Thermal-mass nonequilibrium model for water splitting hydrogen production by solar thermochemical cycle of porous cerium oxide

doi:10.11949/0438-1157.20211747

Abstract

Abstract:

The complex reactions and heat and mass transfer processes in porous media involved in the thermal chemical cycle solar fuel technology process have not yet established a relatively complete mathematical model. In this paper, the thermochemical cycling hydrolysis process of porous cerium oxide is taken as the research object, the oxygen transport and surface chemical reaction at particle scale is coupled with the heat and mass transport at macro scale, and complete thermal-mass nonequilibrium model of porous media driven by photo-thermal is proposed. The effects of local thermal nonequilibrium, incident radiant heat flux and reactant concentration on the dynamic process at two scales (particle and bed) are analyzed. Under the volume effect of the bed by incident radiation, the axial temperature gradient makes the maximum oxygen vacancy concentration controlled by thermodynamic equilibrium of the defect reaction appear in front of the bed. High incident radiation density can increase the reaction rate, and the effect is more obvious at the initial stage of the reaction. In the dynamic process of the defect reaction, the oxidation process is faster than the reduction reaction. Increase of H₂ concentration in the porous oxygen carrier reactor should mainly start from the reaction process and conditions in the reduction stage. Compared with the existing experimental data, the reliability of the kinetic and heat and mass transport model is verified. This paper can provide a relatively complete theoretical basis and reference path for the modeling and process design of this kind of problems.

Key words: photo-thermal driven, porous media, multiscale, cerium oxide, thermochemical cycle, hydrogen production

摘要：

热化学循环太阳燃料技术过程所涉及的多孔介质中复杂反应及热质传递过程，尚未建立较为完善的数学模型。以多孔氧化铈热化学循环解水过程为研究对象，将颗粒尺度的氧输运与宏观尺度的热质输运相耦合，提出完整的光热驱动条件下多孔介质非热质平衡模型，实验数据对比验证了动力学及热质输运模型的可靠性，分析了两种尺度(颗粒及床层)下，非热平衡效应、入射辐射热流、反应物浓度对动态过程的影响。入射辐射在床层的体积效应下，轴向的温度梯度使得缺陷反应的热力学平衡控制最大氧空位浓度出现在床层前侧，在缺陷反应的动态过程中，氧化过程相较于还原反应更快，提高多孔载氧体反应器的产物H₂浓度应主要从还原阶段中反应过程及条件出发。可为该类问题的建模和过程设计提供较为完整的理论基础和参考路径。

关键词: 光热驱动, 多孔介质, 多尺度, 氧化铈, 热化学循环, 制氢

CLC Number:

TQ 116.2

Pei WANG, Rongkuo WEI. Thermal-mass nonequilibrium model for water splitting hydrogen production by solar thermochemical cycle of porous cerium oxide[J]. CIESC Journal, 2022, 73(7): 2885-2894.

王沛, 魏荣阔. 光热驱动多孔氧化铈热化学循环解水制氢非热质平衡模型[J]. 化工学报, 2022, 73(7): 2885-2894.

Figures/Tables 10

Fig.1 Schematic diagram of reactor

Table 1 Values of some model variable parameters

参数	数值
多孔床（氧化铈）
床层孔隙率φ/孔径d_p	0.8/2 mm
氧化铈密度 $ρ C e$	$7.22 ? g / c m 3$
晶格常数a*	0.54112 nm
晶格氧扩散系数 $D V O$ ^[30]	$10 - 8 ? m 2 / s$
表面摩尔密度 $ρ ? C e, s$	$2.267 × 10 - 5 ? m o l / m 2$
体积摩尔密度 $ρ ? C e, b$	$653.16 ? m o l / m 3$
颗粒表面积 $S p$	3.14 $× 10 - 6$ m²
比表面积α_sf^[29]	$3.99 ? m 2 / g$
反应床厚度L	21.6 mm/50 mm
多孔体积密度 $ρ b$	$0.51 ? g / c m 3$
动力学参数^[29]
反应式（9）正反应活化能 $E 1, f$	-7 kJ/mol
反应式（9）逆反应活化能 $E 1, b$	-230 kJ/mol
反应式（10）正反应活化能 $E 2, f$	-190 kJ/mol
反应式（10）逆反应活化能 $E 2, b$	-102 kJ/mol
反应式（9）正反应动力学参数 $k 1, f$	130 $e x p ? (E 1, f / R T)$
反应式（9）逆反应动力学参数 $k 1, b$	$8.2 × 1014 e x p ? (E 1, b / R T)$
反应式（10）正反应动力学参数 $k 2, f$	$1.5 × 1014 e x p ? (E 2, f / R T)$
反应式（10）逆反应动力学参数 $k 2, b$	$4.4 × 1014 e x p ? (E 2, b / R T)$
CeO₂体积缺陷平衡反应摩尔焓 $h T$	-113.7 J/mol
CeO₂体积缺陷平衡反应摩尔熵 $s T$	-42.1 J/(mol·K)
实验参数
还原气浓度 $C r e, f$	$10.156 ? m o l / m 3$ （H₂+Ar）
氧化气浓度 $C o x, f$	$10.156 ? m o l / m 3$ （H₂O+Ar）
进气压力 $P f e e d$	$1.0133 × 105 ? P a$
进气流量 $q f e e d$	0.2 g/s
进气黏度 $μ f e e d$	$2.8 × 10 - 5 ? k g / (m 2 ? s)$
进气密度 $ρ f e e d$	$1.292 ? k g / m 3$
进气温度	100℃
床层温度	恒温1000℃/ 辐射热通量1 MW/m²
H₂初始摩尔分数	0.1/0.143/0.2/0.3/0.4/0.5/0.6
H₂O初始摩尔分数	0.1/0.2/0.26/0.3/0.4

