Numerical simulation of performance of thermally regenerative ammonia-based battery with copper foam electrode

doi:10.11949/0438-1157.20200126

Abstract

Abstract:

A steady-state mathematical model that coupled the mass transfer and electrochemical reaction in a porous medium was proposed for a thermally regenerative ammonia-based battery (TRAB) with copper foam electrode. The battery performance and internal mass transfer characteristics of the porous electrode were obtained and the effects of electrolyte concentration and electrode porosity on battery performance were studied. The results showed that the anode ammonia and cathode copper ions were gradually consumed from the mainstream to the inside of the porous electrode, which led to a concentration gradient. With the increase of the reaction current, the concentration gradient increased obviously. In a certain range, with the increase of the concentration of anodic ammonia and cathode copper ions, the material transfer from the main flow area to the porous electrode improved. As the concentration of ammonium sulfate increases, the electrolyte conductivity increases, and the battery performance gradually improves, but the increase decreases gradually. In addition, the porous electrode porosity will also affect the battery performance. In this study, TRAB obtained the highest maximum power (15.3 mW) when the electrode porosity was 0.6.

Key words: thermally regenerative ammonia-based battery, porous foam electrode, numerical simulation, electrochemistry, mass transfer, maximal power, porosity

摘要：

以采用泡沫铜电极的热再生氨电池（thermally regenerative ammonia-based battery，TRAB）为研究对象，建立了多孔介质内物质传输与电化学反应耦合的稳态模型，计算获得了电池性能及多孔电极内物质传输特性，并研究了电解质浓度和电极孔隙率对电池性能的影响。研究结果表明，从主流区界面到多孔电极内部，阳极氨和阴极铜离子浓度逐渐降低，存在一定的浓度梯度，而且随着反应电流的增大，浓度梯度明显增大。在一定的范围内分别增大阳极氨浓度和阴极铜离子浓度，从主流区向多孔电极内物质传输增强，电池性能均能不断提升；随着硫酸铵浓度的增大，电解质电导率增大，电池性能逐渐提升，但增幅逐渐减小。此外，多孔电极孔隙率也会影响电池性能，本研究中TRAB在电极孔隙率为0.6时获得最高的最大功率(15.3 mW)。

关键词: 热再生氨电池, 多孔泡沫电极, 数值模拟, 电化学, 传质, 最大功率, 孔隙率

CLC Number:

TM 911.3

Yongsheng ZHANG, Liang ZHANG, Jun LI, Qian FU, Xun ZHU, Qiang LIAO, Yu SHI. Numerical simulation of performance of thermally regenerative ammonia-based battery with copper foam electrode[J]. CIESC Journal, 2020, 71(8): 3770-3779.

张永胜, 张亮, 李俊, 付乾, 朱恂, 廖强, 石雨. 采用泡沫铜电极的热再生氨电池性能数值模拟[J]. 化工学报, 2020, 71(8): 3770-3779.

Figures/Tables 11

Fig.1 Calculation model and meshing of the TRAB with copper foam electrodes

Table 1 Dimensional parameters of geometrical domain

参数	符号	数值/mm
阳极腔室长度	L_AL	30
阴极腔室长度	L_CL	30
泡沫铜阳极厚度	L_AC	4
泡沫铜阴极厚度	L_CC	4
阴离子交换膜厚度	L_AEM	1
电极高度	H	30

Table 2 Parameters used in the model

参数	符号	数值	来源
Cu²⁺扩散系数/(m²/s)	$D C u 2 +$	1.5×10^-9	文献[33]
$C u (N H 3) 4 2 +$ 扩散系数/ (m²/s)	$D C u (N H 3) 4 2 +$	0.6 ×10^-9	文献[33]
NH₃扩散系数/ (m²/s)	$D N H 3$	1.7×10^-9	文献[33]
$N H 4 +$ 扩散系数/ (m²/s)	$D N H 4 +$	0.95 ×10^-9	文献[33]
电极孔隙率	$ε$	0.9	—
电极活性比表面积/ (m²/m³)	$a V$	4985	测量
Cu²⁺参考浓度/ (mol/L)	$c C u 2 +, r e f$	1	—
操作温度/K	T	298.15	测量
阳极电解质电导率/ (S/m)	$κ a$	6.3	测量
阴极电解质电导率/ (S/m)	$κ c$	7.8	测量
阳极反应速度常量/ (m/s)	$K 0 a$	7 ×10^-7	文献[33]
阴极反应速度常量/(m/s)	$K 0 c$	5 ×10^-6	文献[33]
Cu²⁺初始浓度/ (mol/L)	$c C u 2 + 0$	0.1	—
$N H 4 +$ 初始浓度/ (mol/L)	$c N H 4 + 0$	0.5	—
$C u (N H 3) 4 2 +$ 初始浓度/ (mol/L)	$c C u (N H 3) 4 2 + 0$	0.1	—
NH₃?H₂O初始浓度/ (mol/L)	$c N H 3 0$	0.6	—
反应(9)阴极传递系数	$α c c$	0.36	—
反应(10)阴极传递系数	$α c a$	0.64	—
式(11)阳极传递系数	$α a c$	0.5	—
式(12)阳极传递系数	$α a a$	0.5	—

