变径抽水井降深和涌水量关系的混合井模型

齐跃明; 吴佳欣; 王旭升; 周来; 董贵明; 刘博; 许进鹏; 马超; 周沛

doi:10.19509/j.cnki.dzkq.tb20220699

变径抽水井降深和涌水量关系的混合井模型

doi: 10.19509/j.cnki.dzkq.tb20220699

齐跃明^1a,,
吴佳欣^1a,
王旭升^2, ,,
周来^1b,
董贵明^1a,
刘博^1a,
许进鹏^1a,
马超³,
周沛^1a

1a.
中国矿业大学资源与地球科学学院, 江苏徐州 221116
1b.
中国矿业大学环境与测绘学院, 江苏徐州 221116
2.
中国地质大学(北京)水资源与环境学院, 北京 100083
3.
山东省地矿工程勘察院, 济南 250014

基金项目:

国家重点研发计划课题 2022YFC3702203

国家自然科学基金项目 52274243

国家自然科学基金项目 42272292

江苏省研究生科研创新计划 2766

江苏省研究生科研创新计划 2767

中国矿业大学研究生创新计划项目资助 2023WLJCRCZL003

中国矿业大学研究生创新计划项目资助 2023WLJCRCZL004

详细信息

作者简介:
齐跃明(1977—), 男, 副教授, 主要从事水文地质和矿山水害防治方面的教学和科研工作。E-mail: ym_qi@126.com

通讯作者:
王旭升(1974—), 男, 教授, 博士生导师, 主要从事地下水动力学研究工作。E-mail: wxsh@cugb.edu.cn

中图分类号: P641
计量
- 文章访问数: 586
- PDF下载量: 74
- 被引次数: 0
出版历程
- 收稿日期: 2022-12-22
- 录用日期: 2023-05-04
- 修回日期: 2023-04-11

Mixed-well model of the relation between drawdown and water inflow in a pumping well with variable-diameter

Qi Yueming^{1a
,},
Wu Jiaxin^1a,
Wang Xusheng^{2
, ,},
Zhou Lai^1b,
Dong Guiming^1a,
Liu Bo^1a,
Xu Jinpeng^1a,
Ma Chao³,
Zhou Pei^1a

1a.
School of Resources and Earth Sciences, China University of Mining and Technology, Xuzhou Jiangsu 221116, China
1b.
School of Environment and Spatial Informatics, China University of Mining and Technology, Xuzhou Jiangsu 221116, China
2.
School of Water Resources and Environment, China University of Geosciences(Beijing), Beijing 100083, China
3.
Shandong Provincial Geo-mineral Engineering Exploration Institute, Jinan 250014, China

