controlling the air flow rate to [GASC] and to the cathode in [FCS] and the fuel flow rate to [RFM]. More detailed description including the first law of thermodynamics for the major components is as follows. 4.1. Fuel process system Hydrogen-rich gas needed for the electrochemical reaction in [FCS] can be produced from the natural gas (primary CH4) via the reforming process of steam from [HTX1]. The possible reactions in the reforming process
H.-Y. Kwak et al. / Fuel 83 (2004) 2087–2094
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Fig. 1. Schematic of 200-kW phosphoric acid fuel cells (PAFC) system (modified from Ref. [12]).
[12] are given as 1 Cn Hm þ 2nH2 O ! nCO2 þ 2n þ m H2 2 1 Cn Hm þ nH2 O ! nCO þ n þ m H2 2
ð6Þ
reactant
product
ð7Þ
The chemical reaction in [RFM] including these endothermic reactions may be written as aCaj Hbj þ bCak Hbk þ cCal Hbl þ dCam Hbm þ yH2 O
1 ! fnat CO2 þ ð1 2 f Þnat CO þ ð1 þ f Þnat þ nbt H2 2
þ y 2 ð1 þ f Þnat H2 O ð8Þ where aaj þ bak þ cal þ dam ¼ nat ; abj þ b b k þ c bl þ d bm ¼ n b t ; and f is the ratio of the reaction given in Eq. (6) to the reaction given in Eq. (7), which may be determined from the heat balance for [RFM] and [GASB]. The value of f which affects the outlet temperature of the hydrogen-rich gas stream in [HTX1] is about 0.795 –0.80. Applying the first law to [RFM], we obtain QRFM þ QEX RFM ¼ hRP;RFM
where h RP;RFM is the enthalpy of combustion for the reaction given in Eq. (8), which is given by X X e2 i h RP;RFM ¼ ne ðh 0f þDhÞ ni ðh 0f þDhÞ
ð9Þ
¼fnat ðh 0f ÞCO2 þð12f Þnat ðh 0f ÞCO 2ð1þf Þnat ðh 0f ÞH2 O 2aðh 0f ÞCaj Hbj 2bðh 0f ÞCa Hb 2cðh 0f ÞCa Hb k k l l n 0 CO þð12f Þnat ðDhÞ CO 2dðh f ÞC H þ fnat ðDhÞ am
bm
2
1 H þ½y2ð1þf Þnat þð1þf Þnat þ nbt ðDhÞ 2 o 2 n HO C H þbðDhÞ C H ðDhÞ 2 aðDhÞ 2 aj bj ak bk Te;RFM o C H þdðDhÞ C H þyðDhÞ HO þcðDhÞ ð10Þ a b am bm 2 l
l
Ti;RFM
where h 0f is the enthalpy of formation and Dh is the sensible enthalpy. The heat transfer rates, QRFM and QEX RFM are heat exchange with environment and gas burner, respectively. The reformed hydrogen-rich gas is cooled by the natural gas and steam in [HTX1], and the remaining CO gas from [RFM] is converted to CO2 in [COSC] through the following reaction. These gases are fed into the anode in [FCS].
1 fnat CO2 þ ð1 2 f Þnat CO þ ð1 þ f Þnat þ nbt H2 2 þ ½y 2 ð1 þ f Þnat H2 O ! pCO þ ðnat 2 pÞCO2
1 þ ð2nat 2 pÞ þ nbt H2 þ ½y 2 2nat þ pH2 O 2
ð11Þ
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The concentration of CO gas leaving [COSC] may be estimated by the following equation ½CO2 ½H2 KP ðTÞ ½CO ¼ ½H2 O
ð12Þ
where [ ] in Eq. (12) denotes gas concentration and KP ðTÞ is the equilibrium constant for the reaction, CO þ H2 O ! CO2 þ H2 [13].The first law in [COSC] is given by C C H þbðDhÞ ½aðDhÞ aj bj a
k
Hbk
C H þdðDhÞ C H T þcðDhÞ a b am b m i;COSC l
l
C H þbðDhÞ C þQCOSC ¼ h RP;COSC þ½aðDhÞ aj bj a
k
H bk
C H þdðDhÞ C H T þcðDhÞ a b am bm e;COSC l
ð13Þ
l
where QCOSC is the heat exchange with environment and the h RP;COSC is the enthalpy of combustion for the reaction given in Eq. (11). That is h RP;COSC ¼½p2ð12f Þnat ½ðh 0f ÞCO 2ðh 0f ÞCO2 þðh 0f ÞH2 O n CO CO þðnat 2pÞðDhÞ þ pðDhÞ 2 1 H þ½y22nat þp þ 2nat þ nbt 2p ðDhÞ 2 2 o n CO HO 2 fnat ðDhÞ ðDhÞ 2 2 Te;COSC
CO þ ð1þf Þnat þ 1 nbt ðDhÞ H þð12f Þnat ðDhÞ 2 2 o HO þ½y2ð1þf ÞðDhÞ ð14Þ 2
nwv ¼ nwvH þnwvG The first law in [GASB] may be written as QGASB 2QEX RFM ¼ hRP;GASB
ð16Þ
where QGASB is the heat exchanger with environment and h RP;GASB is the enthalpy of combustion for the reaction given in Eq. (15). This is given by
1 h RP;GASB ¼ðn0at þpÞðh 0f ÞCO2 þ ðnbt þn0bt Þþ2nat 22g2p 2 0 0 0 ðhf ÞH2 O 2a ðhf ÞCaj Hbj 2b0 ðh 0f ÞCa Hb 2c0 ðh 0f ÞCa Hb k k l l n 0 0 0 2d ðhf ÞCam Hbm þ ðnat þnat ÞðDhÞCO2
1 0 HO þ ðnbt þnbt Þþnwv þy22g ðDhÞ 2 2
1 O þ ðnto þgÞ2ðnat þn0at Þ2 ðnbt þn0bt Þ ðDhÞ 2 4 N þ0:044nto ðDhÞ Ar gT þ3:728nto ðDhÞ 2 e;GASB n Ar 2 nto ðDhÞO2 þ3:728nto ðDhÞN2 þ0:044nto ðDhÞ H O þeðDhÞ H þ½nwv þy22nat þpðDhÞ 2 2 0 þðnat 2pÞðDhÞCO þpðDhÞCO þa ðDhÞC 2
2b0 ðh 0f ÞCa
H 2c k bk
0
aj H bj
ðh 0f ÞCa Hb 2d 0 ðh 0f ÞCam Hbm l
l
o Ti;GASB
ð17Þ
Ti;COSC
The heat required for the endothermic reactions in [RFM] is supplied from the combustion process in [GASB]. The unconsumed hydrogen-rich gas after the anodic reaction in [FCS] with additional natural gas from line are burned with heated air from [HTX2]. This combustion process in [GASB] may be described as a0 Caj Hbj þb0 Cak Hbk þc0 Cal Hbl þd0 Cam Hbm þnto O2 þ3:728nto N2 þ0:044nto Arþ½nwv þy22nat þpH2 O
where
The PAFC stack, which has been used in co-generation system produces electricity and heat from the reaction of hydrogen and oxygen. The primary reaction in [FCS] are given as Anode : 2H2 ! 4Hþ þ 4e2
ð18Þ
Cathode : O2 þ 4Hþ þ 4e2 ! 2H2 O
ð19Þ
So that the overall reaction is as
þeH2 þðnat 2pÞCO2 þpCO!ðnat þn0at ÞCO2
1 0 þ ðnbt þnbt Þþnwv þy22g H2 O 2
1 0 0 þ ðnto þgÞ2ðnat þnat Þ2 ðnbt þnbt Þ O2 4 þ3:728nto N2 þ0:044nto Ar
4.2. Power system
2H2 þ O2 ! 2H2 O þ HEAT
ð15Þ
Assuming that only 2 g kmol among the hydrogen gas from [COSC] participates in the above anodic reaction, all the gases such as N2 and O2 escaped through cathode and anode in [FCS] may be written as 1 pCO þ ðnat 2 pÞCO2 þ 2nat þ nbt 2 p 2 2g H2 2
n0at ¼ a0 aj þb0 ak þc0 al þd0 am
þ ½y 2 2nat þ pH2 O ðanodeÞ þ ðntoH3 2 gÞO2
n0bt ¼ a0 bj þb0 bk þc0 bl þd0 bm
þ 3:728ntoH3 N2 þ 0:044ntoH3 Ar þ nwvH3 H2 O þ ð2gÞ
1 e ¼ 2nat þ nbt 2p22g 2
H2 O ðcathodeÞ
nto ¼ ntoH þntoG
ð20Þ
ð21Þ
The value of g is to be determined by the input flow rate of fuel and air to the system.
