Coupled model for contaminant diffusion, osmosis and consolidation in soil considering thermal effects
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摘要: 为探究温度对污染物运移进程的影响，建立了考虑热效应的污染物在土中扩散、渗透和固结耦合模型，该模型不仅能够体现污染物运移过程中土体物理特性及输运性质的动态变化，同时实现了扩散、渗透和固结机制的耦合。在验证模型有效性的基础上，分析了热扩散、热渗透、热固结及其综合效应对污染物运移规律的影响。结果表明：热扩散、热渗透能够显著加快污染物运移，且随着索雷特系数和热渗透系数的增大，热扩散和热渗透效应对污染物运移的促进作用增强。而热固结效应则能够减缓污染物运移，但随着土体热膨胀系数的增加，垫层底部污染物积累质量浓度变化不大。当温差为40 K时，与不考虑热效应工况相比，考虑热扩散、热渗透和热固结综合效应影响下的污染物击穿时间缩短54 a。Abstract: To explore the influences of temperature on pollutant transport, a coupled model for contaminant diffusion in soils, osmosis and consolidation considering the thermal effects is proposed to reflect the dynamic changes of physical properties of soils and transport properties in the process of pollutant transport and realize the coupling of diffusion, osmosis and consolidation. On the basis of verifying the validity of the model, the effects of thermal diffusion, thermo-osmosis, thermal consolidation and their combined effect on pollutant transport are analyzed. The simulated results show that the thermal diffusion and thermo-osmosis can accelerate contaminant transport, and with the increase of Soret coefficient and thermal permeability, the thermal diffusion and thermo-osmosis effects enhance. However, the thermal consolidation can slow down the pollutant transport rate, but with the increase of expansion coefficient of soils, the accumulation concentration of pollutant at the bottom of clay layer has little change. When the temperature difference is 40 K, the breakthrough time with considering the combined effects of thermal diffusion, thermo-osmosis and thermal consolidation can be shortened by 53.97 years compared with the results without considering the thermal effects.
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Keywords:
- thermal diffusion /
- thermo-osmosis /
- thermal consolidation /
- contaminant transport
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图 1 不同温差条件下溶质质量浓度积累对比结果
Figure 1. Comparison of solute concentration accumulation under different temperature differences
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图 2 不同索雷特系数条件下溶质质量浓度积累对比结果
Figure 2. Comparison of solute concentration accumulation under different Soret coefficients
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图 3 Neumann边界条件下溶质质量浓度分布对比结果
Figure 3. Comparison of solute concentration distribution under Neumann boundary conditions
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图 4 Dirichle边界条件下溶质质量浓度分布对比结果
Figure 4. Comparison of solute concentration distribution under Dirichle boundary conditions
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图 7 热扩散效应对污染物质量浓度随深度变化影响
Figure 7. Influences of thermal diffusion on variation of contaminant concentration with depth
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图 8 热扩散效应对污染物积累质量浓度随时间变化规律影响
Figure 8. Influences of thermal diffusion on variation of contaminant accumulation concentration with time
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图 9 热渗透效应对污染物质量浓度随深度变化影响
Figure 9. Influences of thermo-osmosis on variation of contaminant concentration with depth
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图 10 热渗透效应对污染物积累质量浓度随时间变化影响
Figure 10. Influences of thermo-osmosis on variation of contaminant accumulation concentration with time
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图 11 热固结效应对污染物质量浓度随深度变化影响
Figure 11. Influences of thermal consolidation on variation of contaminant concentration with depth
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图 12 热固结效应对污染物积累质量浓度随时间变化影响
Figure 12. Influences of thermal consolidation on variation of contaminant accumulation concentration with time
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图 13 热效应对污染物质量浓度随深度变化影响
Figure 13. Influences of thermal effect on variation of contaminant concentration with depth
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图 14 热效应对污染物积累质量浓度随时间变化影响
Figure 14. Influences of thermal effect on contaminant accumulation concentration with time
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图 15 索雷特系数变化对污染物积累质量浓度影响
Figure 15. Influences of variation of Soret coefficient on contaminant accumulation concentration
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图 16 热渗透系数变化对污染物积累质量浓度影响
Figure 16. Influences of variation of coefficient of thermo-osmosis on contaminant accumulation concentration
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图 17 土体热膨胀系数变化对污染物积累质量浓度影响
Figure 17. Influences of variation of coefficient of thermal expansion of soil on contaminant accumulation concentration
表 1 模型参数
Table 1 Model parameters
初始孔隙率n0 扩散系数
D0索雷特系数ST 分配系数
Rd0.5 2.8×10-10 m2/s 0.03K-1 1 注：参数取值与文献[6]相同。 
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表 2 模型参数
Table 2 Model parameters
初始孔隙率n0 扩散系数
D0索雷特系数ST 分配系数
Rd0.5 1×10-10 m2·s-1 0.01K-1 1 注：参数取值与文献[30]相同。
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表 3 模型参数
Table 3 Model parameters
扩散系数
D0/(10-11 m2·s-1)初始孔隙率n0 摩尔质量/(kg·m-3) Zn2+ Cd2+ 1.15，4.05 0.43 0.065 0.112 注：参数取值与文献[31]相同。
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表 4 模型参数
Table 4 Model parameters
参数 取值 自由水体分子扩散系数D0 5×10-10 m2·s-1 初始渗透系数k0 1×10-10 m·s-1 泊松比ν 0.3 弹性模量E 1.49×10-10 Pa-1 化学渗透效率系数ω 0.005 初始孔隙率n0 0.5 吸附系数kd 0.814×10-3 m3 荷载引起的体变系数mv 5×10-7 m·s2·kg-1 质量浓度引起的体变系数mc 0.105×10-7 m-1·s2·kg-1 索雷特系数ST 0.033 K-1 热渗透系数kT 3.14×10-12 m·K·s-1 土体热膨胀系数α 2×10-4 K-1 流体压缩系数βT 4.5×10-10 Pa-1 流体热膨胀系数βTf 3.5×10-4 K-1 固体土颗粒比热容Cps 732 J·kg-1·K-1 孔隙流体比热容Cpf 4186 J·kg-1·K-1 土体固有热传导系数λT 1.69 W·m-1·K-1 水力梯度i 3
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