摘要

摘要:
抽水试验是确定含水层水文地质参数和评价地下水资源的重要手段。对于单井抽水试验分析, 现有井流模型假定抽水井的直径不随深度变化、含水层为单一的潜水或承压含水层, 未考虑抽水井变径及穿越多个含水层的情况。建立多含水层异径抽水的稳定态混合井流模型, 假设地下水仅发生水平流动, 推导出了抽水井涌水量与降深关系的理论解析公式, 探讨根据变径抽水井的单井稳定流抽水试验获取含水层参数的方法, 提出了承压含水层段抽水井等效半径精确解和替代半径计算公式。把混合井流模型用于分析淄河源区的傍河抽水试验, 根据3个流量的阶梯式抽水试验数据确定了涌水量Q_w与降深s_w的抛物线型关系, 预测允许降深s_w为25 m时抽水井涌水量为4 093.8 m³/d, 反算得到潜水含水层渗透系数为1.88 m/d, 用替代半径计算的承压含水层渗透系数约为0.43 m/d, 相对误差小于5%。混合井模型为多含水层抽水井的涌水量预报提供了理论依据, 其适用性也受到假设条件的限制。在完整河情景下忽略三维流将导致反求的渗透系数偏大, 在非完整河情景下解析解反求的渗透系数则偏小。
- 多层含水层 /
- 稳定流 /
- 变径单孔混合抽水 /
- 钻孔涌水量估算 /
- 混合井模型
Abstract: Objective
Pumping tests are an important method for determining the hydrogeological parameters of aquifers and evaluating groundwater resources. For the analysis of single-well pumping tests, existing models assume that the well diameter remains constant with depth and that the aquifer is either unconfined or confined. They do not consider situations where the well diameter varies or when multiple aquifers are encountered.
Methods
In this study, we developed a steady-state mixed-well flow model to account for a pumping well with a variable diameter that penetrates multiple aquifers with the assumption of horizontal flow within the aquifers. The analytical solutions for the relation between pumping discharge and drawdown were derived. This study explores the methodology of using single-well steady-state pumping tests with variable-diameter wells to obtain aquifer parameters. Additionally, accurate solutions for the equivalent radius of a confined aquifer segment and alternative radius calculation formulas are proposed.
Results
The mixed-well flow model was applied to analyze pumping tests near the Zihe River. Based on the data from three stepped pumping tests, a parabolic relationship between pumping discharge Q_w and drawdown s_w was established.The model predicted a pumping discharge of 4 093.8 m³/d when the maximum drawdown s_w was 25 m. The hydraulic conductivity of the unconfined aquifer was estimated to be 1.88 m/d, and the hydraulic conductivity of the confined aquifer was estimated as 0.43 m/d, with a relative error of less than 5%.
Conclusion
The mixed-well model serves as a theoretical foundation for predicting water yield from pumping wells in multiple aquifers system. However, it is important to acknowledge that the model's applicability is constrained by certain assumptions. In situations where rivers fully penetrate aquifers, there is a possibility of overestimating the hydraulic conductivity. On the other hand, when rivers only partially penetrate aquifers, the analytical solution may underestimate the hydraulic conductivity.
- multi-layered aquifers /
- steady flow /
- mixed pumping in single borehole with variable-diameter /
- prediction of water inflow of borehole /
- mixed-well model
注释:

(所有作者声明不存在利益冲突)

HTML全文

图 1 2种混合井抽水稳定流模型

r₀, r₁, r₂, …, r_n分别为抽水井所揭露第1, 第2, …, 第n+1含水层进水段井半径(m)；K₀, K₁, K₂, …, K_n分别为抽水井所揭露第1, 第2, …, 第n+1含水层水平渗透系数(m/d)；z₁, z₂, z₃, …, z_n, z_b分别为抽水井所揭露第1, 第2, …, 第n+1含水层底部标高(m)；M₁, M₂, M₃, …, M_n分别为抽水井所揭露第2, 第3, …, 第n+1含水层厚度(m)；Q_w为混合抽水井抽水流量(m³/d)；h_R为圆岛外边界定水头水位(m)；h_w为开采井中水位(m)；R为开采井中心距圆岛外边界水平距离(m)；L为开采井中心与定水头边界的水平距离(m); 下同
a.圆岛中心抽水；b.定水头边界附近抽水

Figure 1. Two types of steady state flow models for a multilayer mixed pumping well

下载: 全尺寸图片幻灯片

图 2 淄河附近XK1钻孔剖面特征

Figure 2. Profile map of the borehole XK1 near the Zi River

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图 3 稳定流抽水试验降深(s_w)与涌水量(Q_w)的关系

Figure 3. Relationship between the drawdown(s_w) and pumping rate(Q_w) in steady-state pumping test

下载: 全尺寸图片幻灯片

图 4 三维有限差分模型及其模拟结果

a.三维模型网格；b.抽水井水位下降20 m时含水层底部降深分布；c.抽水井水位下降20 m中心剖面降深分布；d.抽水井涌水量与降深关系曲线

Figure 4. 3D finite-difference model and its simulation modeling results

下载: 全尺寸图片幻灯片

表 1 抽水井分段特征

Table 1. Sectional characteristics of the pumping well

编号	底面深度/m	井孔直径/mm	揭露地层	含水层岩性	有效厚度/m	分段体积/m³	分段侧面积m²
顶层	16.3	426	Q、O₂b	砂层、白云岩		套管阻隔、侧面不进水
Ⅰ	26.1	377	O₂b	白云岩	潜水含水层段
Ⅱ	105.9	377	O₂b、O₂d、∈₄O₁s、∈₄O₁ĉ	白云岩、灰岩	79.8	8.91	94.5
Ⅲ	250.2	325	∈₄O₁s、∈₄O₁ĉ	白云岩、灰岩	144.3	11.97	147.3
Ⅳ	353.2	273	∈₄O₁ĉ	灰岩为主	74.2	4.34	63.6
注：Q.第四系；O₂b.北奄庄组；O₂d.东黄山组；∈₄O₁s.三山子组；∈₄O₁ĉ.炒米店组