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The electricity produced from the above reaction is given as WT ¼ 131:74ghFCS kJ=kmol
ð22Þ
where hFCS is the efficiency of the FCS. The heat release inside components due to condensation or any other chemical reaction described in Eq. (20) was treated as a kind of water (or steam) exergy in this analysis because the heat released contributes increases the water (or steam) exergy.
5. Cost-balance equations In the fuel cell plant, the species of the fluid streams change after reforming or any other chemical processes. So, it is convenient to divide all the working fluids as gas and water (or steam) stream simply. Also it is better to use integrated exergy without decomposing the exergy stream into thermal and mechanical exergy. In this case, the concept of junction and branch related to thermal and mechanical exergy is no longer needed so that the number of unknowns for the unit exergy costs are considerably reduced. Therefore, the cost-balance equation given in Eq. (2) should be applied to an appropriate component or a group of component depending on the function of its principal product in the energy system. For example, all the components in the fuel cell plant may be rearranged into four groups of components and a system boundary to provide sufficient but not redundant cost-balance equations. The groups of components are (1) the first heat exchanger, and CO shift converter, reformer, gas burner and air preheater for the fuel process system (2) fuel cell stack and the third heat exchanger for power system (3) steam/water separator, the fourth heat exchanger and system boundary for the water treatment system. The cost-balance equations for those groups of components yield the unit cost of each exergy. These are unit costs of gas stream, CE ; electricity, CW ; and steam exergy, CBQ : All the cost-balance equations formulated for fuel cell plant are as follows.
(1) Fuel process system ([HTX1], [COSC], [GASB], [RFM], and [HTX2]) ðE_ LHV;2 þ E_ LHV;3 þ E_ LHV;4 ÞCo þðE_ x;011 þ E_ x;041 þ E_ x;141 þ E_ x;151 þ E_ x;241 2 E_ x;552 2 E_ x;222 ÞCE þ E_ x;311 CBQ þðZ_ HTX1 þ Z_ COSC þ Z_ GASB þ Z_ RFM þ Z_ HTX2 Þ¼0 ð23Þ (2) Power system ([FCS] and [HTX3]) E_ LHV;6 Co þðE_ x;171 þ E_ x;261 2 E_ x;572 2 E_ x;262 ÞCE þðE_ x;461 2 E_ x;462 ÞCBQ þðZ_ FCS þ Z_ HTX3 Þ¼ E_ W CW ð24Þ
(3) Water treatment system ([SWS], [HTX4], [WTS], and system boundary) ðE_ x;591 2 E_ x;592 ÞCE þðE_ x;481 þ E_ x;485 þ E_ x;491 2 E_ x;382 2 E_ x;384 2 E_ x;461 2 E_ x;492 ÞCBQ þðZ_ SWS þ Z_ HTX4 þ Z_ WTS Þ¼0 ð25Þ
The cost structure of the thermal system turned out to be dependent on the chosen level of aggregation that specifies the subsystems [10,14]. In this study, the cost-balance equations for the PAFC system were formulated based on the lowest level of aggregation, which are represented by Eqs. (23) –(25) because the unit cost of products does not Table 1 Property values and enthalpy, entropy and exergy at various state points in the PAFC system for the case of 100% load condition State m _ (kg/h) T (K)
P (kPa) H (kJ/h)
011 34.24 012 34.24 021 34.24 022 34.24 041 0.64 141 13.04 143 234.92 151 234.92 152 234.92 161 677.63 171 677.63 172 677.63 211 135.35 212 135.35 221 135.35 222 135.35 231 34.24 232 135.35 241 122.85 261 135.35 262 122.85 311 101.10 312 101.10 331 101.10 382 101.10 384 216.18 4101 101.10 4102 100.63 461 387.32 462 387.32 481 387.32 482 387.32 483 101.00 485 216.00 491 1212.00 492 1212.00 494 101.10 542 371.44 551 371.44 552 371.44 562 689.39 571 689.39 572 689.39 591 1060.83 592 959.73
101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 790.20 101.30 101.30 790.20 792.00 792.00 792.00 790.20 800.00 800.00 790.20 792.00 792.00 101.30 101.30 792.00 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30
288.15 723.15 573.15 723.15 288.15 298.15 703.15 298.15 703.15 423.15 298.15 424.96 823.15 343.08 343.08 463.15 723.15 823.15 453.15 463.15 453.15 443.15 723.15 723.15 443.15 443.15 353.15 323.15 443.15 443.15 443.58 443.15 323.15 363.15 316.15 338.15 353.15 820.00 820.00 611.10 463.15 463.15 352.15 442.82 323.20
2697.29 39,785.03 23,338.37 39,785.03 212.97 0.00 99,146.45 0.00 99,146.45 86,268.37 0.00 87,413.64 117,816.25 15,296.24 15,296.24 60,934.39 41,435.27 120,344.03 29,441.23 61,150.20 29,441.23 279,916.86 341,954.76 341,954.76 279,916.86 598,540.33 33,771.20 21,131.57 278,565.29 1,072,551.88 1,072,551.88 278,565.29 21,141.31 81,412.49 218,258.32 329,709.21 33,699.01 236,336.77 236,336.77 137,194.62 134,195.42 129,538.15 42,125.09 175,184.06 30,021.87
S (kJ/h)
Ex (kJ/h)
22.38 79.76 54.35 79.76 2.04 2.13 274.32 38.30 247.32 352.06 110.36 354.57 348.71 141.25 141.25 242.92 90.38 352.37 130.68 242.85 130.68 673.96 878.30 878.30 673.96 1441.12 107.75 70.82 790.86 2580.65 2580.65 790.86 71.08 257.57 742.05 1082.79 108.19 581.03 581.03 441.69 542.05 519.84 304.14 804.79 422.89
0.00 16,814.16 7690.43 16,814.16 0.00 2.24 38,957.52 40.37 38,957.52 16,780.22 116.31 17,160.93 44,321.56 1581.95 1581.95 14,184.01 17,524.06 45,701.97 6607.83 14,241.29 6607.83 85,858.42 89,430.72 89,430.73 85,858.42 183,589.26 3278.12 1280.31 51,333.92 329,592.61 329,592.61 51,333.92 831.41 7558.24 6481.92 19,749.98 2693.08 106,119.16 106,119.16 47,128.84 31,186.85 30,102.33 4841.61 37,481.20 2365.09
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Table 2 Exergy-balances at each group of components in the PAFC system for the case of 100% load condition Component
E_ LHV (kJ/h)
E_ x (kJ/h)
E_ BQ x (kJ/h)
E_ lost (kJ/h) x
E_ W x (kJ/h)
Fuel processing system Power system Water treatment system
2266,544.4 2749,719.5 0.0
54,335.4 21434.9 232,740.1
285,858.4 2531,967.5 530,795.6
298,067.4 547,906.1 2498,055.5
0.0 735,220.8 0.0
depend on the level of aggregation crucially. The overall cost-balance equation for the PAFC system, which may be obtained from the first principle in the thermoeconomics [11], is given by
E_ CHE Co þ x
X _ BQ Z_ ic ¼ E_ W x CW þ Ex CBQ
ð26Þ
The calculated unit cost of products should satisfy the above equation.
