Primary Controlling Factors and Statistical Modeling of Plume Stability for BTEX in Typical Phreatic Aquifers
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摘要: 场地或区域地下水污染羽能否达到稳定及其稳定性特征直接决定自然衰减修复的可行性.本文构建了从上到下依次为潜水层、弱透水层、承压层的典型含水结构，模拟量化潜水层恒定源地下水污染羽迁移扩散，以污染羽稳定面积、稳定浓度和稳定所需时间为特征因子，充分考虑可能影响污染羽迁移扩散的水文地质和水化学参数.首先通过敏感性分析筛选出较敏感因子，然后利用正交试验进行主控因子识别，最后采用多元回归模型构建特征因子与主控因子的定量统计关系.结果表明，对污染羽特征因子具有广泛影响的主控因子为降解系数、弥散度、渗流速度和源浓度，特征因子与主控因子之间具有良好的统计关系，根据实际情况可选用不同主控因子数量表征的统计模型对特征因子进行预测，这将为基于自然衰减修复的场地或区域地下水污染优化控制与高效修复提供重要依据.Abstract: Whether the groundwater pollution plume of a contaminated site or a regional area can be stabilized and the stability characteristics of the plume would directly determine the feasibility of the natural attenuation restoration. In this study, a typical aquifer structure with a phreatic aquifer, an impermeable aquifer, and a confined aquifer from top to bottom was constructed to simulate the migration and diffusion of the constant source pollution plume of phreatic water. The stable area, stable concentration and starting stable time of the groundwater pollution plume were taken as characteristic variables. Firstly, the sensitive factors were identified from numerous influence factors through sensitivity analysis method. Secondly, orthogonal experiments were used to identify the main controlling factors. Finally, the multiple regression model was used to construct the quantitative statistical relationship for characteristic variables. The results show that the common primary controlling factors are the degradation coefficient, dispersivity, seepage velocity and the source concentration. Moreover, there are adequate statistical relationships between the characteristic variables and the primary controlling factors. The statistical models characterized by different numbers of factors can be used to predict the characteristic variables. This study would provide an important basis for optimization of the site pollution control and effective remediation which are based on natural attenuation remediation.
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图 4 污染羽稳定性特征因子随各参数变幅的变化
Fig. 4. Changes of pollution plume stable characteristic factors as the parameter changed
图 6 污染羽稳定面积、稳定浓度、稳定时间的回归模型残差
Fig. 6. Regression model residuals of stable area, stable concentration and stable time of pollution plume
表 1 模型初始参数设置
Table 1. Model initial parameters setting
参数名称 输入值 降水入渗补给强度R（m/d） 0.000 2 有效孔隙度P 0.2 潜水含水层渗透系数Kw（m/d） 50 弱透水层渗透系数Ka（m/d） 0.008 承压水含水层渗透系数（m/d） 50 潜水含水层厚度Mw（m） 12 弱透水层厚度Ma（m） 3 承压含水层厚度（m） 5 潜水与承压水水头差ΔHv（m） 1 上游与下游水头差ΔHh（m） 5 降解系数Dg（1/d） 0.005 吸附系数Kd（m3/kg） 0.000 1 污染源浓度C0（mg/L） 500 弥散度D（m） 60 污染源面积A（m2） 900 污染源厚度占潜水含水层比值 0.25 注：表中污染物迁移相关系数参考BIOSCREEN: Natural Attenuation Decision Support System. User's Manual ( Newell et al., 1996 ).