Table 1 Values of some model variable parameters

参数	数值
多孔床（氧化铈）
床层孔隙率φ/孔径d_p	0.8/2 mm
氧化铈密度 $ρ C e$	$7.22 ? g / c m 3$
晶格常数a*	0.54112 nm
晶格氧扩散系数 $D V O$ ^[30]	$10 - 8 ? m 2 / s$
表面摩尔密度 $ρ ? C e, s$	$2.267 × 10 - 5 ? m o l / m 2$
体积摩尔密度 $ρ ? C e, b$	$653.16 ? m o l / m 3$
颗粒表面积 $S p$	3.14 $× 10 - 6$ m²
比表面积α_sf^[29]	$3.99 ? m 2 / g$
反应床厚度L	21.6 mm/50 mm
多孔体积密度 $ρ b$	$0.51 ? g / c m 3$
动力学参数^[29]
反应式（9）正反应活化能 $E 1, f$	-7 kJ/mol
反应式（9）逆反应活化能 $E 1, b$	-230 kJ/mol
反应式（10）正反应活化能 $E 2, f$	-190 kJ/mol
反应式（10）逆反应活化能 $E 2, b$	-102 kJ/mol
反应式（9）正反应动力学参数 $k 1, f$	130 $e x p ? (E 1, f / R T)$
反应式（9）逆反应动力学参数 $k 1, b$	$8.2 × 1014 e x p ? (E 1, b / R T)$
反应式（10）正反应动力学参数 $k 2, f$	$1.5 × 1014 e x p ? (E 2, f / R T)$
反应式（10）逆反应动力学参数 $k 2, b$	$4.4 × 1014 e x p ? (E 2, b / R T)$
CeO₂体积缺陷平衡反应摩尔焓 $h T$	-113.7 J/mol
CeO₂体积缺陷平衡反应摩尔熵 $s T$	-42.1 J/(mol·K)
实验参数
还原气浓度 $C r e, f$	$10.156 ? m o l / m 3$ （H₂+Ar）
氧化气浓度 $C o x, f$	$10.156 ? m o l / m 3$ （H₂O+Ar）
进气压力 $P f e e d$	$1.0133 × 105 ? P a$
进气流量 $q f e e d$	0.2 g/s
进气黏度 $μ f e e d$	$2.8 × 10 - 5 ? k g / (m 2 ? s)$
进气密度 $ρ f e e d$	$1.292 ? k g / m 3$
进气温度	100℃
床层温度	恒温1000℃/ 辐射热通量1 MW/m²
H₂初始摩尔分数	0.1/0.143/0.2/0.3/0.4/0.5/0.6
H₂O初始摩尔分数	0.1/0.2/0.26/0.3/0.4

Fig.2 Comparison of product generation rates of ceria particles in reduction and oxidation stages with reference experiments[29]

Fig.3 Temperature Ts and oxygen vacancy concentration VO?? unsteady changes in the reduction step （Dp=500 μm）

Fig.4 Unsteady change of bed oxygen vacancy concentration VO?? in the oxidation step (Dp=500 μm)

Fig. 5 Two-phase temperature change of cerium oxide bed

Fig.6 Bed temperature Ts and oxygen vacancy concentration VO?? unsteady changes with different qin in the reduction step (Dp=500 μm)

Fig.7 Variation of H2 concentration at bed outlet of different qin in the oxidation step

Fig.8 Variation of molar concentration of gas at outlet of bed in the reduction stage

Fig.9 Variation of H2 concentration at bed outlet in the oxidation step

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