6. Computer program A computer program for the exergetic and thermoeconomic analyses of a 200-kW PAFC plant has been developed. The program was designed to use the following input data. (a) Standard pressure ðP0 Þ and temperature ðT0 Þ; (b) Fuel compositions and its mass flow rate to the plant, (c) Air composition, relative humidity and its mass flow rate, (d) Pressure (kPa) and temperature (K) for every fluid streams at the inlet and outlet of each component (e) Fuel exergy cost and initial investment for each component. Using these input data, one can calculate the number of moles produced and the corresponding enthalpy of combustion in the various chemical reactions, enthalpy and entropy for fluid streams at various state points. The temperature of one of the outlet streams in heat exchangers was calculated by the heat balance equation. Also the outlet temperature of the hydrogen-rich gas in the [COSC] was calculated by the first law. For the case of mixing of gas streams, the final gas temperature was also estimated by the energy conservation. The net flow rate of various exergy and entropy, the exergy efficiency of the components and the lost exergy occurred in each component were then calculated by using these property values obtained. Once exergy-balances for the components were established, the unit cost of various exergies and products were calculated by solving the costbalance equations for the group of components simultaneously.
7. Results and discussions Table 1 gives details of thermal, mechanical exergy flow rates and entropy flow rates at various state points shown in Fig. 1. These flow rate values were calculated based on the measured property values such as pressures and temperatures and mass flow rates at the points. The enthalpy and entropy of each non-interacting gas species were calculated by using appropriate polynomials [5] fitted into the thermophysical data in the JANAF Tables [15]. Also the values of the physical properties such as enthalpy and entropy for water and steam were evaluated by using the equations suggested by the IFC (International Formulation Committee) [6]. The net flow rates for the various exergies crossing the boundaries of each physical component in the PAFC plant for the case of 100% load condition are shown in Table 2. The positive value of exergies indicate the exergy flow rate of ‘products’ while the negative values represent the exergy flow rate of ‘resource’ or ‘fuel’ in the sense that the product of a component corresponds to the ‘added’ exergy while the resource to the ‘consumed’ one [16] so that the Table itself represents the ‘productive structure’ of the system. The entropy productions in each component play as products in the exergy-balance equations. Considerable entropy generation due to combustion process in the [GASB] can be reduced by the heat transfer to the [RFM] where an endothermic process takes place for the reforming process of steam. In fact, the heat transfer from the [GASB] to the [RFM] at full load condition is about 490,000 kJ/h, which is about 87% of LHV of the fuel consumed in the [GASB]. This is remarkable exergy saving which can be possible in the PAFC plant in the sense that almost 50% chemical exergy is destroyed during combustion process. The productive structure for the PAFC, shown in Table 2 states that electricity is produced by consuming fuel exergy. Table 3 Cost flow rate for each group of components in the PAFC system for the case of 100% load condition Group of components
Co ($/h)
CE ($/h)
CBQ ($/h)
CW ($/h)
Z_ K ($/h)
Fuel processing system 22.186 6.519 20.670 0.0 23.659 Power system 26.148 20.172 24.152 13.804 23.336 Water treatment system 0.0 23.928 4.143 0.0 20.215
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Table 4 Calculated production rate and the corresponding unit cost of electricity and water for the PAFC system at various load conditions with 15 years’ service of the system Load (%)
m _ fuel (kg/h)
E_ LHV;p =E_ LHV;f (kJ/h)
E_ W x (kJ/h)
Electrical efficiency
Overall exergetic efficiency
CW ($/GJ)
CBQ ($/GJ)
50 75 100
18.96 27.72 34.88
576,681.2/930,911.8 836,131.5/1,361,165.1 1,016,263.9/1,681,899.4
367,610.4 551,415.6 735,220.8
39.5 40.5 55.0
59.5 54.3 55.0
30.38 22.80 18.78
8.82 8.30 7.80
E_ LHV;p and E_ LHV;f are the utilized chemical exergy flow of fuel and the lower heating value of the primary fuel flow. The unit cost of fuel Co employed in the calculation is 8.2 $/GJ.