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表 2 各参数变化情况下污染羽稳定性特征因子变化率
Table 2. The amplitude of pollution plume stable characteristic factors under different amplitudes of parameters
稳定面积变化率 稳定浓度变化率 稳定时间变化率 参数变幅 增大50% 减小50% 平均变化率 增大50% 减小50% 平均变化率 增大50% 减小50% 平均变化率 降水入渗补给强度 0.066 0.125 0.095 0.220 0.316 0.268 0.038 0.058 0.048 有效孔隙度 0.271 0.267 0.269 0.226 0.006 0.116 0.135 0.423 0.279 潜水含水
层厚度0.253 0.220 0.236 0.097 0.084 0.091 0.077 0.115 0.096 弱透水
层厚度0.011 0.011 0.011 0.009 0.008 0.008 0.000 0.115 0.058 潜水层渗
透系数0.542 0.564 0.553 0.210 0.720 0.465 0.019 0.058 0.038 弱透水层渗透系数 0.004 0.026 0.015 0.002 0.018 0.010 0.019 0.000 0.010 上下游
水头差0.476 0.418 0.447 0.195 0.114 0.154 0.096 0.115 0.106 潜水与承压水头差 0.004 0.011 0.007 0.001 0.008 0.004 0.000 0.019 0.010 降解系数 0.264 0.659 0.462 0.215 0.243 0.229 0.288 0.808 0.548 吸附系数 0.004 0.011 0.007 0.003 0.010 0.007 0.269 0.154 0.212 弥散度 0.297 0.341 0.319 0.141 0.313 0.227 0.192 0.019 0.106 污染源浓度 0.377 0.385 0.381 0.089 0.188 0.138 0.154 0.038 0.096 污染源面积 0.143 0.165 0.154 0.234 0.303 0.269 0.019 0.019 0.019 源厚度与含水层比值 0.136 0.114 0.125 0.053 0.284 0.169 0.058 0.019 0.038 注：此表中变化率均为绝对值.
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表 3 因素水平表
Table 3. Design of parameter levels
水平 降解系数（1/d） 吸附系数
（m3/kg）弥散度
（m）源浓度（mg/L） 源面积
（400m2）源厚度占比
(%)渗流速度（m/d） 有效
孔隙度1 0.002 0.000 01 10 10 1 0.2 0.005 0.10 2 0.005 0.000 05 30 50 2 0.4 0.020 0.15 3 0.01 0.000 10 60 100 3 0.6 0.050 0.20 4 0.05 0.000 50 100 200 4 0.8 0.100 0.30 5 0.1 0.001 0 200 500 5 1.0 0.200 0.40
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表 4 正交设计表及试验结果
Table 4. Orthogonal experimental design table and experimental results
序号 降解
系数吸附
系数弥散度 源浓度 源面积 源厚度占比 渗流
速度有效
孔隙度稳定面积
（103m2）稳定浓度
（mg/L）稳定时间（a） 1 1 1 1 1 1 1 1 1 18.0 0.18 2.9 2 1 2 2 2 2 2 2 2 61.6 1.18 8.6 3 1 3 3 3 3 3 3 3 118.8 3.09 16.2 4 1 4 4 4 4 4 4 4 517.2 3.79 33.2 5 1 5 5 5 5 5 5 5 2 006.0 8.10 68.2 6 2 1 2 3 4 5 1 2 60.8 9.38 3.6 7 2 2 3 4 5 1 2 3 61.6 2.45 4.8 8 2 3 4 5 1 2 3 4 61.6 4.26 5.9 9 2 4 5 1 2 3 4 5 125.2 0.42 16.6 10 2 5 1 2 3 4 5 1 368.0 1.44 9.1 11 3 1 3 5 2 4 4 1 72.0 15.2 0.6 12 3 2 4 1 3 5 5 2 65.2 0.66 0.6 13 3 3 5 2 4 1 1 3 22.4 0.51 1.2 14 3 4 1 3 5 2 2 4 4.4 0.90 1.2 15 3 5 2 4 1 3 3 5 4.8 11.21 1.7 16 4 1 4 2 5 3 5 3 297.6 1.70 2.4 