Analysis of Energy, Exergy and Ecology Characteristics of Phosphoric Acid Fuel Cell

doi:10.12096/j.2096-4528.pgt.21040

Abstract

Abstract:

Phosphoric acid fuel cell (PAFC) has become one of the fastest growing commercial fuel cells due to its short start-up time, no pollution and simple structure. According to the first and second laws of thermodynamics, the energy, exergy and ecology performances of PAFC were studied. The mathematical expressions of electric efficiency, output power, exergy destruction rate, exergy efficiency, ecological function and ecological coefficient of performance for fuel cell were derived. Considering the trade-off between various optimization criteria, the optimal working area of PAFC under different performance parameters was obtained. Finally, the effects of some main operating conditions and design parameters on the performance of PAFC system were discussed in detail. This work considers the benefits and losses of energy from the perspective of protecting natural resources, and the results can provide some theoretical support for the design of high-performance PAFC system.

Key words: phosphoric acid fuel cell (PAFC), energy efficiency, exergy, ecology characteristics

CLC Number:

TK 02

Xinru GUO, Yumin GUO, Fang LUO, Jiangfeng WANG, Pan ZHAO. Analysis of Energy, Exergy and Ecology Characteristics of Phosphoric Acid Fuel Cell[J]. Power Generation Technology, 2022, 43(1): 73-82.

Figures/Tables 14

Fig. 1 Schematic diagram of PAFC system

Tab. 1 Thermodynamic parameters for H2, O2 and H2O

i	$Δ g 0$ /(J·mol^-1)	$Δ h 0$ /(J·mol^-1)	$Δ s 0$ /(J·mol^-1)	$C m$ /(J·mol^-1·K^-1)	$L v$ /(J·mol^-1)	$ε c h e m, i 0$ /(J·mol^-1)
H₂(g)	0	0	131	27.28+0.003 26T+50 000/T²	—	236 090
O₂(g)	0	0	205	29.96+0.004 18T-167 000/T²	—	3 970
H₂O(g)	—	—	—	30.00+0.010 17T+33 000/T²	40 700	—
H₂O(l)	237 200	285 800	70	75.44	—	9 500

Tab. 1 Thermodynamic parameters for H2, O2 and H2O

i	$Δ g 0$ /(J·mol^-1)	$Δ h 0$ /(J·mol^-1)	$Δ s 0$ /(J·mol^-1)	$C m$ /(J·mol^-1·K^-1)	$L v$ /(J·mol^-1)	$ε c h e m, i 0$ /(J·mol^-1)
H₂(g)	0	0	131	27.28+0.003 26T+50 000/T²	—	236 090
O₂(g)	0	0	205	29.96+0.004 18T-167 000/T²	—	3 970
H₂O(g)	—	—	—	30.00+0.010 17T+33 000/T²	40 700	—
H₂O(l)	237 200	285 800	70	75.44	—	9 500

Tab. 2 Parameters of PAFC system

参数	数值	参数	数值
F/(C·mol^-1)	96 485	$b$	0.000 03
R/(J·mol^-1·K^-1)	8.314	$c$	0.000 8
$n e$	2	α	0.5
p/Pa	101 325	j₀/(A·m^-2)	0.06
T/K	453	t_ele/m	0.002
T₀/K	298	A/m²	0.001 5

Tab. 2 Parameters of PAFC system

参数	数值	参数	数值
F/(C·mol^-1)	96 485	$b$	0.000 03
R/(J·mol^-1·K^-1)	8.314	$c$	0.000 8
$n e$	2	α	0.5
p/Pa	101 325	j₀/(A·m^-2)	0.06
T/K	453	t_ele/m	0.002
T₀/K	298	A/m²	0.001 5

Fig. 2 Change curves of Erev, Econ, Eact, Eohm and U with j

Fig. 3 Energy, exergy and ecology performances of PAFC

Tab. 3 Comparison of some key performance parameters

i	$η i$ /%	$Ω i *$ /(W·m^-2)	$φ i$ /%	$ϕ i$ /%
增率/%	29.3	-55.1	29.1	66.7
P	43.7	7 629.1	44.4	1.2
E	56.5	3 425.5	57.3	2.0