On the other hand, the gas exergy for the reforming process turns out to be produced by consuming steam exergy from the [SWS]. It is inevitable, of course, that some exergy is destructed during this process. The cost flow rates corresponding to the various exergy flow rates at each group of components aggregated in the plant in the case of 100% load condition are given in Table 3. The unit cost value of primary fuel, 5 £ 1023 $/ MJ ( ¼ 0.018 $/kWh) was used in this calculation. However, only 60% of the chemical exergy of the primary fuel is utilized in the fuel cell system so that the unit cost of fuel increases to 8.2 £ 1023 $/MJ in the estimation of the unit cost of products. Same sign convention for the cost flow rates related to the products and resources was used as the case of the exergy-balances shown in Table 2. The overall cost-balance for the system indicates that the cost flow rates of products such as electricity and steam are determined primary from the input cost flow rates of fuel and initial investment. Note that the steam plays a role as fuel rather than product because the heat release in FCS is regarded as steam exergy flow. The unit cost of electricity and hot water (or steam) at various loads estimated by the thermoeconomic analysis of MOPSA are shown in Table 4. Calculation results show that the unit costs of electricity increases significantly at lower loads. However, the overall exergetic efficiency rather increases at lower loads. The reason is that almost same amount of heat with less fuel is recovered by water at part loads. The unit cost of electricity at full load, 0.068 $/kWh ( ¼ 18.78 $/GJ) is higher than that obtained from the 1000 kW gas turbine co-generation plant, 0.054 $/kWh ( ¼ 15.06 $/GJ) [4]. Such higher unit cost of electricity reduces to 0.0526 $/ kWh ( ¼ 14.6 $/GJ), which is comparable to the unit cost of electricity for the 1000-kW gas turbine co-generation plant if the initial investment per power for the PAFC system reduces to 1500 $/kW. The input cost flow rate for the PAFC system, which is represented by the LHS of Eq. (26) is about 15.62 $/h for 100% load, 14.02 $/h for the 75% load and 11.86 $/h for 50% load condition. On the other hand, the values of the RHS of Eq. (26) with the calculated unit cost of products at each load
condition are 15.29, 14.10 and 12.82 $/h, respectively, so that our calculation results have maximum error of 8%. Also the electrical and the overall exergetic efficiency based on the LHV of the primary fuel fed into the system, which are about 43.7 and 55.0%, respectively, at the full load are better than those from any other co-generation plants so that the PAFC plant may be an excellent candidate for a co-generation system if one overcomes long term reliability of the system and the investment cost per power becomes cheaper.
8. Conclusion Thermoeconomic analysis with integrated exergy stream of working fluids has been done to a 200-kW PAFC plant. The calculated cost of electricity, based on the primary fuel cost of 0.018 $/kWh, which is about 0.068 $/kWh is 125% higher than that obtained from the 1000-kW gas turbine co-generation plant. However, this fuel cell system can be viable economically when the initial investment cost per power is reduced to 1500 $/kW.
References [1] Betts DA, Roan VP. Discussion and analysis of fuel gas utilization in a phosphoric acid fuel cell engine during idle operation. In: AES—Vol. 40, Proceedings of the ASME Advanced Energy Systems Division; 2000. p. 283–90. [2] So¨drelund E, Martin AR, Alvfors P, Forman J, Sarko¨zi L. Heat recovery enhancement and operational issues of a 200-kW fuel cell cogeneration plant. In: AES—Vol. 39, Proceedings of the ASME Advanced Energy Systems Division; 1999. p. 297–303. [3] Oh S, Pang H, Kim S, Kwak H. Exergy analysis for a gas turbine cogeneration system. J Eng Gas Turbine Power 1996;118: 782–91. [4] Kim S, Oh S, Kwon Y, Kwak H. Exergoeconomic analysis of thermal system. Energy 1998;23:393–406. [5] Gordon S, Mcbride B. Computer program for calculation of complex chemical equilibrium compositions, rocket performance, incident and reflected shocks, and Chapman– Jougouet detonations. NASA report SP-2773; 1971. [6] JSME steam tables. Japanese Society Of Mechanical Engineers; 1968. [7] Bejan A. Advanced engineering thermodynamics. New York: Wiley; 1997.
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[8] Kim D, Lee H, Kwak H, Hong J. Thermoeconomic analysis of power plants with integrated exergy system. In: AES—Vol. 40, Proceedings of the ASME Advanced Energy Systems Division; 2000. p. 393–404. [9] Lozano MA, Valero A. Theory of the exergetic cost. Energy 1993;18: 939–60. [10] Torres C, Serra L, Valero A, Lozano MA. Theories of system optimization. In: AES—Vol. 36, Proceedings of the ASME Advanced Energy System Division; 1996. p. 429 –36. [11] Moran J. Availability analysis: a guide to efficient energy use. Englewood Cliffs: Prentice-Hill Inc.; 1982.
[12] Kordesch K, Simader G. Fuel cells and their applications. Weinheim: VCH; 1996. [13] Ferguson CR. Internal combustion engines. New York: Wiley; 1986. [14] Kwak H, Byun K, Kwan Y, Yang H. Cost structure of CGAM cogeneration system. Int. J. Energy Research. 2004; 28 (in press). [15] JANAF thermochemical tables. National Bureau of Standard Publications, NSRDS-N3537, Washington, DC; 1971. [16] Lazzaretto A, Tsatsaronis G. On the guest for objective equation in exergy costing. In: AES—Vol. 37, Proceedings of the ASME Advanced Energy Systems Division; 1997. p. 197 –210.
Exergetic and thermoeconomic analysis of a 200-kW phosphoric acid fuel cell plant Ho-Young Kwaka,*, Hyun-Soo Leea, Jung-Yeul Junga, Jin-Seok Jeonb, Dal-Ryung Parkb a
Mechanical Engineering Department, Chung-Ang University, 221, Huksuk-Dong, Dongjak-Ku, Seoul 156-756, South Korea b R&D Center, Korea Gas Corporation, Ansan 425-790, South Korea Received 9 February 2002; revised 9 February 2002; accepted 7 April 2004; available online 4 May 2004
Abstract Exergetic and thermoeconomic analysis were performed for a 200-kW phosphoric acid fuel cell plant which offers many advantages for co-generation in the aspect of high electrical efficiency and low emission. This analytical study was based on the data obtained by in-field measurement of PC25C fuel cell plant to find whether this system is viable economically. For 100% load condition, the electrical efficiency obtained, 43.7% turned out to be much better than that for the 1000-kW gas turbine co-generation plant. However, the calculated unit cost of electricity with the initial investment cost per power of fuel cell plant of 3000 $/kW, 0.068 $/kWh turned out to be 125% higher than the cost obtained for the 1000-kW gas turbine co-generation plant. This fuel cell system may be viable economically when the initial investment cost per power is reduced to the level of the gas turbine co-generation plant of 1500 $/kW. q 2004 Elsevier Ltd. All rights reserved. Keywords: Exergy analysis; Fuel cell plant; Modified Productive structure; Phosphoric acid fuel cell; Thermoeconomic analysis
1. Introduction Exergetic analysis permits to predict the performance of energy systems as well as the efficiency of each component of the systems. On the other hand, thermoeconomic analysis provides a tool to estimate the unit cost of products properly and the monetary loss associated with the entropy generation in the components of the system. One of the merits of the fuel cell system is that considerable entropy generation occurred during combustion process inevitably at gas burner can be saved by reformer where endothermic reaction takes place, even though only 40% of the chemical exergy of natural gas is utilized to produce electricity at fuel cell stack and the life time of the system is shorter [1]. In this study, exergetic and thermoeconomic analysis were performed for a 200-kW phosphoric acid fuel cell (PAFC) plants which offers many advantages for co-generation in the aspect of high electrical efficiency and low emissions [2] to find whether the system is viable economically. This system analysis based on the detailed conservation laws employed the data obtained by * Corresponding author. Tel.: þ 82-28205278; fax: þ 82-28267464. E-mail address: [email protected] (H.-Y. Kwak). 0016-2361/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.fuel.2004.04.002
the in-field measurement of PC25C fuel cell power plant (ONSI corporation), installed and operated at Korea Gas Corporation. The exergy-balance equation developed by Oh et al. [3] and the corresponding cost-balance equation by Kim et al. [4] were utilized in this analysis. Detail computational works on the estimation of property values were done by using the polynomial for gases [5] and the equations suggested by International Formulation Committee for water and steam [6]. For hydrocarbon fuels, Benedict – Webb –Rubin equation of state [7] was utilized. Rearrangement of the components depending on their function of the PAFC system was done to apply the developed cost-balance equation with integrated exergy stream [8] to the system concerned. The performance and the unit cost of products of the system were evaluated at various loads. For 100% load condition, the electrical efficiency of the PAFC system was about 43.7%, which turned out to be much better than that for the 1000-kW gas turbine cogeneration plant [4]. However, the calculated unit cost of electricity with the initial investment cost of fuel cell plant of 3000 $/kW, 0.068 $/kWh turned out to be 125% higher than the cost obtained for the gas turbine co-generation plant.