17 4 2 5 3 1 4 1 4 57.6 2.43 2.6 18 4 3 1 4 2 5 2 5 8.0 23.79 2.7 19 4 4 2 5 3 1 3 1 41.6 3.03 12.4 20 4 5 3 1 4 2 4 2 68.0 0.40 8.5 21 5 1 5 4 3 2 4 3 48.0 3.76 0.4 22 5 2 1 5 4 3 5 4 16.0 48.35 0.5 23 5 3 2 1 5 4 1 5 6.8 3.05 0.3 24 5 4 3 2 1 5 2 1 7.2 3.58 1.0 25 5 5 4 3 2 1 3 2 6.4 0.25 1.2 26 1 1 1 4 5 4 3 2 73.2 12.22 9.5 27 1 2 2 5 1 5 4 3 359.2 5.41 15.6 28 1 3 3 1 2 1 5 4 248.0 0.46 9.3 29 1 4 4 2 3 2 1 5 90.8 1.24 20.3 30 1 5 5 3 4 3 2 1 703.2 1.34 114.5 31 2 1 2 1 3 3 2 4 14.4 1.26 2.1 32 2 2 3 2 4 4 3 5 30.4 4.17 3.8 33 2 3 4 3 5 5 4 1 565.6 2.60 15.9 34 2 4 5 4 1 1 5 2 1 132.0 0.98 32.6 35 2 5 1 5 2 2 1 3 26.4 6.80 15.3 36 3 1 3 3 1 2 5 5 38.0 1.43 0.7 37 3 2 4 4 2 3 1 1 46.4 8.40 1.2 38 3 3 5 5 3 4 2 2 57.2 24.96 1.8 39 3 4 1 1 4 5 3 3 10.4 1.90 3.6 40 3 5 2 2 5 1 4 4 19.2 0.54 3.9 41 4 1 4 5 4 1 2 5 31.2 3.25 2.5 42 4 2 5 1 5 2 3 1 78.0 0.47 2.5 43 4 3 1 2 1 3 4 2 29.2 1.85 2.6 44 4 4 2 3 2 4 5 3 161.2 2.87 9.0 45 4 5 3 4 3 5 1 4 38.0 10.95 10.0 46 5 1 5 2 2 5 3 4 10.4 5.05 0.3 47 5 2 1 3 3 1 4 5 2.0 0.44 0.2 48 5 3 2 4 4 2 5 1 46.4 4.26 0.7 49 5 4 3 5 5 3 1 2 20.8 55.48 1.7 50 5 5 4 1 1 4 2 3 4.8 1.02 0.7
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表 5 正交试验极差分析结果
Table 5. Range analysis results of the orthogonal experiment
降解系数 吸附系数 弥散度 源浓度 源面积 源厚度占比 渗流速度 有效孔隙度 稳
定
面
积K1 1 049.00 165.90 138.90 159.70 428.10 395.60 97.00 486.60 K2 611.50 194.50 194.00 234.20 191.40 130.80 238.40 393.60 K3 202.60 291.00 175.70 429.50 211.00 344.10 108.90 277.60 K4 85.00 527.70 421.70 493.90 376.50 337.10 451.40 246.70 K5 42.20 811.20 1 060.00 673.00 783.30 782.70 1 094.60 585.80 R 1 006.80 645.30 921.10 513.30 591.90 651.90 997.60 339.10 主次： 降解系数 > 渗流速度 > 弥散度 > 源厚度占比 > 吸附系数 > 源面积 > 源浓度 > 有效孔隙度 稳
定
浓
度K1 3.701 5.343 9.787 0.982 3.235 1.209 9.842 4.050 K2 3.376 7.396 4.219 2.126 6.442 2.470 6.373 10.736 K3 5.074 6.883 9.721 2.473 5.083 13.310 4.565 2.951 K4 6.571 7.419 2.717 8.181 7.735 7.115 3.441 7.799 K5 12.524 4.205 4.802 17.484 8.751 7.142 7.025 5.710 R 9.15 3.21 7.07 16.50 5.52 12.10 6.40 7.79 主次： 源浓度 > 源厚度占比 > 降解系数 > 有效孔隙度 > 弥散度 > 渗流速度 > 源面积 > 吸附系数 稳
定
时
