考虑不均匀性的SOEC电堆3D建模优化分析

doi:10.11949/0438-1157.20250142

摘要/Abstract

摘要：

针对SOEC电堆内部温度、电流不均匀性对系统制氢效率、安全稳定运行及寿命造成的影响，首先根据SOEC电堆的几何结构建立能精准分析SOEC电荷传输过程、流体流动、物质传输过程、热能传递过程的多物理场耦合的3D模型，其次为优化模型仿真过程对模型进行边界约束并将其结构网格化，得到满足约束条件的自适应增量Kriging代理模型优化方式，印证该模型优化的精准性并减少了仿真时间与计算资源总量，最后通过分析电堆内部温度、物料分布、电流密度、电压等不均匀分布特性及原因提出考虑增加电解制氢效率及改善不均匀性的SOEC电堆稳态运行多目标优化算法，并通过算例仿真和实验验证，考虑电堆内部温度、电流均匀性分布的优化方式，可大大提高电堆安全稳定运行及产氢量。

关键词: SOEC, 不均匀性, Kriging代理模型, 效率, 多目标优化, 稳态运行

Abstract:

To address the impact of temperature and current inhomogeneity inside the solid oxide electrolysis cell (SOEC) stack on the system's hydrogen production efficiency, safe and stable operation, and lifetime, first, based on the geometric structure of the SOEC power reactor, a three-dimensional (3D) model coupled with multi-physics fields that can accurately analyze the charge transport process, fluid flow, material transport process and heat energy transfer process of the SOEC is established. Secondly, in order to optimize the simulation process of the model, boundary constraints are imposed on the model and its structure is meshed to obtain an adaptive incremental Kriging agent model optimization that satisfies the constraints, which confirms the accuracy of the model optimization and reduces the simulation time and the total amount of computational resources. Finally, the multi-objective optimization algorithm for the steady-state operation of SOEC reactors is proposed to increase the efficiency of electrolytic hydrogen production and improve the inhomogeneity by analyzing the characteristics and causes of the inhomogeneous distribution of temperature, material, current density and voltage inside the stacks, and through numerical simulation and experimental verification, considering the optimization method of temperature and current uniformity distribution inside the stacks, it can greatly improve the safe and stable operation and hydrogen production of the stacks.

Key words: SOEC, inhomogeneity, Kriging agent model, efficiency, multi-objective optimization, steady-state operation

中图分类号:

TQ 116.2⁺1

赫亚庆, 王维庆, 池映天, 李佳蓉, 王海云, 张新燕, 刘博文. 考虑不均匀性的SOEC电堆3D建模优化分析[J]. 化工学报, 2025, 76(8): 4129-4144.

Yaqing HE, Weiqing WANG, Yingtian CHI, Jiarong LI, Haiyun WANG, Xinyan ZHANG, Bowen LIU. Optimization analysis of 3D modelling of SOEC stacks taking into account inhomogeneities[J]. CIESC Journal, 2025, 76(8): 4129-4144.

图/表 21

图1 板式SOEC单堆示意图

Fig.1 Schematic diagram of a plate SOEC single stack

图2 SOEC电解制氢原理图

Fig.2 Schematic diagram of hydrogen production by SOEC electrolysis

图3 SOEC电堆3D模型几何结构[18-20]

Fig.3 Geometry of SOEC stack 3D model[18-20]

图4 SOEC电堆3D模型模拟流程图[21-23]

Fig.4 Flowchart of 3D model simulation of SOEC stack[21-23]

表1 SOEC电堆3D空间多物理场模型边界约束

Table 1 Boundary constraints of 3D spatial multiphysics field model of SOEC stack

参数约束条件	数值
氧电极侧集流体电势/V	0
氢电极侧集流体电势/V	1～2
空气流道入口O₂与N₂摩尔比	21∶79
氢气流道入口H₂O与H₂摩尔比	9∶1
空气流道出口压强/kPa	101
氢气流道出口压强/ kPa	101
空气流道入口温度/℃	810
氢气流道入口温度/℃	810
空气流道入口速度/（m/s）	4～6
氢气流道入口速度/（m/s）	2～4