Tab. 3 Comparison of some key performance parameters

i	$η i$ /%	$Ω i *$ /(W·m^-2)	$φ i$ /%	$ϕ i$ /%
增率/%	29.3	-55.1	29.1	66.7
P	43.7	7 629.1	44.4	1.2
E	56.5	3 425.5	57.3	2.0

Fig. 4 Variations of exergy efficiency and ecology function densitywith power density

Fig. 5 Effect of working temperature T on output voltage U

Fig. 7 Effect of operating pressure p on reversible potential Erev

Fig. 8 Effect of operating pressure p on output power density, exergy efficiency andecology function density

Fig. 9 Effect of electrolyte thickness tele on output power density, exergy efficiency andecology function density

Fig. 10 Effect of exchange current density j0 on activation overpotential Eact

Fig. 11 Effect of exchange current density j0 on output power density, exergy efficiency and ecology function density

References 49

1	刘旭坡，张运丰，邓邵峰，等．燃料电池用聚合物质子交换膜的研究进展[J]．电化学，2020，26(1)：103-120． doi:10.13208/j.electrochem.181217
	LIU X， ZHANG Y， DENG S，et al ．Research progresses in polymeric proton exchange membranes for fuel cells[J]．Journal of Electrochemistry，2020，26(1)：103-120． doi:10.13208/j.electrochem.181217
2	MORADI M， MEHRPOOYA M ．Optimal design and economic analysis of a hybrid solid oxide fuel cell and parabolic solar dish collector，combined cooling，heating and power (CCHP) system used for a large commercial tower[J]．Energy，2017，130(1)：530-543． doi:10.1016/j.energy.2017.05.001
3	薛晓东，韩巍，王晓东，等．适合分布式冷热电联供系统的中小型发电装置[J]．发电技术，2020，41(3)：252-260． doi:10.12096/j.2096-4528.pgt.20031
	XUE X D， HAN W， WANG X D，et al ．Small and medium-scale power generation devices suiting for distributed combined cooling, heating and power system[J]．Power Generation Technology，2020，41(3)：252-260． doi:10.12096/j.2096-4528.pgt.20031
4	张伟，向洪坤．燃料电池汽车基本技术及发展综述[J]．智慧电力，2020，48(4)：36-41． doi:10.3969/j.issn.1673-7598.2020.04.006
	ZHANG W， XIANG H K ．Review on basic technology and development of fuel cell vehicle[J]．Smart Power，2020，48(4)：36-41． doi:10.3969/j.issn.1673-7598.2020.04.006
5	陈骞，周竞，陆翌，等．一种适用于燃料电池-超级电容发电系统的控制策略[J]．浙江电力，2021，40(1)：116-122．
	CHEN Q， ZHOU J， LU Y，et al ．A control strategy for fuel cell-ultracapacitor power generation system[J]．Zhejiang Electric Power，2021，40(1)：116-122．
6	WILAILAK S， YANG J H， HEO C G，et al ．Thermo-economic analysis of phosphoric acid fuel-cell (PAFC) integrated with organic ranking cycle (ORC)[J]．Energy，2021，220(1)：119744． doi:10.1016/j.energy.2020.119744
7	ITO H ．Economic and environmental assessment of phosphoric acid fuel cell-based combined heat and power system for an apartment complex[J]．International Journal of Hydrogen Energy，2017，42(23)：15449-15463． doi:10.1016/j.ijhydene.2017.05.038
8	WANG S， JIANG S P ．Prospects of fuel cell technologies[J]．National Science Review，2017，4(2)：163-166． doi:10.1093/nsr/nww099
9	SONG R H， KIM C S， SHIN D R ．Effects of flow rate and starvation of reactant gases on the performance of phosphoric acid fuel cells[J]．Journal of Power Sources，2000，86(1/2)：289-293． doi:10.1016/s0378-7753(99)00450-4
10	DHEENADAYALAN S， SONG R H， SHIN D R ．Characterization and performance analysis of silicon carbide electrolyte matrix of phosphoric acid fuel cell prepared by ball-milling method[J]．Journal of Power Sources，2002，107(1)：98-102． doi:10.1016/s0378-7753(01)00991-0
11	NEERGAT M， SHUKLA A K ．A high-performance phosphoric acid fuel cell[J]．Journal of Power Sources，2001，102(1/2)：317-321． doi:10.1016/s0378-7753(01)00766-2
12	SEO S J， JOH H I， KIM H T，et al ．Properties of Pt/C catalyst modified by chemical vapour deposition of Cr as a cathode of phosphoric acid fuel cell [J]．Electrochim Acta，2006，52(4)：1676-1682． doi:10.1016/j.electacta.2006.03.104
13	ZERVAS P L， KOUKOU M K， MARKATOS N C ．Predicting the effects of process parameters on the performance of phosphoric acid fuel cells using a 3-D numerical approach[J]．Energy Conversion and Management，2006，47(18/19)：2883-2899． doi:10.1016/j.enconman.2006.03.030
