﻿ 膜电容去离子法海水淡化装置单元脱盐过程的数值模拟
 舰船科学技术  2020, Vol. 42 Issue (6): 110-114    DOI: 10.3404/j.issn.1672-7649.2020.06.022 PDF

Numerical simulation of desalting process in seawater desalination plant by membrane capacitive deionization
XIAO Min, JIN Miao-miao, YAO Shou-guang
School of Energy and Power Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China
Abstract: Based on the middle inflow type desalting module in membrane capacitance method, a three-dimensional transient analysis model of desalting unit was established. Then the applicability of the model was verified by linear regression fitting of simulation results, and the desalting unit was analyzed by numerical simulation. The results show that with the increase of inlet aperture, the minimum outlet concentration of MCDI desalting unit increases, while the maximum decreases. The larger the inlet aperture, the longer the desalting unit reaches the adsorption saturation time, and the smaller the adsorption efficiency, yet the more the desorption time increases, and the higher the desorption efficiency peak. Under the same inlet aperture, the maximum outlet concentration in reverse desorption mode both achieves higher than that in short.
Key words: membrane capacitive deionization     middle inflow type     numerical simulation
0 引　言

1 模型建立 1.1 MCDI模型几何结构

 图 1 中部流入式MCDI模型几何结构图 Fig. 1 Geometric structure diagram of MCDI model in the middle inflow type
1.2 数学模型

 $\frac{{\partial {c_{sp}}\left( y \right)}}{{\partial t}} = - \frac{{{J_{ion}}\left( y \right)}}{{{\delta _{sp}}}} - {v_{sp}}\frac{{\partial {{\text{c}}_{sp}}\left( y \right)}}{{\partial y}}\text{。}$ (1)

2个膜/溶液的界面上都具有Donnan平衡，且两者分别分布在膜边缘与流道的接触面和膜边缘与电极的接触面。这2个Donnan势如下式：

 ${\Delta {\rm{\phi }}}_{{\rm{d}}{\rm{o}}{\rm{n}}{\rm{n}}{\rm{a}}{\rm{n}}}={\rm{sin}}{{{h}}}^{-1}\frac{\omega {{X}}}{2{{c}}_{{\rm{s}}{\rm{a}}{\rm{l}}{\rm{t}}}}\text{。}$ (2)

 ${{\text{J}}_{{\text{ion}},{\text{mem}}}}\left( y \right) = - \frac{{{D_{mem}}}}{{{\delta _{mem}}}}\left( {{c_{{\text{T}},{\text{mem}}}}\left( y \right) - \omega X\Delta {\phi _{{\text{mem}}}}\left( y \right)} \right)\text{。}$ (3)

 $\frac{{\partial {c_{sp,i}}}}{{\partial t}} = - \frac{{{J_{ion,i}}}}{{{\delta _{sp}}}} - \frac{M}{{{\tau _{sp}}}}\left( {{c_{sp,i}} - {c_{sp,i - 1}}} \right)\text{。}$ (4)

 $\begin{split} & \frac{1}{2}{V_{{\text{cell}}}}/{V_{\text{T}}} = \Delta {\phi _{{\text{sp}},{\text{half}}}} + \Delta {\phi _{{\text{donnan}},{\text{membrane}}/{\text{spacer}}}} + \\ & \Delta {\phi _{{\text{mem}}}} - \Delta {\phi _{{\text{donnan}},{\text{membrane}}/{\text{electrode}}}} + \Delta {\phi _{{\text{elec}}}} + \\ & {{{\left( {\Delta {\phi _{\text{d}}} + \Delta {\phi _{{\text{St}}}}} \right)}_{{\text{micropores}}}}} \;{\text{。}} \end{split}$ (5)

1.3 边界条件及模型参数 1.3.1 入口与出口边界条件

MCDI单元模型包含流场、离子浓度场、电场等，因此该模型边界条件如下：

 $\left\{ {\begin{array}{*{20}{c}} {{{V = }}{{{v}}_{{\rm{in}}}}}\text{，}\\ {{{p = }}{{{p}}_{{\rm{out}}}}}\text{，}\\ {\nabla {{P}} \cdot \overrightarrow {{n}} {\rm{ = 0}}}\text{。} \end{array}} \right.$ (6)

 $\overrightarrow {{u}} {\rm{ = }}{{{v}}_{{{in}}}}{\rm{, }}{{{c}}_{{i}}}{{ = c}}_{{i}}^{{\rm{ref}}}{{,T = }}{{{T}}_{{{in}}}}\text{。}$ (7)

 $\overrightarrow {{u}} {\rm{ = 0, }}{{{c}}_{{i}}}{{ = c}}_{{i}}^0\text{。}$ (8)
1.3.2 模型参数

2 模拟结果与分析 2.1 边界条件及模型参数

Lagergren准一级和准二级动力学方程[15]为：

 $\ln\left(1-\frac{{q}_{t}}{{q}_{e}}\right)=-{K}_{1}t\text{，}$ (9)
 $\frac{1}{{{{q}}}_{{{t}}}}=\frac{1}{{K}_{2}{q}_{e}^{2}}\left(\frac{1}{{{t}}}\right)+\frac{1}{{{{q}}}_{{{e}}}}\text{。}$ (10)

2.2 入口孔径对脱盐性能的影响 2.2.1 两种脱附方式下的结果分析

 图 2 MCDI脱盐单元在不同入口孔径下2种脱附方式的脱盐曲线图 Fig. 2 Desalting curves of MCDI desalting module under different inlet aperture in two desorption methods

2.2.2 吸、脱附效率

 图 3 MCDI脱盐单元在不同入口孔径下2种脱附方式的吸、脱附效率图 Fig. 3 Adsorption and desorption efficiency charts of MCDI desalting module under different inlet aperture in two desorption methods

3 结　语

1）对模拟得到中部流入式MCDI脱盐模拟过程中Na+出口浓度的数值结果进行线性回归拟合研究表明，本文所建立的中部流入式膜电容法脱盐分析模型适用于对MCDI脱盐单元的数值模拟。

2）MCDI脱盐单元的出口最低浓度随入口孔径的增大而增大，且入口孔径越大，其达到吸附饱和的时间越长，但脱盐单元的吸附效率越小；随着入口孔径的增大，出口最高浓度逐渐递减，脱附时间相应增加，脱盐单元能够达到的脱附效率峰值也越大，同一入口孔径条件下，反接脱附方式下能够达到的最高出口浓度均高于短接脱附方式。

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