无机污染物离子在电动土工屏障中的一维对流–扩散模型及其解析解

One-dimensional advection-diffusion model and analytical solution for inorganic contaminant ion transport in electro-kinetic barrier

电动修复是一项十分具有应用前景的土壤修复技术,利用该技术原理提出的电动土工屏障,可以有效阻止污染物往周围土体和地下水中的扩散。考虑无机污染物离子在浓度梯度、水力梯度以及电渗和电迁移共同作用下的迁移规律,建立电动土工屏障中无机离子的一维对流–扩散模型,并采用Laplace变换法推导其解析解,给出屏障中任一断面的离子流出质量通量计算公式,并通过与文献中的一维模型试验结果进行对比验证其正确合理性。在此基础上,利用提出的解析解,开展参数研究,分析无机污染物离子在电动土工屏障中的迁移规律。结果表明:阳极边界处的Pb2+稳定流出质量通量随着平均电势梯度、黏土层厚度、土体电渗透系数的增大而显著减小;对于扩散系数大的污染物离子,建议提高平均电势梯度以增强其电动迁移效果;吸附阻滞因子对最终稳定流出质量通量影响较小,但可以有效延长电动土工屏障被击穿的时间。所提出的解析模型为电动土工屏障的设计提供一种简便的计算方法,还可验证相关数值模型的正确性。

Electro-kinetic remediation is one soil remediation technology with a significant application prospect,and the electro-kinetic barrier developed based on the principle of this technology can effectively prevent the diffusion of contaminant ions to nearby soils or underground water. In this paper,a 1 D advection-diffusion model for contaminant ion transport was established for the electro-kinetic barrier considering the combined action of concentration gradient,hydraulic gradient,electro-osmosis and electro-migration. Analytical solution was then derived by using the Laplace transform method,and the formula for calculating the mass flux was also given. Thereafter,the proposed analytical solution was verified by the 1 D mode test results in the previous study. Finally,parameter study was conducted to analyze the migration of contaminant ions in the electro-kinetic barrier. The results indicate that the mass flux of Pb2+ at anode boundary decreases remarkably with increasing average potential gradient,barrier thickness or electro-osmotic conductivity. For the contaminant ions with a large diffusion coefficient,it is suggested to increase the potential gradient to improve the effect of electro-kinetic migration. The soil adsorption retardation coefficient has an unremarkable effect on the final stable outflow mass flux but can effectively prolong the breakthrough time of the electro-kinetic barrier. The proposed analytical solution can not only provide a simple calculation method for the design of electro-kinetic barrier but also be used to verify the corresponding numerical models.