14	PYUN S I， LEE S B ．Effect of surface groups on the electro catalytic behaviour of Pt-Fe-Co alloy-dispersed carbon electrodes in the phosphoric fuel cell[J]．Journal of Power Sources，1999，77(2)：170-177． doi:10.1016/s0378-7753(98)00191-8
15	LAN R， XU X， TAO S，et al ． A fuel cell operating between room temperature and 250 ℃ based on a new phosphoric acid based composite electrolyte[J]．Journal of Power Sources，2010，195(20)：6983-6987． doi:10.1016/j.jpowsour.2010.04.076
16	CHOUDHURY S R， DESHMUKH M B， RENGASWAMY R ．A two dimensional steady-state model for phosphoric acid fuel cells (PAFC)[J]．Journal of Power Sources，2002，112(1)：137-152． doi:10.1016/s0378-7753(02)00369-5
17	GHOUSE M， ABAOUD H， AL-BOEIZ A，et al ．Development of a 1 kW phosphoric acid fuel cell stack[J]．Applied Energy，1998，60(3)：153-167． doi:10.1016/s0306-2619(98)00031-2
18	ASCOLI A， PANDYA J D， REDAELLI G ．Electrical characterization of a 2.5 kW phosphoric acid fuel cell stack operating on simulated reformed biogas[J]．Energy，1989，14(12)：875-878． doi:10.1016/0360-5442(89)90042-x
19	PATHAK S， DAS J N， RANGARAJAN J，et al ．Development of prototype phosphoric acid fuel cell pick-up electric vehicle[C]//IEEE Electric and Hybrid Vehicles，December 18-20，2006，Pune，India：IEEE，2006：9529652． doi:10.1109/icehv.2006.352292
20	SUN Q， LIN D， KHAYATNEZHAD M，et al ．Investigation of phosphoric acid fuel cell, linear Fresnel solar reflector and organic Rankine cycle polygeneration energy system in different climatic conditions[J]．Process Safety and Environmental Protection，2021，147(3)：993-1008． doi:10.1016/j.psep.2021.01.035
21	CHAN S H， LOW C F， DING O L ．Energy and exergy analysis of simple solid-oxide fuel-cell power systems[J]．Journal of Power Sources，2002，103(2)：188-200． doi:10.1016/s0378-7753(01)00842-4
22	HUSSAIN M M， BASCHUK J J， LI X，et al ．Thermodynamic analysis of a PEM fuel cell power system[J]．International Journal of Thermal Sciences，2005，44(9)：903-9011． doi:10.1016/j.ijthermalsci.2005.02.009
23	BARELLI L， BIDINI G， GALLORINI F，et al ．An energetic/exergetic analysis of a residential CHP system based on PEM fuel cell[J]．Applied Energy，2011，88(12)：4334-4342． doi:10.1016/j.apenergy.2011.04.059
24	ANGULO-BROWN F ．An ecological optimization criterion for finite-time heat engines[J]．Journal of Applied Physics，1991，69(11)：7465-7469． doi:10.1063/1.347562
25	TYAGI S， KAUSHIK S， SALHOTRA R ．Ecological optimization and performance study of irreversible Stirling and Ericsson heat engines[J]．Journal of Physics D：Applied Physics，2002，35(20)：2668． doi:10.1088/0022-3727/35/20/330
26	CHENG C Y ．Ecological optimization of an irreversible Brayton heat engine[J]．Journal of Physics D：Applied Physics，1999，32(3)：350． doi:10.1088/0022-3727/32/3/024
27	CHEN T H ．Ecological optimization of quantum spin-1/2 heat engine at the classical limit[J]．Journal of Physics D：Applied Physics，2006，39(7)：1442-1450． doi:10.1088/0022-3727/39/7/016
28	LONG R， LI B， LIU Z，et al ．Ecological analysis of a thermally regenerative electrochemical cycle[J]．Energy，2016，107(15)：95-102． doi:10.1016/j.energy.2016.04.004
29	GUO Y， GUO X， ZHANG H，et al ．Energetic，exergetic and ecological analyses of a high-temperature proton exchange membrane fuel cell based on a phosphoric- acid-doped polybenzimidazole membrane [J]．Sustainable Energy Technologies and Assessments，2020，38：100671． doi:10.1016/j.seta.2020.100671
30	WU M， ZHANG H， ZHAO J，et al ．Performance analyses of an integrated phosphoric acid fuel cell and thermoelectric device system for power and cooling cogeneration[J]．International Journal of Refrigeration，2018，89：61-69． doi:10.1016/j.ijrefrig.2018.02.018