下载: 导出CSV

表 2 不同解析模型涌水量计算值相对数值模拟结果的误差

Table 2. Errors of the flow rate estimated from different analytical models with respect to numerical simulations

抽水井降深s_w/m	单井涌水量
	数值模拟Q_w/(m³·d^-1)	传统解析模型(定半径均质含水层)				混合井解析模型
		取r_w=136.5 mm		取r_w=188.5 mm		涌水量Q_w/ (m³·d^-1)	相对误差/ %
		Q_w/(m³·d^-1)	相对误差/%	Q_w/(m³·d^-1)	相对误差/%	涌水量Q_w/ (m³·d^-1)	相对误差/ %
5	939.0	789.9	-15.9	835.6	-11.0	924.4	-1.6
10	1 877.0	1 568.4	-16.4	1 659.1	-11.6	1 795.9	-4.3
15	2 813.0	2 335.4	-17.0	2 470.5	-12.2	2 614.7	-7.1
20	3 679.2	3 091.0	-16.0	3 269.8	-11.1	3 380.6	-8.1
25	4 154.5	3 835.2	-7.7	4 057.0	-2.3	4 093.8	-1.5
30	4 985.8	4 567.9	-8.4	4 832.1	-3.1	4 754.2	-4.6
35	5 816.1	5 289.2	-9.1	5 595.1	-3.8	5 361.8	-7.8

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参考文献(36)