间K1 31.15 2.50 9.76 3.76 5.93 6.37 6.78 19.53 K2 13.77 3.99 5.79 9.39 6.48 7.26 13.99 6.37 K3 5.47 4.93 5.56 15.81 11.31 14.95 5.56 7.69 K4 1.62 12.46 8.69 9.88 18.08 12.06 9.15 7.80 K5 0.70 28.83 22.91 13.87 10.91 12.07 17.23 11.32 R 30.45 26.33 17.35 12.05 12.15 8.58 11.67 13.16 主次： 降解系数 > 吸附系数 > 弥散度 > 有效孔隙度 > 源面积 > 源浓度 > 渗流速度 > 源厚度占比
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表 6 影响因子方差分析
Table 6. Variance analysis of influencing factors
稳定面积 稳定浓度 稳定时间 参数 均方 F值 显著性 均方 F值 显著性 均方 F值 显著性 降解系数 1 830 318 5.93 0.004** 139 2.15 0.119 1 593 10.00 0.000** 吸附系数 735 720 2.38 0.092 20 0.31 0.866 1 193 7.49 0.001** 弥散度 1 492 429 4.84 0.009** 108 1.67 0.203 511 3.21 0.039* 源浓度 423 578 1.37 0.285 472 7.29 0.001** 216 1.36 0.289 源面积 568 692 1.84 0.167 47 0.73 0.583 238 1.50 0.248 源厚度占比 565 024 1.83 0.169 228 3.51 0.029* 131 0.82 0.530 渗流速度 1 719 388 5.57 0.005** 61 0.94 0.467 244 1.53 0.238 孔隙度 201 315 0.65 0.633 96 1.49 0.250 286 1.80 0.176 注：**表示P小于0.01，表明参数变化对结果有非常显著的影响，*表示P大于0.01且小于0.05，表明参数变化对结果有显著影响.
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表 7 多元回归分析结果
Table 7. Results of multiple regression analysis
因变量 模型 稳定
面积
lnS1
R2=0.781参数 (常量) lnDg lnv lnD lnP 系数 ‒0.281 ‒0.696 0.599 0.437 ‒0.71 显著性 0.667 0.000 0.000 0.000 0.001 2
R2= 0.81参数 (常量) lnDg lnv lnD lnP lnC0 系数 ‒1.17 ‒0.696 0.599 0.437 ‒0.71 0.199 显著性 0.094 0.000 0.000 0.000 0.001 0.08 3
R2= 0.825参数 (常量) lnDg lnv lnD lnP lnC0 lnA 系数 ‒1.17 ‒0.696 0.599 0.437 ‒0.71 0.199 0.352 显著性 0.163 0.000 0.000 0.000 0.000 0.006 0.032 4
R2= 0.839参数 (常量) lnDg lnv lnD lnP lnC0 lnA lnr 系数 ‒1.17 ‒0.696 0.599 0.437 ‒0.71 0.199 0.352 0.333 显著性 0.023 0.000 0.000 0.000 0.000 0.004 0.026 0.034 稳定
浓度
lnC1
R2=0.756参数 (常量) lnC0 lnr 系数 ‒1.353 0.693 1.230 显著性 0.000 0.000 0.000 2
R2= 0.772参数 (常量) lnC0 lnr lnv 系数 ‒1.822 0.693 1.230 ‒0.146 显著性 0.000 0.000 0.000 0.043 稳定
时间
lnT1
R2= 0.899参数 (常量) lnDg lnKd 系数 1.066 ‒0.848 0.384 显著性 0.014 0.000 0.000 2
R2= 0.917参数 (常量) lnDg lnKd lnC0 系数 0.391 ‒0.848 0.384 0.151 显著性 0.366 0.000 0.000 0.002 3
R2= 0.933参数 (常量) lnDg lnKd lnC0 lnD 系数 ‒0.333 ‒0.848 0.384 0.151 0.184 显著性 0.448 0.000 0.000 0.001 0.001 4
R2= 0.938参数 (常量) lnDg lnKd lnC0 lnD lnv 系数 ‒0.685 ‒0.848 0.384 0.151 0.184 0.222 显著性 0.136 0.000 0.000 0.000 0.001 0.04 5
R2= 0.943参数 (常量) lnDg lnKd lnC0 lnD lnv lnA 系数 1.127 ‒0.848 0.384 0.151 0.184 0.222 0.189 显著性 0.023 0.000 0.000 0.000 0.000 0.033 0.036
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