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2. Cost-balance equation based on modified productive structure analysis
the annualized cost by using the capital recovery factor CRFði; nÞ; i.e.
A general exergy-balance equation that is applicable to any component of thermal system may be formulated by utilizing the first and second law of thermodynamics [3]. With some modification on the exergy-balance equation for the non-adiabatic components to account the exergy losses due to heat transfer, the general exergy-balance equation may be written as with integrated exergy stream 0 1 ! X X X X BQ BQ A @ _ECHE _ _ _ _ þ Ex;i 2 Ex;j þ Ex;i 2 Ex;j x
C_ ð$=yearÞ ¼ PW £ CRFði; nÞ
output
input
X
þ To
S_ i 2
inlet
X
inlet
outlet
!
_ CV =T ¼ E_ W S_ j þ Q
ð1Þ
output
input
þTo
inlet
S_ i 2
Dividing the levelized cost by 8000 annual operating hours, we obtain the following capital cost for the kth component of the plant. Z_ k ¼ fk C_ k =ð3600 £ 8000Þ
ð5Þ
The maintenance cost is taken into consideration through the factor of fk ¼ 1:06 for each plant component whose expected life is assumed to be 15 years.
outlet
where E_ and S_ denote the flow rate of exergy and entropy, _ CV in the fifth term denotes the heat respectively, and Q transfer interaction between a component and environment. The superscripts CHE, BQ and W denote chemical exergy, steam and work (or electricity), respectively. Assigning a unit exergy cost to each decomposed exergy system, the cost-balance equation corresponding to the exergy-balance equation given in Eq. (1) may be written as 0 1 ! X BQ X BQ X X CHE E_ x Co þ@ E_ x;i 2 E_ x;j ACBQ þ E_ x;i 2 E_ x;j CE X
ð4Þ
X
!
inlet
outlet
_ CV =To CS þZ_ ½k ¼ E_ W CW S_ j 2Q
ð2Þ
outlet
where Co ;CBQ ;CE ;CS and CW are the unit cost of fuel, steam, gas exergy and negentropy, and electricity, respectively. The term Z_ ½k includes all financial charges associated with owning and operating the kth plant component. Eqs. (1) and (2) are two basic equations used in this analysis. We call the exergy-costing method based on these equations as modified productive structure analysis (MOPSA) one in the sense that the cost-balance equation given in Eq. (2) yields the productive structure of thermal system at hand [4], which has been suggested and developed by Lozano and Valero [9] and Torres et al. [10].
3. Cost equation for plant component All costs due to owing and operating a plant depend on the type of financing, required capital, expected life of a component, etc. The annualized (levelized) cost method of Moran [11] was employed in this study. The amortization cost for a particular plant component may be written as present worth (PW) PW ¼ Ci 2 Sn PWFði; nÞ
ð3Þ
where Ci is initial investment cost and PWFði; nÞ is the PW factor. The PW of the component may be converted to
4. System descrition for 200-kW phosphoric acid fuel cell plant A schematic of a 200-kW phosphoric acid fuel cell (PAFC) is given in Fig. 1, and shows every state point which we accounted for in this analysis. Every state in the plant is described by three digits. The first digit indicates a specific fluid stream (0 for natural gas, 1 for air, 2 for hydrogen-rich gas, 3 for steam, 4 for water and 5 for flue gas), and the second digit indicates each component in the plant (1 for the first heat exchanger [HTX1], 2 for CO shift converter [COSC], 3 for reformer [RFM], 4 for gas burner [GASB], 5 for the air preheater [HTX2], 6 for fuel cell stack [FCS], 7 for the third heat exchanger [HTX3], 8 for steam/water separator [SWS] and 9 for the fourth heat exchanger [HTX4]). The final digit indicates the inlet (1) and outlet (2) stream of working fluids at each component. The fuel cell plant consists of fuel process system ([HTX1], [COSC], [RFM], and [GASB]) which converts natural gas into hydrogen-rich gas, power system ([FCS]) which converts chemical exergy of gas into electricity by electrochemical process and thermal management system ([SWS], [HTX4], and water treatment system [WTS]). At full load condition, the air to [GASB] and the fuel flow rate to the system are approximately 248 and 35 kg/h, respectively. The air flow rate to the cathode in [FCS] at the full load is about 678 kg/h. Part load condition can be achieved by controlling the air flow rate to [GASC] and to the cathode in [FCS] and the fuel flow rate to [RFM]. More detailed description including the first law of thermodynamics for the major components is as follows. 4.1. Fuel process system Hydrogen-rich gas needed for the electrochemical reaction in [FCS] can be produced from the natural gas (primary CH4) via the reforming process of steam from [HTX1]. The possible reactions in the reforming process
H.-Y. Kwak et al. / Fuel 83 (2004) 2087–2094
2089
Fig. 1. Schematic of 200-kW phosphoric acid fuel cells (PAFC) system (modified from Ref. [12]).
[12] are given as 1 Cn Hm þ 2nH2 O ! nCO2 þ 2n þ m H2 2 1 Cn Hm þ nH2 O ! nCO þ n þ m H2 2
ð6Þ
reactant
product
ð7Þ
The chemical reaction in [RFM] including these endothermic reactions may be written as aCaj Hbj þ bCak Hbk þ cCal Hbl þ dCam Hbm þ yH2 O
1 ! fnat CO2 þ ð1 2 f Þnat CO þ ð1 þ f Þnat þ nbt H2 2
þ y 2 ð1 þ f Þnat H2 O ð8Þ where aaj þ bak þ cal þ dam ¼ nat ; abj þ b b k þ c bl þ d bm ¼ n b t ; and f is the ratio of the reaction given in Eq. (6) to the reaction given in Eq. (7), which may be determined from the heat balance for [RFM] and [GASB]. The value of f which affects the outlet temperature of the hydrogen-rich gas stream in [HTX1] is about 0.795 –0.80. Applying the first law to [RFM], we obtain QRFM þ QEX RFM ¼ hRP;RFM
where h RP;RFM is the enthalpy of combustion for the reaction given in Eq. (8), which is given by X X e2 i h RP;RFM ¼ ne ðh 0f þDhÞ ni ðh 0f þDhÞ
ð9Þ
¼fnat ðh 0f ÞCO2 þð12f Þnat ðh 0f ÞCO 2ð1þf Þnat ðh 0f ÞH2 O 2aðh 0f ÞCaj Hbj 2bðh 0f ÞCa Hb 2cðh 0f ÞCa Hb k k l l n 0 CO þð12f Þnat ðDhÞ CO 2dðh f ÞC H þ fnat ðDhÞ am
bm
2
1 H þ½y2ð1þf Þnat þð1þf Þnat þ nbt ðDhÞ 2 o 2 n HO C H þbðDhÞ C H ðDhÞ 2 aðDhÞ 2 aj bj ak bk Te;RFM o C H þdðDhÞ C H þyðDhÞ HO þcðDhÞ ð10Þ a b am bm 2 l
l
Ti;RFM
where h 0f is the enthalpy of formation and Dh is the sensible enthalpy. The heat transfer rates, QRFM and QEX RFM are heat exchange with environment and gas burner, respectively. The reformed hydrogen-rich gas is cooled by the natural gas and steam in [HTX1], and the remaining CO gas from [RFM] is converted to CO2 in [COSC] through the following reaction. These gases are fed into the anode in [FCS].