Table 2 Parameters used in the model

参数	符号	数值	来源
Cu²⁺扩散系数/(m²/s)	$D C u 2 +$	1.5×10^-9	文献[33]
$C u (N H 3) 4 2 +$ 扩散系数/ (m²/s)	$D C u (N H 3) 4 2 +$	0.6 ×10^-9	文献[33]
NH₃扩散系数/ (m²/s)	$D N H 3$	1.7×10^-9	文献[33]
$N H 4 +$ 扩散系数/ (m²/s)	$D N H 4 +$	0.95 ×10^-9	文献[33]
电极孔隙率	$ε$	0.9	—
电极活性比表面积/ (m²/m³)	$a V$	4985	测量
Cu²⁺参考浓度/ (mol/L)	$c C u 2 +, r e f$	1	—
操作温度/K	T	298.15	测量
阳极电解质电导率/ (S/m)	$κ a$	6.3	测量
阴极电解质电导率/ (S/m)	$κ c$	7.8	测量
阳极反应速度常量/ (m/s)	$K 0 a$	7 ×10^-7	文献[33]
阴极反应速度常量/(m/s)	$K 0 c$	5 ×10^-6	文献[33]
Cu²⁺初始浓度/ (mol/L)	$c C u 2 + 0$	0.1	—
$N H 4 +$ 初始浓度/ (mol/L)	$c N H 4 + 0$	0.5	—
$C u (N H 3) 4 2 +$ 初始浓度/ (mol/L)	$c C u (N H 3) 4 2 + 0$	0.1	—
NH₃?H₂O初始浓度/ (mol/L)	$c N H 3 0$	0.6	—
反应(9)阴极传递系数	$α c c$	0.36	—
反应(10)阴极传递系数	$α c a$	0.64	—
式(11)阳极传递系数	$α a c$	0.5	—
式(12)阳极传递系数	$α a a$	0.5	—

Table 3 Source items of the mass conservation equation

源/汇	阳极	阴极
S₁( $N H 3$ )	$2 ? j a F$	0
S₂( $C u (N H 3) 4 2 +$ )	$- ? j a 2 F$	0
S₃( $C u 2 +$ )	0	$- ? j c 2 F$

Table 3 Source items of the mass conservation equation

源/汇	阳极	阴极
S₁( $N H 3$ )	$2 ? j a F$	0
S₂( $C u (N H 3) 4 2 +$ )	$- ? j a 2 F$	0
S₃( $C u 2 +$ )	0	$- ? j c 2 F$

Fig.2 Verification of proposed model against experimental results

Fig.3 Distribution of ammonia concentration (a) and Cu2+ concentration (b) at different voltages

Fig.4 Effects of different ammonia concentration on battery performance (a) and distribution of ammonia concentration (b)

Fig.5 Effects of different Cu2+ concentration on battery performance(a) and distribution of Cu2+ concentration(b)

Table 4 Conductivity of the electrolyte with different concentration of (NH4)2SO4

硫酸铵浓度/(mol/L)	阴极电解液电导率 $κ c$ /(S/m)	阳极电解液电导率 $κ a$ /(S/m)
0.5	7.8	6.3
1	13.3	11.3
1.5	22	19.9
2	25.6	23.5
2.5	28.9	26.7

Table 4 Conductivity of the electrolyte with different concentration of (NH4)2SO4

硫酸铵浓度/(mol/L)	阴极电解液电导率 $κ c$ /(S/m)	阳极电解液电导率 $κ a$ /(S/m)
0.5	7.8	6.3
1	13.3	11.3
1.5	22	19.9
2	25.6	23.5
2.5	28.9	26.7

Fig.6 Effects of different (NH4)2SO4 concentration on battery performance

Fig.7 Effects of different electrode porosity on battery performance

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