Analytical model for one-dimensional transport of organic contaminants in multi-layered media considering advection-diffusion-adsorption-degradation
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摘要: 针对成层介质中有机污染物一维运移问题，建立了考虑对流-扩散-吸附-降解时成层介质中有机污染物的一维运移模型，并采用分离变量法获得了该模型解析解。通过将一维运移解析模型的计算结果分别与现有解析解的计算结果和数值方法的计算结果进行对比分析，对所建模型正确性进行了验证。基于所建解析模型，以4层土体为例，对有机污染物一维运移过程展开了参数分析。结果表明，渗滤液水头hw引起的对流作用会加快运移过程，增大底部通量。与hw为0.0 m时相比，hw为2.0 m下的底部通量可增大一个数量级以上；降解作用会降低质量浓度和底部通量。当运移过程达到稳态时，与降解半衰期t1/2趋近于无穷大时相比，t1/2为100a下的底部通量可降低约45%；Robin边界常数α的增大会使得底部范围内的质量浓度降低，同时也会使得底部通量增大，但不同α下的底部通量在同一数量级内变化。
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关键词:
- 有机污染物 /
- 成层介质 /
- 对流-扩散-吸附-降解 /
- 一维运移 /
- 解析解
Abstract: For the problem of one-dimensional transport of organic contaminants in multi-layered media, a one-dimensional organic contaminants transport model in multi-layered media considering advection-diffusion-adsorption-degradation is established, and the analytical solution for the model is obtained by using the separation variable method. The correctness of the established one-dimensional transport analytical model is verified by comparing the calculated results with those of the existing analytical solution and the numerical method. Based on the established analytical model, the one-dimensional transport process of organic contaminants in a four-layer soil is taken as an example to conduct the parameter analysis. The results show that the advection caused by the leachate head hw will accelerate the transport process and increase the bottom flux. Compared with that at hw of 0.0 m, the bottom flux at 2.0 m can be increased by more than one order of magnitude. The degradation will reduce the concentration and bottom flux. When the transport process reaches the steady state, the bottom flux at degradation half-life t1/2 of 100 a can be reduced by about 45% compared with that at t1/2 of infinity. The increase of the Robin boundary constant α will reduce the concentration in the bottom region, and also will increase the bottom flux, which varies in the same order of magnitude under different α. -
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图 2 本文所建解析模型与陈云敏等[24]解析解的对比
Figure 2. Comparison between proposed analytical model and analytical solution proposed by Chen et al.
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图 3 本文所建解析模型与数值方法计算结果的对比
Figure 3. Comparison between proposed analytical model and numerical method
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图 4 不同渗滤液水头下有机污染物质量浓度的分布曲线
Figure 4. Distribution curves of concentration of organic contaminants under different leachate heads
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图 5 不同渗滤液水头下底部通量随时间的变化曲线
Figure 5. Distribution curves of bottom flux with time under different leachate heads
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图 6 不同降解半衰期下有机污染物质量浓度的分布曲线
Figure 6. Distribution curves of concentration of organic contaminants under different degradation half-lives
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图 7 不同降解半衰期下底部通量随时间的变化曲线
Figure 7. Distribution curves of bottom flux with time under different degradation half-lives
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图 8 不同Robin边界常数下有机污染物质量浓度的分布曲线
Figure 8. Distribution curves of concentration of organic contaminants under different Robin boundary constants
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图 9 不同Robin边界常数下底部通量随时间的变化曲线
Figure 9. Distribution curves of bottom flux with time under different Robin boundary constants
表 1 4层土体的物理力学参数及相关的环境参数
Table 1 Physical-mechanics parameters of four-layer soils and environment-related parameters
土层编号 渗透系数kv/(10-9m·s-1) 有效扩散系数De/(10-10m2·s-1) 纵向弥散度αL/m 降解半衰期t1/2/a 吸附阻滞因子Rd 孔隙率n 厚度l/m 渗滤液水头hw/m 质量浓度C0/(mg·L-1) Robin边界常数α/(m-1) 土层1 1.0 4.0 0.02 150 6.6 0.35 0.50 1.0 1.0 1.0 土层2 0.2 2.0 0.01 100 9.8 0.30 0.50 1.0 1.0 1.0 土层3 20.0 6.0 0.04 200 4.2 0.40 0.25 1.0 1.0 1.0 土层4 100.0 8.0 0.05 250 2.8 0.45 0.75 1.0 1.0 1.0 
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