31	SHIN Y， PARK W， CHANG J，et al ．Evaluation of the high temperature electrolysis of steam to produce hydrogen[J]．International Journal of Hydrogen Energy，2007，32(10/11)：1486-1491． doi:10.1016/j.ijhydene.2006.10.028
32	ZHANG H， LIN G， CHEN J ．Performance analysis and multiobjective optimization of a new molten carbonate fuel cell system[J]．International Journal of Hydrogen Energy，2011，36(6)：4015-4021． doi:10.1016/j.ijhydene.2010.12.103
33	CHEN X， WANG Y， CAI L，et al ．Maximum power output and load matching of a phosphoric acid fuel cell-thermoelectric generator hybrid system[J]．Journal of Power Sources，2015，294：430-436． doi:10.1016/j.jpowsour.2015.06.085
34	LEE W Y， KIM M， SOHN Y J，et al ．Performance of a combined system consisting of a high-temperature polymer electrolyte fuel cell and an absorption refrigerator[J]．Energy，2017，141(15)：2397-2407． doi:10.1016/j.energy.2017.11.129
35	AÇIKKALP E， AHMADI M H ．Parametric investigation of phosphoric acid fuel cell-Thermally regenerative electro chemical hybrid system[J]．Journal of Cleaner Production，2018，203：585-600． doi:10.1016/j.jclepro.2018.07.231
36	WATOWICH S J， BERRY R S ．Optimal current paths for model electrochemical system[J]．Journal of Physical Chemistry，1986，90：4624-4631． doi:10.1021/j100410a031
37	ZHANG H， LIN G， CHEN J ．Multi-objective optimisation analysis and load matching of a phosphoric acid fuel cell system[J]．International Journal of Hydrogen Energy，2012，37(4)：3438-3446． doi:10.1016/j.ijhydene.2011.11.030
38	CHIN A T， CHANG H H ．On the conductivity of phosphoric acid electrolyte[J]．Journal of Applied Electrochemistry，1989，19(1)：95-99． doi:10.1007/bf01039396
39	CHEN X， WANG Y， ZHAO Y，et al ．A study of double functions and load matching of a phosphoric acid fuel cell/heat-driven refrigerator hybrid system[J]．Energy，2016，101：359-365． doi:10.1016/j.energy.2016.02.029
40	AÇIKKALP E ．Performance assessment of phosphoric acid fuel cell-thermoelectric generator hybrid system with economic aspect[J]．Journal of Thermal Engineering，2018，5(2)：29-45． doi:10.18186/thermal.529072
41	AL-SULAIMAN F A， DINCER I， HAMDULLAHPUR F ．Exergy analysis of an integrated solid oxide fuel cell and organic Rankine cycle for cooling，heating and power production[J]．Journal of Power Sources，2010，195(8)：2346-2354． doi:10.1016/j.jpowsour.2009.10.075
42	DINCER I， HUSSAIN M M， AL-ZAHARNAH I ．Energy and exergy utilization in agricultural sector of Saudi Arabia[J]．Energy Policy，2005，33(11)：1461-1467． doi:10.1016/j.enpol.2004.01.004
43	SZARGUT J ．Exergy method：technical and ecological applications[M]．Ashurst：WIT Press，2005．
44	AL-SULAIMAN F A， DINCER I， HAMDULLAHPUR F ．Energy and exergy analyses of a biomass trigeneration system using an organic Rankine cycle[J]．Energy，2012，45(1)：975-985． doi:10.1016/j.energy.2012.06.060
45	UST Y， SAHIN B， KODAL A，et al ．Ecological coefficient of performance analysis and optimization of an irreversible regenerative-Brayton heat engine[J]．Applied Energy，2006，83(6)：558-572． doi:10.1016/j.apenergy.2005.05.009
46	UST Y， SAHIN B， SOGUT O S ．Performance analysis and optimization of an irreversible dual-cycle based on an ecological coefficient of performance criterion[J]．Applied Energy，2005，82(1)：23-39． doi:10.1016/j.apenergy.2004.08.005
47	WANG H S， CHANG C P， HUANG Y J，et al ．A high-yield and ultra-low-temperature methanol reformer integratable with phosphoric acid fuel cell (PAFC)[J]．Energy，2017，133：1142-1152． doi:10.1016/j.energy.2017.05.140
48	SONG R H， SHIN D R ．Influence of CO concentration and reactant gas pressure on cell performance in PAFC[J]．International Journal of Hydrogen Energy，2001，26(12)：1259-1262． doi:10.1016/s0360-3199(01)00064-7
49	KIENITZ B ．Optimizing polymer electrolyte membrane thickness to maximize fuel cell vehicle range[J]．International Journal of Hydrogen Energy，2020，46(19)：11176-11182． doi:10.1016/j.ijhydene.2020.03.126