1 fnat CO2 þ ð1 2 f Þnat CO þ ð1 þ f Þnat þ nbt H2 2 þ ½y 2 ð1 þ f Þnat H2 O ! pCO þ ðnat 2 pÞCO2
1 þ ð2nat 2 pÞ þ nbt H2 þ ½y 2 2nat þ pH2 O 2
ð11Þ
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The concentration of CO gas leaving [COSC] may be estimated by the following equation ½CO2 ½H2 KP ðTÞ ½CO ¼ ½H2 O
ð12Þ
where [ ] in Eq. (12) denotes gas concentration and KP ðTÞ is the equilibrium constant for the reaction, CO þ H2 O ! CO2 þ H2 [13].The first law in [COSC] is given by C C H þbðDhÞ ½aðDhÞ aj bj a
k
Hbk
C H þdðDhÞ C H T þcðDhÞ a b am b m i;COSC l
l
C H þbðDhÞ C þQCOSC ¼ h RP;COSC þ½aðDhÞ aj bj a
k
H bk
C H þdðDhÞ C H T þcðDhÞ a b am bm e;COSC l
ð13Þ
l
where QCOSC is the heat exchange with environment and the h RP;COSC is the enthalpy of combustion for the reaction given in Eq. (11). That is h RP;COSC ¼½p2ð12f Þnat ½ðh 0f ÞCO 2ðh 0f ÞCO2 þðh 0f ÞH2 O n CO CO þðnat 2pÞðDhÞ þ pðDhÞ 2 1 H þ½y22nat þp þ 2nat þ nbt 2p ðDhÞ 2 2 o n CO HO 2 fnat ðDhÞ ðDhÞ 2 2 Te;COSC
CO þ ð1þf Þnat þ 1 nbt ðDhÞ H þð12f Þnat ðDhÞ 2 2 o HO þ½y2ð1þf ÞðDhÞ ð14Þ 2
nwv ¼ nwvH þnwvG The first law in [GASB] may be written as QGASB 2QEX RFM ¼ hRP;GASB
ð16Þ
where QGASB is the heat exchanger with environment and h RP;GASB is the enthalpy of combustion for the reaction given in Eq. (15). This is given by
1 h RP;GASB ¼ðn0at þpÞðh 0f ÞCO2 þ ðnbt þn0bt Þþ2nat 22g2p 2 0 0 0 ðhf ÞH2 O 2a ðhf ÞCaj Hbj 2b0 ðh 0f ÞCa Hb 2c0 ðh 0f ÞCa Hb k k l l n 0 0 0 2d ðhf ÞCam Hbm þ ðnat þnat ÞðDhÞCO2
1 0 HO þ ðnbt þnbt Þþnwv þy22g ðDhÞ 2 2
1 O þ ðnto þgÞ2ðnat þn0at Þ2 ðnbt þn0bt Þ ðDhÞ 2 4 N þ0:044nto ðDhÞ Ar gT þ3:728nto ðDhÞ 2 e;GASB n Ar 2 nto ðDhÞO2 þ3:728nto ðDhÞN2 þ0:044nto ðDhÞ H O þeðDhÞ H þ½nwv þy22nat þpðDhÞ 2 2 0 þðnat 2pÞðDhÞCO þpðDhÞCO þa ðDhÞC 2
2b0 ðh 0f ÞCa
H 2c k bk
0
aj H bj
ðh 0f ÞCa Hb 2d 0 ðh 0f ÞCam Hbm l
l
o Ti;GASB
ð17Þ
Ti;COSC
The heat required for the endothermic reactions in [RFM] is supplied from the combustion process in [GASB]. The unconsumed hydrogen-rich gas after the anodic reaction in [FCS] with additional natural gas from line are burned with heated air from [HTX2]. This combustion process in [GASB] may be described as a0 Caj Hbj þb0 Cak Hbk þc0 Cal Hbl þd0 Cam Hbm þnto O2 þ3:728nto N2 þ0:044nto Arþ½nwv þy22nat þpH2 O
where
The PAFC stack, which has been used in co-generation system produces electricity and heat from the reaction of hydrogen and oxygen. The primary reaction in [FCS] are given as Anode : 2H2 ! 4Hþ þ 4e2
ð18Þ
Cathode : O2 þ 4Hþ þ 4e2 ! 2H2 O
ð19Þ
So that the overall reaction is as
þeH2 þðnat 2pÞCO2 þpCO!ðnat þn0at ÞCO2
1 0 þ ðnbt þnbt Þþnwv þy22g H2 O 2
1 0 0 þ ðnto þgÞ2ðnat þnat Þ2 ðnbt þnbt Þ O2 4 þ3:728nto N2 þ0:044nto Ar
4.2. Power system
2H2 þ O2 ! 2H2 O þ HEAT
ð15Þ
Assuming that only 2 g kmol among the hydrogen gas from [COSC] participates in the above anodic reaction, all the gases such as N2 and O2 escaped through cathode and anode in [FCS] may be written as 1 pCO þ ðnat 2 pÞCO2 þ 2nat þ nbt 2 p 2 2g H2 2
n0at ¼ a0 aj þb0 ak þc0 al þd0 am
þ ½y 2 2nat þ pH2 O ðanodeÞ þ ðntoH3 2 gÞO2
n0bt ¼ a0 bj þb0 bk þc0 bl þd0 bm
þ 3:728ntoH3 N2 þ 0:044ntoH3 Ar þ nwvH3 H2 O þ ð2gÞ
1 e ¼ 2nat þ nbt 2p22g 2
H2 O ðcathodeÞ
nto ¼ ntoH þntoG
ð20Þ
ð21Þ
The value of g is to be determined by the input flow rate of fuel and air to the system.