图5 SOEC电堆3D状态空间模型示意

Fig.5 Schematic of 3D state-space model of SOEC stack

图6 SOEC代理模型流程

Fig.6 Flowchart of SOEC agent model

表2 单堆参数

Table 2 Single-stack parameters

相关参数	数值
SOEC长度/ mm	75.0
SOEC宽度/ mm	30.0
SOEC厚度/ mm	2.1
氢电极功能层厚度/μm	50.0
氧电极长度/ mm	72.0
氧电极宽度/ mm	28.0
氧电极厚度/μm	30.0
电解质厚度/ μm	8.0
氢电极支撑层厚度/μm	500.0
金属支撑体长度/ mm	75.0
金属支撑体宽度/ mm	30.0
金属支撑体厚度/ mm	1.5
流道宽度/ mm	1.5
流道高度/ mm	0.8

图7 SOEC电堆3D模型优化仿真情况对比

Fig.7 Comparison of 3D model optimisation simulations of SOEC stacks

图8 H2O(g)分布情况

Fig.8 H2O(g) distribution

图9 电解质中间界面上的电流密度情况

Fig.9 Current density distribution at intermediate electrolyte interface

图10 不同模型下SOEC电流密度分布仿真对比

Fig.10 Simulation comparison of SOEC current density distribution under different models

图11 不同模型下SOEC伏安特性曲线仿真对比

Fig.11 Simulation comparison of SOEC volt-ampere characteristic curves under different models

图12 不同模型下SOEC电堆温度变化仿真对比

Fig.12 Comparison of simulation of temperature variation of SOEC stack under different models

图13 Pareto Frontier示意图

Fig.13 Schematic diagram of Pareto Frontier

表3 不同优化对象权重系数

Table 3 Weight coefficient of different optimization objects

类别	$U s c$	$V H 2 O$	$V a i r$	$T s c$	$U E I$	$U E T$
方式1	1	1	1	1	1	1
方式2	1	1	1	1	0	0

表3 不同优化对象权重系数

Table 3 Weight coefficient of different optimization objects

类别	$U s c$	$V H 2 O$	$V a i r$	$T s c$	$U E I$	$U E T$
方式1	1	1	1	1	1	1
方式2	1	1	1	1	0	0

图14 SOEC单堆功率60 W时的Pareto Frontier理想解

Fig.14 Ideal solution of Pareto Frontier for SOEC at 60 W single stack power

图15 Pareto Frontier下的不同电堆功率稳态运行曲线

Fig.15 Steady state operating curves of different stack power under Pareto Frontier

表4 对比电堆功率为16 W时不同模型及方式下的决策结果

Table 4 Comparison of decision-making results under different models and approaches for a stack power of 16 W

模型类型	方式/占比	$T s c$ /℃	$U E T$ /℃	$I s c$ /A	$U E I$	$U R H 2 O$ /%	$U s c$ /V
I-KAM代理模型	方式1	807.50	0.04	12.62	0.19	77.80	1.27
	方式2	808.00	0.07	12.10	0.32	87.10	1.29
	优化占比	0.06%	42.86%	-4.30%	40.63%	10.68%	1.55%
经典3D模型	方式1	807.50	0.03	12.63	0.19	77.80	1.27
	方式2	808.00	0.06	12.10	0.32	87.10	1.29
	优化占比	0.06%	50.00%	-4.38%	40.63%	10.68%	1.55%

表4 对比电堆功率为16 W时不同模型及方式下的决策结果

Table 4 Comparison of decision-making results under different models and approaches for a stack power of 16 W

