固体氧化物燃料电池直接内重整的模型研究进展

doi:10.19799/j.cnki.2095-4239.2024.0107

摘要/Abstract

摘要：

固体氧化物燃料电池（SOFCs）是一种通过电化学氧化反应直接将化学能高效率地转化为电能的装置，在大规模发电、联产以及一体化燃料升级等可再生能源系统领域具有广阔的市场前景。为进一步拓宽SOFCs的应用场景，降低运行成本，直接内重整（DIR）技术可将CH₄等烷烃类物质在阳极催化生成H₂，减少了燃料预处理要求且提高了转化效率，是目前SOFCs研究领域的热点之一。为了优化该技术的系统设计和操作条件，模型模拟的研究可显著减少实验工作量，并为其提供理论支撑和指导性建议。通过DIR-SOFC系统的模型模拟，结合场分布、动力学参数等，可以量化评估系统内的反应，从而了解其物理、化学过程的复杂性。本文总结了DIR-SOFC建模工作的现状，介绍了体积平均模型和针对微观结构的模型；重点讨论多尺度数学模型，对现有研究中的反应动力学过程描述、“能量-质量-动量”平衡方程、“1D-2D-3D”DIR-SOFC单元描述等进行了综述，能更好地评估变量对DIR的影响；对DIR-SOFC模型中不同液体燃料的重整反应及相关的反应动力学参数进行总结；指出现有模型的不足，并对DIR-SOFC系统模型的未来发展进行展望，使模型更加精准。

关键词: 固体氧化物燃料电池, 直接内重整, 模型模拟, 甲烷重整模型

Abstract:

Solid oxide fuel cells (SOFCs) efficiently convert chemical energy into electric energy via electrochemical oxidation reactions, holding promise for various engineering applications in large-scale power generation, cogeneration, and integrated fuel upgrading. Direct internal reforming (DIR) technology, catalyzing alkanes like CH₄ at the anode to produce H₂, enhances SOFC application scenarios and reduces operational costs, thereby reducing fuel pretreatment requirements and improving conversion efficiency, which represents a hotspot in SOFC research. Model simulation studies aid in optimizing system design and operational conditions, reducing experimental work, and providing theoretical data support and guidance suggestions. Through the model simulation of the DIR–SOFC system, combined with the field distribution and kinetic parameters, the system reactions can be quantitatively evaluated to understand the complexity of physical and chemical processes. This paper summarizes the current situation of DIR-SOFC modeling work, introducing volume average and microstructural models. It discusses the multiscale mathematical model and reviews the description of the reaction dynamics process "energy-mass-momentum" balance equations as well as the description of the "1D-2D-3D" DIR-SOFC unit. This can be used to evaluate the variables on the DIR. Furthermore, it summarizes the reforming reactions of different liquid fuels in the DIR-SOFC model and the related reaction kinetic parameters. This study highlights existing model limitations and prospects for the future development of the DIR-SOFC system model to increase model accuracy.

Key words: solid oxide fuel cell, direct internal reforming, model simulation, methane reforming model

中图分类号:

T 669.2

孙航宇, 李卓华, 王亚丽, 李晓艳, 付云枫, 杜国山, 陈宋璇. 固体氧化物燃料电池直接内重整的模型研究进展[J]. 储能科学与技术, 2024, 13(4): 1277-1292.

Hangyu SUN, Zhuohua LI, Yali WANG, Xiaoyan LI, Yunfeng FU, Guoshan DU, Songxuan CHEN. Research progress of model simulation of direct internal reforming in solid oxide fuel cells[J]. Energy Storage Science and Technology, 2024, 13(4): 1277-1292.

图/表 10

图1

图2

表1

SOFC中的电子和离子传输过程的相关描述"

传输方式	传输方程	ASL	ACL	AFL	EL	IL	CFL	CCL
电子传递	$d d x σ e l e e f f d φ e l e d x$	0	0	-i_tpb,a	0	0	i_tpb,c+i_dpb,c	i_dpb,c
离子传递	$d d x σ i o n e f f d φ i o n d x$	0	0	-i_tpb,a	0	0	i_tpb,c+i_dpb,c	i_dpb,c

表1

表2

离子和电子导电相电导率"

