Research progress of model simulation of direct internal reforming in solid oxide fuel cells

doi:10.19799/j.cnki.2095-4239.2024.0107

Abstract

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

CLC Number:

T 669.2

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.

Figures/Tables 10

Fig. 1

Fig. 2

Table 1

Relevant descriptions of electron and ion transport processes in SOFC"

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

Table 1

Table 2

Ionic and electronic conductive phase conductivity"

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	$ε Y S Z τ Y S Z σ Y S Z b u l k$	$ε Y S Z τ Y S Z σ Y S Z b u l k$	$σ Y S Z b u l k$	$σ G D C b u l k$	$ε G D C τ G D C σ G D C b u l k + ε L S C F τ L S C F σ L S C F b u l k$	$σ L S C F b u l k$

Table 2

Table 3

Description of gas diffusion equations using DGM"

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	—	—	$d d x - ∑ j = 1 n D O 2, j D G M R T d p j d x = i d p b, c 4 F$	$d d x - ∑ j = 1 n D O 2, j D G M R T d p j d x = i t p b, c + i d p b, c 4 F$

Table 3

Fig. 3

Table 4

Table 5

CH4 reforming reaction rate equation and WGS rate expression"

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)

Table 5

Table 6

Table 7

Reaction kinetics parameters of methanol and ethanol steam reforming"

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)

Table 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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