H.-Y. Kwak et al. / Fuel 83 (2004) 2087–2094
2091
The electricity produced from the above reaction is given as WT ¼ 131:74ghFCS kJ=kmol
ð22Þ
where hFCS is the efficiency of the FCS. The heat release inside components due to condensation or any other chemical reaction described in Eq. (20) was treated as a kind of water (or steam) exergy in this analysis because the heat released contributes increases the water (or steam) exergy.
5. Cost-balance equations In the fuel cell plant, the species of the fluid streams change after reforming or any other chemical processes. So, it is convenient to divide all the working fluids as gas and water (or steam) stream simply. Also it is better to use integrated exergy without decomposing the exergy stream into thermal and mechanical exergy. In this case, the concept of junction and branch related to thermal and mechanical exergy is no longer needed so that the number of unknowns for the unit exergy costs are considerably reduced. Therefore, the cost-balance equation given in Eq. (2) should be applied to an appropriate component or a group of component depending on the function of its principal product in the energy system. For example, all the components in the fuel cell plant may be rearranged into four groups of components and a system boundary to provide sufficient but not redundant cost-balance equations. The groups of components are (1) the first heat exchanger, and CO shift converter, reformer, gas burner and air preheater for the fuel process system (2) fuel cell stack and the third heat exchanger for power system (3) steam/water separator, the fourth heat exchanger and system boundary for the water treatment system. The cost-balance equations for those groups of components yield the unit cost of each exergy. These are unit costs of gas stream, CE ; electricity, CW ; and steam exergy, CBQ : All the cost-balance equations formulated for fuel cell plant are as follows.
(1) Fuel process system ([HTX1], [COSC], [GASB], [RFM], and [HTX2]) ðE_ LHV;2 þ E_ LHV;3 þ E_ LHV;4 ÞCo þðE_ x;011 þ E_ x;041 þ E_ x;141 þ E_ x;151 þ E_ x;241 2 E_ x;552 2 E_ x;222 ÞCE þ E_ x;311 CBQ þðZ_ HTX1 þ Z_ COSC þ Z_ GASB þ Z_ RFM þ Z_ HTX2 Þ¼0 ð23Þ (2) Power system ([FCS] and [HTX3]) E_ LHV;6 Co þðE_ x;171 þ E_ x;261 2 E_ x;572 2 E_ x;262 ÞCE þðE_ x;461 2 E_ x;462 ÞCBQ þðZ_ FCS þ Z_ HTX3 Þ¼ E_ W CW ð24Þ
(3) Water treatment system ([SWS], [HTX4], [WTS], and system boundary) ðE_ x;591 2 E_ x;592 ÞCE þðE_ x;481 þ E_ x;485 þ E_ x;491 2 E_ x;382 2 E_ x;384 2 E_ x;461 2 E_ x;492 ÞCBQ þðZ_ SWS þ Z_ HTX4 þ Z_ WTS Þ¼0 ð25Þ
The cost structure of the thermal system turned out to be dependent on the chosen level of aggregation that specifies the subsystems [10,14]. In this study, the cost-balance equations for the PAFC system were formulated based on the lowest level of aggregation, which are represented by Eqs. (23) –(25) because the unit cost of products does not Table 1 Property values and enthalpy, entropy and exergy at various state points in the PAFC system for the case of 100% load condition State m _ (kg/h) T (K)
P (kPa) H (kJ/h)
011 34.24 012 34.24 021 34.24 022 34.24 041 0.64 141 13.04 143 234.92 151 234.92 152 234.92 161 677.63 171 677.63 172 677.63 211 135.35 212 135.35 221 135.35 222 135.35 231 34.24 232 135.35 241 122.85 261 135.35 262 122.85 311 101.10 312 101.10 331 101.10 382 101.10 384 216.18 4101 101.10 4102 100.63 461 387.32 462 387.32 481 387.32 482 387.32 483 101.00 485 216.00 491 1212.00 492 1212.00 494 101.10 542 371.44 551 371.44 552 371.44 562 689.39 571 689.39 572 689.39 591 1060.83 592 959.73
101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30 790.20 101.30 101.30 790.20 792.00 792.00 792.00 790.20 800.00 800.00 790.20 792.00 792.00 101.30 101.30 792.00 101.30 101.30 101.30 101.30 101.30 101.30 101.30 101.30
288.15 723.15 573.15 723.15 288.15 298.15 703.15 298.15 703.15 423.15 298.15 424.96 823.15 343.08 343.08 463.15 723.15 823.15 453.15 463.15 453.15 443.15 723.15 723.15 443.15 443.15 353.15 323.15 443.15 443.15 443.58 443.15 323.15 363.15 316.15 338.15 353.15 820.00 820.00 611.10 463.15 463.15 352.15 442.82 323.20
2697.29 39,785.03 23,338.37 39,785.03 212.97 0.00 99,146.45 0.00 99,146.45 86,268.37 0.00 87,413.64 117,816.25 15,296.24 15,296.24 60,934.39 41,435.27 120,344.03 29,441.23 61,150.20 29,441.23 279,916.86 341,954.76 341,954.76 279,916.86 598,540.33 33,771.20 21,131.57 278,565.29 1,072,551.88 1,072,551.88 278,565.29 21,141.31 81,412.49 218,258.32 329,709.21 33,699.01 236,336.77 236,336.77 137,194.62 134,195.42 129,538.15 42,125.09 175,184.06 30,021.87
S (kJ/h)
Ex (kJ/h)
22.38 79.76 54.35 79.76 2.04 2.13 274.32 38.30 247.32 352.06 110.36 354.57 348.71 141.25 141.25 242.92 90.38 352.37 130.68 242.85 130.68 673.96 878.30 878.30 673.96 1441.12 107.75 70.82 790.86 2580.65 2580.65 790.86 71.08 257.57 742.05 1082.79 108.19 581.03 581.03 441.69 542.05 519.84 304.14 804.79 422.89
0.00 16,814.16 7690.43 16,814.16 0.00 2.24 38,957.52 40.37 38,957.52 16,780.22 116.31 17,160.93 44,321.56 1581.95 1581.95 14,184.01 17,524.06 45,701.97 6607.83 14,241.29 6607.83 85,858.42 89,430.72 89,430.73 85,858.42 183,589.26 3278.12 1280.31 51,333.92 329,592.61 329,592.61 51,333.92 831.41 7558.24 6481.92 19,749.98 2693.08 106,119.16 106,119.16 47,128.84 31,186.85 30,102.33 4841.61 37,481.20 2365.09
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Table 2 Exergy-balances at each group of components in the PAFC system for the case of 100% load condition Component
E_ LHV (kJ/h)
E_ x (kJ/h)
E_ BQ x (kJ/h)
E_ lost (kJ/h) x
E_ W x (kJ/h)
Fuel processing system Power system Water treatment system
2266,544.4 2749,719.5 0.0
54,335.4 21434.9 232,740.1
285,858.4 2531,967.5 530,795.6
298,067.4 547,906.1 2498,055.5
0.0 735,220.8 0.0
depend on the level of aggregation crucially. The overall cost-balance equation for the PAFC system, which may be obtained from the first principle in the thermoeconomics [11], is given by
E_ CHE Co þ x
X _ BQ Z_ ic ¼ E_ W x CW þ Ex CBQ
ð26Þ
The calculated unit cost of products should satisfy the above equation.