电导率	ASL	ACL	AFL	EL	IL	CFL	CCL
$σ e l e e f f$	0	$ε N i τ N i σ N i b u l k$	$ε N i τ N i σ N i b u l k$	0	0	$ε L S C F τ L S C F σ L S C F b u l k$	$ε L S C F τ L S C F σ L S C F b u l k$
$σ i o n e f f$	0	$ε Y S Z τ Y S Z σ Y S Z b u l k$	$ε Y S Z τ Y S Z σ Y S Z b u l k$	$σ Y S Z b u l k$	$σ G D C b u l k$	$ε G D C τ G D C σ G D C b u l k + ε L S C F τ L S C F σ L S C F b u l k$	$σ L S C F b u l k$

表2

表3

使用DGM的气体扩散方程相关描述"

组分	阳极侧扩散		阴极侧扩散
组分	ACL	AFL	CCL	CFL
CH₄	$d d x - ∑ j = 1 n D C H 4, j D G M R T d p j d x = r C H 4$	$d d x - ∑ j = 1 n D C H 4, j D G M R T d p j d x = 0$	—	—
H₂	$d d x - ∑ j = 1 n D H 2, j D G M R T d p j d x = r H 2$	$d d x - ∑ j = 1 n D H 2, j D G M R T d p j d x = i t p b, a 2 F$	—	—
H₂O	$d d x - ∑ j = 1 n D H 2 O, j D G M R T d p j d x = r H 2 O$	$d d x - ∑ j = 1 n D H 2 O, j D G M R T d p j d x = i t p b, a 2 F$	—	—
CO	$d d x - ∑ j = 1 n D C O, j D G M R T d p j d x = r C O$	$d d x - ∑ j = 1 n D C O, j D G M R T d p j d x = 0$	—	—
CO₂	$d d x - ∑ j = 1 n D C O 2, j D G M R T d p j d x = r C O 2$	$d d x - ∑ j = 1 n D C O 2, j D G M R T d p j d x = 0$	—	—
N₂	$d d x - ∑ j = 1 n D N 2, j D G M R T d p j d x = r N 2$	$d d x - ∑ j = 1 n D N 2, j D G M R T d p j d x = 0$	$d d x - ∑ j = 1 n D N 2, j D G M R T d p j d x = 0$	$d d x - ∑ j = 1 n D N 2, j D G M R T d p j d x = 0$
O₂	—	—	$d d x - ∑ j = 1 n D O 2, j D G M R T d p j d x = i d p b, c 4 F$	$d d x - ∑ j = 1 n D O 2, j D G M R T d p j d x = i t p b, c + i d p b, c 4 F$

表3

图3

表4

表5

CH4 重整反应速率方程以及WGS速率表达式"

