Effect Mechanistic of Partially Penetrating Well on Single-Well Push-Pull Tests for Groundwater Velocity Estimation
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摘要: 为了探究非完整井结构对单井注抽试验测算地下水流速的影响机理，采用COMSOL Multiphysics软件建立非完整井条件下的单井注抽试验数值模型，分析了非完整井滤管长度与位置对穿透曲线的影响.同时开展了非完整井单井注抽试验室内试验研究，并利用数值模型拟合示踪剂穿透曲线来进一步验证模型的可靠性.结果表明：滤水管长度越短，示踪剂穿透曲线早期浓度越低；滤水管位置越靠近含水层上部，穿透曲线早期的浓度越高；参数反演误差分析表明数值模型能较好地反演地下水流速、孔隙度以及弥散度.总体而言，非完整井附近复杂流场导致溶质空间的不均匀分布，进而对穿透曲线有显著影响，增大传统完整井模型的参数反演误差；而本文建立的非完整井单井注抽试验模型拟合精度高，能够适用于非完整井条件下的单井注抽试验.Abstract: For the purpose of analyzing the influencing mechanism of partially penetrating well on single-well push-pull (SWPP) tests, this study employed COMSOL Multiphysics to develop a numerical model of SWPP test, in which the impacts of the length and location of screen on breakthrough curves (BTCs) were investigated. Meanwhile, a laboratory experiment of SWPP test with partially penetrating well was conducted, verifying the reliability of the proposed model by fitting the observed and simulated BTCs. The results show that a shorter screen length leads to a lower concentration of BTC in the early stage; meanwhile a shorter unscreened segment near the top of aquifer results in a lower concentration in the early stage. Additionally, the error analysis of parameter inversion indicates that the numerical model is quantified for the estimations of groundwater flow velocity, porosity and dispersion by fitting BTCs. Overall, the complicated flow field in the vicinity of partially penetrating wells leads to a non-uniform spatial distribution of solute, which has a significant effect on the BTCs and increases the parameter inversion error if using the traditional fully penetrating well model. Nevertheless, the SWPP test model developed in this paper has high fitting accuracy and can be applied to SWPP test under partially penetrating conditions.
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图 4 数值解与Wang and Zhan（2019）解析解的穿透曲线对比
Fig. 4. Comparison of breakthrough curves between the numerical and analytical solutions Wang and Zhan (2019)
图 5 完整井、非完整井不同流速的穿透曲线
a.低流速；b.高流速
Fig. 5. BTCs of fully and partially penetrating wells at different groundwater flow velocities
图 7 不同滤水管长度情况下的SWPP试验的穿透曲线
a.低流速；b.高流速
Fig. 7. Breakthrough curves of SWPP tests for different lengths of filter pipe
图 9 不同滤水管位置情况下的SWPP试验的穿透曲线
a.低流速；b.高流速
Fig. 9. Breakthrough curves of SWPP tests for different location of filter pipe
图 10 注入阶段结束（a）和抽水阶段开始（b）时溶质空间分布浓度等值线图
Fig. 10. Contour map of the spatial distribution of solutes at the end of the injection phase (a) and at the beginning of the pumping phase (b)
图 12 不同地下水流速（tdrift=25 min）条件下实测数据拟合
Fig. 12. Fitting of observed data with different groundwater velocities (tdrift=25 min)
图 13 不同自由迁移时间（vd=1.03×10-5 m/s）条件下实测数据拟合
Fig. 13. Fitting of observed data with different rest times (vd=1.03×10-5 m/s)
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) W 50 含水层长度(m) L 50 含水层厚度(m) M 4 滤管长度（m） B 2 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 21.08 边界S2的水头(m) H2 20 纵向弥散度(m) αL 0.1 注入与抽取的流量(m3/d) Q 15，15 注入阶段时间(h) tinj 2 自由迁移时间(h) tdrift 48 抽水阶段时间(h) tpump 48 
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表 2 不同地下水流速数值模拟结果
Table 2. Numerical simulation results with different groundwater velocities
室内实测值 数值模拟值 r2 Ev(%) Eθ(%) trest(min) vobs (m/s) θobs vs(m/s) θ αL(m) 25 6.89×10‒6 0.443 7.576×10‒6 0.435 0.017 0.953 9.96 1.81 25 1.03×10‒5 0.443 9.643×10‒6 0.430 0.018 0.933 6.38 2.93 25 1.37×10‒5 0.443 1.309×10‒5 0.425 0.018 0.949 4.48 4.06
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表 3 不同自由迁移时间数值模拟结果
Table 3. Numerical simulation results with different rest times
室内实测值 数值模拟值 r2 Ev(%) Eθ(%) trest(min) vobs (m/s) θobs vs(m/s) θ αL(m) 10 1.03×10‒5 0.443 9.298×10‒6 0.437 0.014 0.978 9.73 1.35 15 1.03×10‒5 0.443 8.954×10‒6 0.440 0.020 0.975 13.07 0.68 30 1.03×10‒5 0.443 9.643×10‒6 0.428 0.018 0.900 6.38 3.39
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