6. Computer program A computer program for the exergetic and thermoeconomic analyses of a 200-kW PAFC plant has been developed. The program was designed to use the following input data. (a) Standard pressure ðP0 Þ and temperature ðT0 Þ; (b) Fuel compositions and its mass flow rate to the plant, (c) Air composition, relative humidity and its mass flow rate, (d) Pressure (kPa) and temperature (K) for every fluid streams at the inlet and outlet of each component (e) Fuel exergy cost and initial investment for each component. Using these input data, one can calculate the number of moles produced and the corresponding enthalpy of combustion in the various chemical reactions, enthalpy and entropy for fluid streams at various state points. The temperature of one of the outlet streams in heat exchangers was calculated by the heat balance equation. Also the outlet temperature of the hydrogen-rich gas in the [COSC] was calculated by the first law. For the case of mixing of gas streams, the final gas temperature was also estimated by the energy conservation. The net flow rate of various exergy and entropy, the exergy efficiency of the components and the lost exergy occurred in each component were then calculated by using these property values obtained. Once exergy-balances for the components were established, the unit cost of various exergies and products were calculated by solving the costbalance equations for the group of components simultaneously.
7. Results and discussions Table 1 gives details of thermal, mechanical exergy flow rates and entropy flow rates at various state points shown in Fig. 1. These flow rate values were calculated based on the measured property values such as pressures and temperatures and mass flow rates at the points. The enthalpy and entropy of each non-interacting gas species were calculated by using appropriate polynomials [5] fitted into the thermophysical data in the JANAF Tables [15]. Also the values of the physical properties such as enthalpy and entropy for water and steam were evaluated by using the equations suggested by the IFC (International Formulation Committee) [6]. The net flow rates for the various exergies crossing the boundaries of each physical component in the PAFC plant for the case of 100% load condition are shown in Table 2. The positive value of exergies indicate the exergy flow rate of ‘products’ while the negative values represent the exergy flow rate of ‘resource’ or ‘fuel’ in the sense that the product of a component corresponds to the ‘added’ exergy while the resource to the ‘consumed’ one [16] so that the Table itself represents the ‘productive structure’ of the system. The entropy productions in each component play as products in the exergy-balance equations. Considerable entropy generation due to combustion process in the [GASB] can be reduced by the heat transfer to the [RFM] where an endothermic process takes place for the reforming process of steam. In fact, the heat transfer from the [GASB] to the [RFM] at full load condition is about 490,000 kJ/h, which is about 87% of LHV of the fuel consumed in the [GASB]. This is remarkable exergy saving which can be possible in the PAFC plant in the sense that almost 50% chemical exergy is destroyed during combustion process. The productive structure for the PAFC, shown in Table 2 states that electricity is produced by consuming fuel exergy. Table 3 Cost flow rate for each group of components in the PAFC system for the case of 100% load condition Group of components
Co ($/h)
CE ($/h)
CBQ ($/h)
CW ($/h)
Z_ K ($/h)
Fuel processing system 22.186 6.519 20.670 0.0 23.659 Power system 26.148 20.172 24.152 13.804 23.336 Water treatment system 0.0 23.928 4.143 0.0 20.215
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Table 4 Calculated production rate and the corresponding unit cost of electricity and water for the PAFC system at various load conditions with 15 years’ service of the system Load (%)
m _ fuel (kg/h)
E_ LHV;p =E_ LHV;f (kJ/h)
E_ W x (kJ/h)
Electrical efficiency
Overall exergetic efficiency
CW ($/GJ)
CBQ ($/GJ)
50 75 100
18.96 27.72 34.88
576,681.2/930,911.8 836,131.5/1,361,165.1 1,016,263.9/1,681,899.4
367,610.4 551,415.6 735,220.8
39.5 40.5 55.0
59.5 54.3 55.0
30.38 22.80 18.78
8.82 8.30 7.80
E_ LHV;p and E_ LHV;f are the utilized chemical exergy flow of fuel and the lower heating value of the primary fuel flow. The unit cost of fuel Co employed in the calculation is 8.2 $/GJ.
On the other hand, the gas exergy for the reforming process turns out to be produced by consuming steam exergy from the [SWS]. It is inevitable, of course, that some exergy is destructed during this process. The cost flow rates corresponding to the various exergy flow rates at each group of components aggregated in the plant in the case of 100% load condition are given in Table 3. The unit cost value of primary fuel, 5 £ 1023 $/ MJ ( ¼ 0.018 $/kWh) was used in this calculation. However, only 60% of the chemical exergy of the primary fuel is utilized in the fuel cell system so that the unit cost of fuel increases to 8.2 £ 1023 $/MJ in the estimation of the unit cost of products. Same sign convention for the cost flow rates related to the products and resources was used as the case of the exergy-balances shown in Table 2. The overall cost-balance for the system indicates that the cost flow rates of products such as electricity and steam are determined primary from the input cost flow rates of fuel and initial investment. Note that the steam plays a role as fuel rather than product because the heat release in FCS is regarded as steam exergy flow. The unit cost of electricity and hot water (or steam) at various loads estimated by the thermoeconomic analysis of MOPSA are shown in Table 4. Calculation results show that the unit costs of electricity increases significantly at lower loads. However, the overall exergetic efficiency rather increases at lower loads. The reason is that almost same amount of heat with less fuel is recovered by water at part loads. The unit cost of electricity at full load, 0.068 $/kWh ( ¼ 18.78 $/GJ) is higher than that obtained from the 1000 kW gas turbine co-generation plant, 0.054 $/kWh ( ¼ 15.06 $/GJ) [4]. Such higher unit cost of electricity reduces to 0.0526 $/ kWh ( ¼ 14.6 $/GJ), which is comparable to the unit cost of electricity for the 1000-kW gas turbine co-generation plant if the initial investment per power for the PAFC system reduces to 1500 $/kW. The input cost flow rate for the PAFC system, which is represented by the LHS of Eq. (26) is about 15.62 $/h for 100% load, 14.02 $/h for the 75% load and 11.86 $/h for 50% load condition. On the other hand, the values of the RHS of Eq. (26) with the calculated unit cost of products at each load
condition are 15.29, 14.10 and 12.82 $/h, respectively, so that our calculation results have maximum error of 8%. Also the electrical and the overall exergetic efficiency based on the LHV of the primary fuel fed into the system, which are about 43.7 and 55.0%, respectively, at the full load are better than those from any other co-generation plants so that the PAFC plant may be an excellent candidate for a co-generation system if one overcomes long term reliability of the system and the investment cost per power becomes cheaper.
8. Conclusion Thermoeconomic analysis with integrated exergy stream of working fluids has been done to a 200-kW PAFC plant. The calculated cost of electricity, based on the primary fuel cost of 0.018 $/kWh, which is about 0.068 $/kWh is 125% higher than that obtained from the 1000-kW gas turbine co-generation plant. However, this fuel cell system can be viable economically when the initial investment cost per power is reduced to 1500 $/kW.
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