参考文献	阳极	动力学类型	动力学表达式	温度/℃	S/C	动力学参数
Lee等^[77]	Ni/YSZ金属陶瓷	FO	$r C H 4 = k p C H 4 p H 2 O - 1.25$	800～1000	2～7.4	E=17.8～23.5 kJ/mol，k₀=490～4775 mol/(g·h)
Achenbach等^[78]	Ni/ZrO₂金属陶瓷		$r C H 4 = k 1 - p C O p H 2 3 p C H 4 p H 2 O k p p C H 4$	700～940	2.6～8	E=82 kJ/mol，k₀=42720 mol/(s·m²·MPa)
Belyaev等^[79]	Ni/ZrO₂/CeO₂		$r C H 4 = k p C H 4$	800～850	2～4	E=163 kJ/mol
Avetisov等^[80]	Ni/MgO		$r C H 4 = k p C H 4$	500～650		E=99.77 kJ/mol，k₀=2.415×10⁷
Parsons等^[81]	Ni 金属陶瓷	加权	$r C H 4 = k p C H 4 1.25$	960	3	k=2.4×10^-3 mol/(s·bar^1.25)
Fan等^[74]	Ni/GDC		$r C H 4 = k p C H 4 0.7 p H 2 O - 0.08$	650～750	1.5～2.45	E=63～88 kJ/mol，k₀=1.1～18.9 mol/(s·bar^0.6)
Ahmed等^[16]	Ni/YSZ		$r C H 4 = k p C H 4 0.85 p H 2 O - 0.35$	854～907	1.53～2.45	E=95 kJ/mol，k₀=8542 mol/(s·m²·bar^0.5)
	Ni/改良的YSZ		$r C H 4 = k p C H 4 1.4 p H 2 O - 0.8$	838～922	1.4～3	E=208 kJ/mol，k₀=3.6×10⁸ mol/(s·m²·bar^0.6)
Timmermann等^[82]	Ni/CGO		$r C H 4 = k p C H 4 1.19$	800,950	0～3	k₀=4.05×10^-0.5 mol/(s·m²·Pa^1.19)
	Ni/YSZ					E=26.3 kJ/mol
Yakabe等^[55]	Ni/YSZ		$r C H 4 = k p C H 4 1.3 p H 2 O - 1.2 D a$	1000	2	E=1.91×10⁵ kJ/mol，k₀=1.09×10¹⁰ mol/kg，D_a=930 kg/m³
Johnsen等^[83]	NiO/YSZ		$r C H 4 = k p C H 4 1.2$	680～1027	1.5～2.5	E=57.84 kJ/mol，k₀=1.75
Sciazko等^[84]	NiO/YSZ		$r C H 4 = k p C H 4 0.88 p H 2 O - 0.083$	550～750	3.0～6.0	E=121.00 kJ/mol，k₀=6.472×10^-3
Chen等^[85]	Ni/Al₂O₃		$r C H 4 = k p C H 4 0.85$	500～700	1.5～4.5	E=81.69 kJ/mol，k₀=316.6
Fu等^[86]	含稀土金属的Ni		$r C H 4 = k p C H 4 0.8$	400～450		E=151.46 kJ/mol，k₀=168.1 kg/(m²·s·bar^-0.8)
Timmermann等^[87]	Ni/YSZ金属陶瓷	LHHW	$r r = - k p C H 4, s n p H 2 O, s m 1 - p H 2, s 3 p C O, s K r e f p H 2 O, s p C H 4, s$	600～850	1～3	E_A=60 kJ/mol (600～750 ℃)，E_A=30 kJ/mol (750～850 ℃)
Souentie等^[88]	Ni/GDC 和 Au/Ni/GDC		$r C H 4 = k y C H 4 1 + k y C H 4 y H 2 O$	800～900	0.25，1	E=96～117 kJ/mol，k_a=（15～45）×10^-6
Xu等^[89]	Ni/MgAl₂O₄		$R 1 = k p H 2 2.5 p C H 4 p H 2 O - p H 2 3 p C O K 1 D E N 2$	500～550	3～5	E=240 kJ/mol，k₀=1.17×10¹⁵ bar^0.5·mol/(kg·s)
Bebelis等^[90]	Ni/YSZ金属陶瓷		$r C H 4 = k a d p C H 4 1 - k a d k r k H 2 O p H 2 p C H 4 p H 2 O$	800～900	0.2	E=230 kJ/mol
Hou等^[91]	Ni/α Al₂O₃		$R 1 = k p C H 4 p H 2 O 1.25 p H 2 1.25 1 - p H 2 3 p C O K p 1 p C H 4 p H 2 O D E N 2$	475～550	4～7	E=209.20 kJ/mol，k₀=5.922×10⁸
Nakagawa等^[92]	Ni/YSZ/CeO₂		$r C H 4 = K 1 K 2 K 3 p C H 4 p H 2 O 1 + K 2 p C H 4 K 3 p H 2 O 2$	700～1000	2～8	A₁=400～612 mol/(s·m²)，E₁=49 kJ/mol
						A₂=3.01×10^-4～4.96×10^-4 kPa^-1，E₂=-45 kJ/mol
						A₃=0.18～0.28 kPa^-1，E₃=7 kJ/mol
Dicks等^[93]	Ni/YSZ阳极		$r C H 4 = k p C H 4 1 + K H p H 2 0.5 + K S p H 2 O p H 2 2$	700～1000	1～3	E=135 kJ/mol，k₀=210 mol/(s·cm²·MPa)
Fu等^[86]	含稀土金属的Ni	PL	$r C H 4 = k p C H 4 0.8 p H 2 O 1.5$	400～450		E=78.57 kJ/mol，k₀=0.2097 kg/(m²·s·bar^-2.3)
Hou等^[91]	Ni/α Al₂O₃	LHHW	$R 1 = k p C O p H 2 O 0.5 p H 2 0.5 1 - p C O 2 p H 2 K p 2 p C O p H 2 O D E N 2$	475～550	4～7	E=15.40 kJ/mol，k₀=6.028×10^-4
Xu等^[89]	Ni/MgAl₂O₄	LHHW	$R 2 = k p H 2 p C O p H 2 O - p H 2 O p C O 2 K 1 D E N 2$	500～550	3～5	E=67.130 kJ/mol，k₀=5.43×10⁴ MPa·mol/(kg·s)