[1]	Yanbing LI, Shuwang JIA, Junliang ZHANG, Yue FU, Ming LIU, Junjie YAN. Exergy Economic Analysis of Ultra-Supercritical Coal-Fired Power Plants With High-Level Layout of Turbine Under Load-Cycling Conditions [J]. Power Generation Technology, 2024, 45(1): 69-78.
[2]	Hanxiao LIU, Gaofei GUO, Zhaomei CHEN. Study on WESP Multi-pollutant Emission Reduction and Energy Efficiency Test of Ultra-low Emission Unit [J]. Power Generation Technology, 2023, 44(1): 94-99.
[3]	ABD-HAMID Mohamed, Longyu XIA, Gaosheng WEI, Liu CUI, Chao XU, Xiaoze DU. Performance Analysis of Photovoltaic/Thermal Hybrid System Integrated With Phase Change Heat Storage Materials [J]. Power Generation Technology, 2023, 44(1): 53-62.
[4]	Yuxing WANG, Yanjie ZHAO, Zhanye YANG, Hurun ZHANG, Manni LIN. Optimization Analysis of a Combined Ejector-cooling and Power System [J]. Power Generation Technology, 2022, 43(6): 942-950.
[5]	Yajuan LENG,Rui HU,Lin CUI,Yong DONG. Study on Energy Efficiency Characteristics of Wet Flue Gas Desulfurization Tower [J]. Power Generation Technology, 2020, 41(5): 543-551.
[6]	Guohua QIU,Hongge WEI,Xiujin LIANG,Zhuang LI,Fengji WANG,Yue ZHU. Energy Consumption Analysis of Desulphurization Ultra-low Emission Operation and Outlook on Its Energy-saving Operation in Thermal Power Plants [J]. Power Generation Technology, 2020, 41(5): 510-516.
[7]	LIN Dongchao, WANG Heng. Analysis of Energy Consumption Detection Method for Ice Storage System [J]. Power Generation Technology, 2017, 38(6): 64-69.