Numerical simulation of ion transfer during electrodialysis desalination process

doi:10.11949/0438-1157.20200185

Abstract

Abstract:

A mathematical model of steady-state ion transfer during electrodialysis process was established to study the effects of ion charge number, diffusion coefficient and conductivity of ion-exchange membrane on mass transfer during the desalination process. The changes of ion concentration distribution, electric potential distribution and ion transfer flux distribution were described. The results showed that for the divalent ion concentration difference over the membrane decreased, transmembrane potential drop increased and transfer flux decreased in comparison with the monovalent ion. When ion diffusion coefficient was larger, concentration difference over the membrane became smaller, transmembrane potential drop, total flux and electromigration flux became higher. Additionally, ion-exchange membrane with larger conductivity made concentration difference over the membrane larger, transmembrane potential drop lower and transfer flux higher.

Key words: electrodialysis, desalination, ion transfer, model, numerical simulation

摘要：

建立了电渗析脱盐过程离子传递稳态模型，研究了离子电荷数、离子扩散系数和离子交换膜电导率对脱盐过程传质的影响，描述了离子浓度分布、电势分布和离子传递通量分布的变化情况。研究表明：相较于一价离子，二价离子在电渗析过程中膜两侧浓度差较小，跨膜电压降较高，各项传递通量较小；当离子扩散系数增大时，膜两侧浓度差减小，跨膜电压降升高，总传递通量和电迁移通量增大；当离子交换膜电导率增大时，膜两侧浓度差增大，跨膜电压降降低，各项传递通量均增大。

关键词: 电渗析, 脱盐, 离子传递, 模型, 数值模拟

CLC Number:

TQ 028

Haitao ZHU, Bo YANG, Yaqin WU, Congjie GAO. Numerical simulation of ion transfer during electrodialysis desalination process[J]. CIESC Journal, 2020, 71(8): 3518-3526.

祝海涛, 杨波, 吴雅琴, 高从堦. 电渗析脱盐过程离子传递现象的数值模拟[J]. 化工学报, 2020, 71(8): 3518-3526.

Figures/Tables 16

Fig.1 Schematic diagram of electrodialysis setup

Fig.2 Model geometry of membrane and compartment

Table 1 Parameters for numerical modeling

Parameter	Value^①
total voltage drop (V_t)	0.2 V
inlet concentration (c₀)	500 eq/m³
inlet flow velocity (v_inlet)	0.03 m/s
ion exchange capacity of CEM^②	1.4 meq/g
ion exchange capacity of AEM^③	1.0 meq/g
membrane conductivity (σ_m)	0.2 S/m
length of eletrodialysis unit (L)	10 cm
width of compartments (W_c)	0.7 mm
thickness of membranes (δ_m)	0.1 mm
temperature (T)	298.15 K

Fig.3 Concentration at membrane surface at different numbers of grid

Table 2 Concentration of NaCl solution in the diluate

脱盐时间/min	计算值/(mol/m³)	实验值/(mol/m³)
0	500.0	500.0
8	430.4	437.0
16	360.8	367.5
24	291.2	296.9
32	221.6	229.6
40	152.0	157.8

Fig.4 Ion concentration profile at different voltages

Fig.5 Electrolyte potential profile at different voltages

Table 3 Potential drop across the cation-exchange membrane at different voltages

施加电压/V	跨膜电压降/V
施加电压/V	NaCl	CaCl₂
0.2	0.057	0.062
0.3	0.085	0.093
0.4	0.111	0.121

Fig.6 Transfer flux at the voltage of 0.2 V

Table 4 Diffusion coefficient of ions in the solution[27-28]

离子	扩散系数D_i/(m²/s)
Na⁺	1.35×10^-9
Ca²⁺	7×10^-10
K⁺	1.95×10^-9
Cl^-	2.03×10^-9

Fig.7 Effect of diffusion coefficient on concentration distribution

Fig.8 Effect of diffusion coefficient on electrolyte potential distribution

Fig.9 Effect of diffusion coefficient on transfer flux

Fig.10 Effect of membrane conductivity on sodium concentration distribution

Fig.11 Effect of membrane conductivity on electrolyte potential distribution (NaCl solution)

Fig.12 Effect of membrane conductivity on sodium transfer flux

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