表5

表6

表7

甲醇和乙醇蒸气重整的反应动力学参数"

动力学	参考文献	阳极	动力学类型	动力学表达式	温度/℃	S/C	动力学参数
甲醇蒸气重整动力学	Purnama等^[108]	CuO/ZnO/Al₂O₃	PL	$r S R M = k p C H 3 O H 0.6 p H 2 O 0.4$	230～300	1	E=76 kJ/mol，k₀=8.8×10⁸ s^-1·g^-1
	Samms等^[109]	CuO/ZnO/Al₂O₄	PL	$r S R M = k p C H 3 O H 0.63 p H 2 O 0.39 p H 2 - 0.23 p C O 2 - 0.07$	225,250	1.16，5.15	E=74.164 kJ/mol，k₀=6370 mol/(s·bar⁷²)
	Ilinich等^[110]	CuO/ZnO/Al₂O₅	PL	$r S R M = k p C H 3 O H 0.54 p H 2 O 0.10 p H 2 - 0.40 p C O 2 - 0.075$	230～320	1.13	E=54.27 kJ/mol，k₀=34.476 mol/(s·bar⁷²)
	Jiang等^[111]	CuO/ZnO/Al₂O₆	PL	$r S R M = k p C H 3 O H 0.26 p H 2 O 0.03 p H 2 - 0.20$	170～260	—	E=105 kJ/mol，k₀=5.31×10⁹ mol/(kg·s·kPa^0.296)
	Jiang等^[112]	CuO/ZnO/Al₂O₇	LHHW	$r S R M = k K 1 K 3 - 0.5 p C H 3 O H p H 2 - 0.5 1 + K 1 K 3 - 0.5 + p C H 3 O H p H 2 O - 0.5 + K 3 - 0.5 p H 2 - 0.5$	127～327	—	E=110 kJ/mol，k₀=34.476 mol/(s·bar⁷²)

乙醇蒸气重整动力学	Therdhianwong等^[113]	Ni/Al₂O₃	PL	$r S R E = k p E t O H 2.52 p H 2 O 7$	400～650	0.26～10.73	k=280075
	Afolabi等^[114]	Ni/Al₂O₃	FO	$r S R E = k p E t O H$	300～450	3	E=48 kJ/mol，k₀=13394 mol/(s·MPa·g)
	Tosti等^[115]	Pd/Ag	PL	$r S R E = k p E t O H 0.43$	450	8.4～13	E=4410 kJ/mol，k₀=3.123×10^-2 kmol^0.57/(s^-0.57·kg)
	Chen等^[116]	镍基催化剂	FO	$r S R E = k p E t O H p H 2$	400～800	1～10	E=130 kJ/mol，k₀=7.98×10^-10 mol/(s·m³)

表7

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软件	参考文献
COMSOL Multiphysics	[67,69-70]
MATLAB	[9,35,67,71]
Star-CD	[55,72]
Ansys Fluent	[22]
gPROMS Model Builder	[37]
Aspen HYSYS	[52]
LIMEX	[26]
PRO\II	[73]
CFD	[74]

燃料名称	反应式	反应热/(kJ/mol)	参考文献
甲醇	CH₃OH→2H₂+CO	91	[102-103]
甲醇	CH₃OH+H₂O→3H₂+CO₂	50	[102-103]

乙醇	C₂H₅OH+H₂O→4H₂+2CO	239.5	[104]
乙醇	C₂H₅OH+3H₂O→6H₂+2CO₂	173.5	[104]

正丁烷	C₄H₁₀+4H₂O→4CO+9H₂	649.9	[105]
正丁烷	C₄H₁₀+8H₂O→4CO₂+13H₂	485.3	[105]

辛烷	C₈H₁₈+8H₂O→8CO+17H₂	1310	[106-107]
辛烷	C₈H₁₈+16H₂O→8CO₂+25H₂	1684	[106-107]

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