Migration mechanism of lead ions in unsaturated loess under temperature gradient
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摘要: 基于多孔介质理论及连续介质热弹性力学，研究了温度梯度作用下重金属离子在非饱和黄土中的迁移机理。首先，通过非等温吸附试验确定了黄土颗粒对铅离子的吸附模型；其次，以固、液、气三相系统中各组分质量、能量以及动量守恒方程为基础，建立了表征温度梯度下非饱和土中污染物迁移的多场耦合数学模型，模型考虑了重金属离子的吸附、孔隙流体的迁移及相变、温度梯度下土体的变形等因素，以温度、孔隙率、孔隙水压、孔隙气压、重金属离子浓度、吸附浓度、土体骨架位移为基本未知量，较全面反映了非饱和土体中热质迁移规律及变形特点；最后，开展非饱和黄土中铅离子迁移土柱试验，验证理论模型的可靠性，并分析了各因素对铅离子迁移规律的影响。结果表明：Langmuir非线性吸附模型比较符合黄土颗粒对铅离子的吸附特征，最大吸附量随温度升高而降低，温度梯度对非饱和黄土中污染物迁移有较明显促进作用；不计土体湿陷效应时，温度梯度及吸湿膨胀使土柱产生拉伸变形，重力、孔隙水压及孔隙气压共同作用使土柱产生压缩变形，后者影响大于前者，故土柱整体为压缩变形；污染物迁移随时间增长而减弱，吸附作用是长期过程，时间增长对其影响不显著。Abstract: Based on the theory of porous media and the continuum thermoelasticity, the migration mechanism of heavy metal ions in unsaturated soils under temperature gradient is studied. Firstly, the adsorption model for the lead ion by soil particles is determined through the non-isothermal adsorption tests. Secondly, based on the mass conservation, energy conservation and momentum conservation equations for various components in the three-phase system of solid, liquid and gas, a multi-physical field coupling mathematical model characterizing the migration of pollutants in unsaturated soils under temperature gradient is established. The model takes into account the adsorption effects of heavy metal ions, the migration of pore fluid, the compressibility of phase change soil skeleton and pore fluid phase and the deformation of soils regarding the temperature, porosity, pore water pressure, pore gas pressure, heavy metal ion concentration, adsorption concentration and soil skeleton displacement as the basic unknowns, which comprehensively reflect the characteristics of heat and mass migration and deformation in unsaturated soils. Finally, a soil column test on the migration of lead ions in unsaturated loess is carried out to verify the effectiveness of the theoretical model and the numerical results, and the influences of various factors on the migration laws of lead ions are analyzed. The results show that the Langmuir nonlinear adsorption model is more consistent with the adsorption characteristics of unsaturated loess for lead ions, and the maximum adsorption capacity decreases with the increase of temperature. The temperature gradient can obviously promote the migration of pollutants in unsaturated loess. While the pollutants migrate in unsaturated loess soil column, the whole soil column is in tensile deformation state. The migration of pollutants decreases with time. The adsorption is a long-term process, and the effects of time on it are not significant.
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Keywords:
- temperature gradient /
- lead ion /
- multi-field coupling /
- adsorption /
- transfer
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图 5 孔隙水压、基质吸力、水蒸气压强及水蒸气密度变化曲线
Figure 5. Variation curves of pore water pressure, matrix suction, water vapor pressure and water vapor density
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图 6 各点位移、有效应力变化曲线
Figure 6. Variation curves of displacement and effective stress at each point
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图 7 高度方向浓度、吸附浓度变化曲线
Figure 7. Variation curves of concentration and adsorption concentration in height direction
表 1 铅离子吸附试验数值
Table 1 Test values of Pb ion adsorption
温度/
K初始浓度C0/(mg·L-1) 液相浓度C/(mg·L-1) 吸附Cs/(mg·kg-1) 278 100 0.36 1244.51 120 6.48 1619.98 150 13.93 1741.25 180 22.98 1915.12 200 32.34 2021.25 283 100 0.42 1216.86 120 7.28 1548.64 150 14.86 1646.25 180 24.64 1865.46 200 33.48 1986.46 293 100 0.56 1186.88 120 8.64 1508.24 150 15.58 1604.25 180 26.12 1768.56 200 34.64 1868.36 313 100 0.78 1108.46 120 10.16 1428.62 150 16.88 1516.26 180 28.12 1648.36 200 36.46 1726.54 
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表 2 吸附系数
Table 2 Adsorption coefficients
温度
T/K非线性吸附常数
α/(mg·L-1)最大吸附量β/
(mg·g-1)278 0.55 2.32 283 0.50 2.01 293 0.56 1.82 313 0.37 1.79
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表 3 计算参数表
Table 3 Parameters for calculation
参数名称 取值 参数名称 取值 土体试样高度H/m 0.3 土体密度ρs/(kg·m-3) 1560 初始时刻污染物
浓度C0/(kg·m-3)0.5 污染物扩散
系数D0/(m2·s-1)5×10-9 土体试样半径r/m 0.1 土体纵向
弥散度αL/m0.35 n0 0.423 干燥气体摩尔
质量Ma(kg·mol-1)2.88×10-2 气体摩尔常数R/(J·mol·K-1) 8.214 孔隙度n0时
渗透率K0/(1/m2)1×10-16 最大饱和度Ss 0.9 残余饱和度Sr 0.1 吸湿膨胀系数βs 1.5×10-4 弹性模量Es/MPa 25 泊松比μ 0.3 非线性吸附常数α/ (mg·L-1) 0.55 最大吸附量β/(mg·g-1) 2.32 温度T0/K 278.15 正反应速率
常数λ1/(1·s-1)2.5×10-6 P0/Pa 0.9×105 逆反应速率
常数λ2/(1·s-1)1.5×10-6 βm/(1·K-1) -2.1×10-3 土体弯曲因子τ 0.7 液态水质量热容Cw/
(J·kg·K-1)4180 空气质量热容Ca/
(J·kg·K)1000 土体骨架质量热容Cp/ (J·kg·K-1) 1000 水蒸气质量热容Cg/(J·kg·K) 1900 混合气相导热系数λg/ (W·m·K-1) 0.024 液态水导热系数λl/(W·m·K-1) 0.56 土体骨架导热系数λs/ (W·m·K-1) 2.93 液相水相变潜热Lwg/(J·kg-1) 2.4×106 水蒸汽摩尔质量Mw/
(kg·mol-1)0.018 热膨胀系数
βsT/(1·K-1)7.8×10-6 液态水密度ρw/
(kg·m-3)1000
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表 4 边界条件
Table 4 Boundary conditions
初始条件 上边界条件 下边界条件 孔隙率n 0.432 孔隙率n — 孔隙率n — 孔隙水压Pl/kPa -190 孔隙水压Pl/kPa — 孔隙水压
Pl0 孔隙气压Pg/kPa 102.1 孔隙气压Pg/kPa 102.1 孔隙气压
Pg0 位移u/
m0 位移u/
m— 位移u 0 浓度C/
(kg·m-3)0 浓度C/
(kg·m-3)— 浓度C/
(kg·m-3)0.5 吸附浓度
Cs/(kg·kg-1)0 吸附浓度
Cs/(kg·kg-1)— 吸附浓度
Cs/(kg·kg-1)— 温度
T/K278.15 温度
T/K278.15 温度
T/K303.15
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