考虑非等温环境下污染物在黏土中的运移解析模型

Analytical solutions of contaminant transport in clay liner system under non-isothermal condition

利用广义积分变换法推导了非等温条件下污染物在压实黏土衬垫中的运移解析解。所提出的解析解考虑了分子扩散、对流、吸附和热扩散的耦合效应,并考虑了压实黏土的渗透系数、分布系数和有效扩散系数3个参数随温度的变化。通过与热扩散试验结果、已有的解析解和基于COMSOL软件的数值模型的对比,验证了所提出的解析解。利用经过验证的解析解,研究了非等温环境以及压实黏土的渗透系数、有效扩散系数和分布系数3个参数随温度的变化对甲苯在压实黏土衬垫系统中迁移的影响。结果表明,非等温环境以及压实黏土的渗透系数、有效扩散系数和分布系数随温度的变化均对甲苯在压实黏土衬垫中迁移有着显著的影响。不考虑非等温环境的影响将极大低估污染物的溢出量和污染物的击穿时间。既有解析解忽略压实黏土的渗透系数和有效扩散系数随温度的变化会极大低估甲苯的流出速率,而忽略压实黏土分布系数随温度的变化会极大高估甲苯击穿衬垫系统的时间和达到稳态的时间。所提出的解析解能够考虑热扩散作用,同时考虑了压实黏土的渗透系数、分布系数和有效扩散系数3个参数随温度的变化,较既有解析解更贴近工程实际,能够为压实黏土衬垫系统的设计和服役性能评价提供指导和借鉴。

Analytical solutions of contaminant transport in a compacted clay liner(CCL) under non-isothermal condition are derived through the generalized integral transform technique. The proposed analytical solutions account for the coupling effects of molecular diffusion, advection, sorption and thermal diffusion. In addition, the variations of CCL permeability coefficient, CCL distribution coefficient and CCL effective diffusion coefficient with temperature are also considered in the analytical solutions. The proposed analytical solutions are successfully validated against the experimental results of thermal diffusion tests, the analytical solutions available in previous studies and COMSOL numerical results, respectively. Then the effects of non-isothermal condition, permeability coefficient, effective diffusion coefficient and distribution coefficient of CCL on the transport of benzene in CCL system were studied through the verified analytical solutions. The results indicate that the non-isothermal condition and the variations of permeability coefficient, effective diffusion coefficient and distribution coefficient of CCL with temperature all have significant effects on benzene transport in the CCL system. The mass flux and breakthrough time of contaminant can be substantially underestimated without considering the effect of non-isothermal condition. The previous analytical solutions that neglect the variations of CCL permeability coefficient and CCL effective diffusion coefficient with temperature can substantially underestimate the benzene outflow rate,whereas neglecting the variation of CCL distribution coefficient with temperature can substantially overestimate the cost time of benzene to penetrate the liner system and reach steady-state. The proposed analytical solutions that consider the effects of thermal diffusion as well as the variations of CCL permeability coefficient, CCL distribution coefficient and CCL effective diffusion coefficient with temperature are more suitable for the engineering practice. It can be adopted to improve the design scheme and the service performance evaluation of CCL system.