Numerical Analysis of Estimating Groundwater Velocity through Single-Well Push-Pull Test
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摘要: 为了分析注入阶段地下水流速及含水层弥散度对单井注抽试验解析模型测算地下水流速的影响机理，通过采用GMS（groundwater modeling system）软件建立了单井注抽试验数值模型，通过与Leap and Kaplan（1988）近似解析模型计算结果对比分析上述因素对解析模型计算结果的影响.研究结果表明：地下水流速越大或自由迁移阶段时间越长，近似解析模型计算的误差越大；注入阶段地下水流速的作用对溶质羽质心迁移的影响较小，故近似解析模型中考虑注入阶段质心位移会导致计算误差增大；含水层弥散度越大，解析模型计算的误差越大.总体而言，注入阶段地下水流速对近似解析模型计算结果影响较小，而弥散度有着显著的影响.Abstract: For the purpose of analyzingthe influencingmechanism of groundwater flow velocity in the injection phase (GFVIP) and dispersivity on calculation of groundwater velocity, this study employed GMS (Groundwater Modeling System)to develop numerical models of single-well push-pull (SWPP) test, and the numerical results are compared with theapproximately analytical ones of Leap and Kaplan (1988)to uncover the effects of GFVIP and dispersivity on the calculation accuracy of the analytical model. The results indicate that a larger groundwater velocity or a longer drift time results in a larger misestimation of groundwater velocity bythe model of Leap and Kaplan (1988); GFVIP has little impact on the migration distance of solute plumecentroid, thus the impact of GFIP on the approximately analytical model can be neglected. Additionally, a greater dispersivity results in a more significant calculation error by the model of Leap and Kaplan (1988). Overall, the GFVIP has limited influence on the calculation results by the approximately analytical modelof Leap and Kaplan (1988), while dispersivity has remarkable influence on the estimation accuracy.
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图 5 不同流速情况下的SWPP试验的穿透曲线
a. 低流速情况；b. 高流速情况
Fig. 5. Breakthrough curves of SWPP tests for different groundwater flow
图 6 SWPP试验计算地下水流速平面示意图
据Paradis et al.（2018）修改
Fig. 6. The conceptual model of single-well push-pull test in a plan view
图 7 相对误差随地下水流速变化图
Fig. 7. Relative errors curves for different groundwater flow velocities
图 8 不同自由迁移时间情况下的SWPP试验的穿透曲线
Fig. 8. Breakthrough curves of SWPP tests for different rest times
图 10 两种模型对于不同地下水流速条件下的相对误差$ {E}_{va} $变化曲线
Fig. 10. Variation curve of relative error $ {E}_{va} $ of the two models under different groundwater velocity conditions
图 11 不同弥散度情况下的SWPP试验的穿透曲线
Fig. 11. Breakthrough curves of SWPP tests for different longitudinal dispersivities
图 12 不同弥散度条件下相对误差的变化图
Fig. 12. Relative errors curves for different longitudinal dispersivities
表 1 模型中默认参数取值
Table 1. Default parameter values used in the model
参数 符号 值 含水层宽度(m) 2W 40 含水层长度(m) 2L 40 含水层厚度(m) M 10 储水系数 Ss 10-6 含水层有效孔隙度 θ 0.3 含水层的渗透系数(m/d) K 8 边界S1的水头(m) H1 21.33 边界S2的水头(m) H2 20 纵向弥散度(m) αL 0.05 注入与抽取的流量(m3/d) Q 15，30 注入阶段时间(h) tinj 2 自由迁移时间(h) tdrift 36 抽水阶段时间(h) tpump 36 
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表 2 计算的地下水流速
Table 2. Calculated groundwater velocities
tdrift(h) ta(h) va(m/s) vx(m/s) Eva 36 13.2 5.28×10-6 1.03×10-5 0.49 36 11.2 5.07×10-6 9.33×10-6 0.46 36 9.2 4.80×10-6 8.33×10-6 0.42 36 7.1 4.42×10-6 7.33×10-6 0.40 36 3.3 3.31×10-6 5.00×10-6 0.34 36 2.3 2.83×10-6 4.00×10-6 0.29 36 1.5 2.34×10-6 3.00×10-6 0.22 36 1.1 2.02×10-6 2.00×10-6 0.01
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