模型类型	方式/占比	$T s c$ /℃	$U E T$ /℃	$I s c$ /A	$U E I$	$U R H 2 O$ /%	$U s c$ /V
I-KAM代理模型	方式1	807.50	0.04	12.62	0.19	77.80	1.27
	方式2	808.00	0.07	12.10	0.32	87.10	1.29
	优化占比	0.06%	42.86%	-4.30%	40.63%	10.68%	1.55%
经典3D模型	方式1	807.50	0.03	12.63	0.19	77.80	1.27
	方式2	808.00	0.06	12.10	0.32	87.10	1.29
	优化占比	0.06%	50.00%	-4.38%	40.63%	10.68%	1.55%

表5 对比电堆功率为32 W时不同模型及方式下的决策结果

Table 5 Comparison of decision-making results under different models and approaches for a stack power of 32 W

模型类型	方式/占比	$T s c$ /℃	$U E T$ /℃	$I s c$ /A	$U E I$	$U R H 2 O$ /%	$U s c$ /V
I-KAM代理模型	方式1	808.30	0.17	24.67	0.20	77.60	1.29
	方式2	807.85	0.20	24.15	0.33	86.10	1.32
	优化占比	-0.06%	15.00%	-2.15%	39.39%	9.87%	2.27%
经典3D模型	方式1	808.30	0.18	24.66	0.20	77.60	1.29
	方式2	807.85	0.21	24.15	0.33	86.10	1.32
	优化占比	-0.06%	14.29%	-2.11%	39.39%	9.87%	2.27%

表5 对比电堆功率为32 W时不同模型及方式下的决策结果

Table 5 Comparison of decision-making results under different models and approaches for a stack power of 32 W

模型类型	方式/占比	$T s c$ /℃	$U E T$ /℃	$I s c$ /A	$U E I$	$U R H 2 O$ /%	$U s c$ /V
I-KAM代理模型	方式1	808.30	0.17	24.67	0.20	77.60	1.29
	方式2	807.85	0.20	24.15	0.33	86.10	1.32
	优化占比	-0.06%	15.00%	-2.15%	39.39%	9.87%	2.27%
经典3D模型	方式1	808.30	0.18	24.66	0.20	77.60	1.29
	方式2	807.85	0.21	24.15	0.33	86.10	1.32
	优化占比	-0.06%	14.29%	-2.11%	39.39%	9.87%	2.27%

表6 对比电堆功率为48 W时不同模型及方式下的决策结果

Table 6 Comparison of decision-making results under different models and approaches for a stack power of 48 W

模型类型	方式/占比	$T s c$ /℃	$U E T$ /℃	$I s c$ /A	$U E I$	$U R H 2 O$ /%	$U s c$ /V
I-KAM代理模型	方式1	809.10	0.38	36.39	0.22	78.00	1.32
	方式2	809.00	0.42	35.87	0.34	86.30	1.35
	优化占比	-0.01%	9.52%	-1.45%	35.29%	9.62%	2.22%
经典3D模型	方式1	809.10	0.37	36.40	0.22	78.00	1.32
	方式2	809.00	0.41	35.88	0.34	86.30	1.35
	优化占比	-0.01%	9.76%	-1.45%	35.29%	9.62%	2.22%

表6 对比电堆功率为48 W时不同模型及方式下的决策结果

Table 6 Comparison of decision-making results under different models and approaches for a stack power of 48 W

模型类型	方式/占比	$T s c$ /℃	$U E T$ /℃	$I s c$ /A	$U E I$	$U R H 2 O$ /%	$U s c$ /V
I-KAM代理模型	方式1	809.10	0.38	36.39	0.22	78.00	1.32
	方式2	809.00	0.42	35.87	0.34	86.30	1.35
	优化占比	-0.01%	9.52%	-1.45%	35.29%	9.62%	2.22%
经典3D模型	方式1	809.10	0.37	36.40	0.22	78.00	1.32
	方式2	809.00	0.41	35.88	0.34	86.30	1.35
	优化占比	-0.01%	9.76%	-1.45%	35.29%	9.62%	2.22%

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