An analytical model for diffusion of chemicals under thermal effects in semi-infinite porous media
An analytical model for diffusion of chemicals under thermal effects in semi-infinite porous media
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DOI：
10.1016/j.compgeo.2015.06.012
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发表时间：
2015-09
影响因子：
5.3
通讯作者：
H. Xie;Chunhua Zhang;M. Sedighi;H. Thomas;Yun-min Chen
中科院分区：
文献类型：
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作者：
H. Xie;Chunhua Zhang;M. Sedighi;H. Thomas;Yun-min Chen
本文给出了化学势和热势耦合作用下一维化学物质扩散的解析解。考虑的理论公式包括热传导和化学扩散由于分子和热扩散势。利用拉普拉斯变换技术，导出了半无限域上问题的解析解。用该解析解计算的结果与盐溶液在粘土中热扩散的实验结果吻合得很好。与数值模型的比较也进行了调查的瞬态热传导和温度依赖性的扩散系数的化学传输由于热梯度的影响。应用该模型研究了压实粘土衬砌（CCL）中热扩散对化学输运的影响。结果表明，随着温度的升高和Soret系数的增大，CCL中的碱浓度和化学通量增大。对于0.6m的压实粘土衬垫，热扩散情况下的40年底通量是仅分子扩散情况下的2-11倍。根据所得结果，热扩散在填埋场设计中表现出相当大的影响。在ST = 5 × 10−21/K的模拟情景中，100年时的化学物质基浓度和通量分别是不考虑热扩散的模拟结果的1.5倍和8倍。使用的分析模型，一系列的无量纲设计图表，可用于估计的CCL的厚度，在非等温条件下。建议的解析解提供了一个简单的方法，替代数值模型的验证，地下水/土壤修复方法的评价和垃圾填埋场粘土衬垫的初步设计。
An analytical solution for one-dimensional diffusion of chemicals under coupled chemical and thermal potentials is presented. The theoretical formulation considered includes heat conduction and chemical diffusion due to both molecular and thermal diffusion potentials. Laplace transformation technique has been used to derive the analytical solution to the problem in a semi-infinite domain. The results obtained by the proposed analytical solution have a good agreement with those obtained from the laboratory tests of thermal diffusion of a salt solution in a compact clay. Comparisons with the numerical model were also carried out to investigate the effects of transient heat conduction and temperature-dependency of diffusion coefficient on the chemical transport due to a thermal gradient. An application of the model to study the effects of thermal diffusion on chemical transport in a compacted clay liner (CCL) is presented. The results show that the base concentration and flux of the chemical in the CCL increases with the increase of the temperature and Soret coefficient. The 40-year bottom fluxes for the case with thermal diffusion are 2–11 times greater than the case with only molecular diffusion for a 0.6 m compacted clay liner. Based on the results achieved, thermal diffusion demonstrates considerable effect in the landfill design. In the simulation scenario withST= 5 × 10−21/K, the base concentration and the flux of the chemical at 100 years is 1.5 times and 8 times larger, respectively than those obtained from the simulation without considering thermal diffusion. Using the analytical model presented, a series of dimensionless design charts are presented that can be used to estimate the thickness of the CCL, under non-isothermal conditions. The proposed analytical solution provides a simple method for the verification of alternative numerical models, evaluation of groundwater/soil remediation methods and preliminary design of landfill clay liners.