[1]	国家市场监督管理总局, 国家标准化管理委员会. 矿区水文地质工程地质勘探规范: GB/T 12719-2021)[S]. 北京: 中华人民共和国自然资源部, 2021. State Administration for Market Regulation, Standardization Administration of the People's Republic of China. Exploration specification of hydrogeology and engineering geology in mining areas: GB/T 12719-2021[S]. Beijing: Ministry of Watural Resources of the Republic of China, 2021(in Chinese).
[2]	国家煤矿安全监察局. 煤矿防治水细则[S]. 北京: 煤炭工业出版社, 2018. State Administration of Coal Mine Safty. Detailed rules for prevention and control of water in coal mines[S]. Beijing: China Coal Industry Publishing House, 2018(in Chinese).
[3]	张竞, 王旭升. 抽水井单位涌水量的多解性及其应用[J]. 工程勘察, 2014(3): 33-37. https://www.cnki.com.cn/Article/CJFDTOTAL-GCKC201403009.htm Zhang J, Wang X S. The multiplicity of solutions for unit water inflow of pumping well and its application[J]. Geotechnical Investigation & Surveying, 2014(3): 33-37(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-GCKC201403009.htm
[4]	王善堂. 松散地层钻孔涌水量预报方法研究[J]. 地下水, 2005, 27(5): 360-361. https://www.cnki.com.cn/Article/CJFDTOTAL-DXSU200505014.htm Wang S T. Study on prediction method of borehole water inflow in loose formation[J]. Ground Water, 2005, 27(5): 360-361(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-DXSU200505014.htm
[5]	成胜, 许模. 云南丘北地区某隧道隧址区岩溶发育特征及涌水量预测[J]. 地下水, 2022, 44(5): 7-9, 283. https://www.cnki.com.cn/Article/CJFDTOTAL-DXSU202205003.htm Cheng S, Xu M. Karst development characteristics and water inflow prediction of a tunnel site in Qiubei area, Yunnan Province[J]. Ground Water, 2022, 44(5): 7-9, 283(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-DXSU202205003.htm
[6]	Wu C, Wu X, Zhu G, et al. Predicting mine water inflow and groundwater levels for coal mining operations in the Pangpangta Coalfield, China[J]. Environmental Earth Sciences, 2019, 78(5): 130-142. doi: 10.1007/s12665-019-8098-2
[7]	Xu Z M, Chen T C, Li J F, et al. Defects and improvement of predicting mine water inflow by virtual large diameter well method[J]. Geofluids, 2022, 2022: 3067983.
[8]	Zhang K, Cao B, Lin G, et al. Using multiple methods to predict mine water inflow in the Pingdingshan No. 10 Coal Mine, China[J]. Mine Water and the Environment, 2017, 36(1): 154-160. doi: 10.1007/s10230-015-0381-1
[9]	王档良, 房亚飞, 邓国伟, 等. 基于改进多元回归模型与GIS的陕北凉水井矿井工作面涌水量预测[J]. 煤炭科技, 2022, 43(4): 85-92. https://www.cnki.com.cn/Article/CJFDTOTAL-META202204010.htm Wang D L, Fang Y F, Deng G W, et al. Prediction of water inflow in the working face of Liangshui well in northern Shaanxi based on improved multiple regression model and GIS[J]. Coal Science & Technology Magazine, 2022, 43(4): 85-92(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-META202204010.htm
[10]	Miladinoviĉ B, Vakanjac V R, Bukumiroviĉ D, et al. Simulation of mine water inflow: Case study of the Štavalj Coal Mine(Southwestern Serbia)[J]. Archives of Mining Sciences, 2015, 60(4): 955-969. doi: 10.1515/amsc-2015-0063
[11]	吴瑞芳, 刘佳. 基于新陈代谢灰色系统模型矿井涌水量预测[J]. 煤炭与化工, 2021, 44(8): 38-40, 43. https://www.cnki.com.cn/Article/CJFDTOTAL-HHGZ202108012.htm Wu R F, Liu J. Prediction of mine water inflow based on metabolism grey system model[J]. Coal and Chemical Industry, 2021, 44(8): 38-40, 43(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-HHGZ202108012.htm
[12]	Dong H B, Tong M M, Liao H M, et al. Study of prediction method of mine water emission based on grey system theory[C]//Anon. Proceedings of 2010 Chinese Control and Decision Conference, [S. l. ]: [s. n. ], 2010: 3947-3950.
[13]	刘晓丹, 潘国营. 基于三种时间序列模型的矿井涌水量预测[J]. 矿业安全与环保, 2022, 49(2): 91-95. https://www.cnki.com.cn/Article/CJFDTOTAL-ENER202202016.htm Liu X D, Pan G Y. Prediction of mine water inflow based on three time series models[J]. Mining Safety & Environmental Protection, 2022, 49(2): 91-95(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-ENER202202016.htm
[14]	王晓蕾. 煤矿开采矿井涌水量预测方法现状及发展趋势[J]. 科学技术与工程, 2020, 20(30): 12255-12267. https://www.cnki.com.cn/Article/CJFDTOTAL-KXJS202030002.htm Wang X L. Current situation and development trend of water inflow prediction methods for coal mines[J]. Science Technology and Engineering, 2020, 20(30): 12255-12267(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-KXJS202030002.htm
[15]	李建林, 高培强, 王心义, 等. 基于混沌-广义回归神经网络的矿井涌水量预测[J]. 煤炭科学技术, 2022, 50(4): 149-155. https://www.cnki.com.cn/Article/CJFDTOTAL-MTKJ202204015.htm Li J L, Gao P Q, Wang X Y, et al. Prediction of mine water inflow based on chaos generalized regression neural network[J]. Coal Science and Technology, 2022, 50(4): 149-155(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-MTKJ202204015.htm
[16]	梁犁丽, 胡宇丰, 柳长顺, 等. 矿井涌水量多方法预测与对比分析[J]. 人民黄河, 2021, 43(增刊2): 66-68. https://www.cnki.com.cn/Article/CJFDTOTAL-RMHH2021S2027.htm Liang L L, Hu Y F, Liu Z S, et al. Multi method prediction and comparative analysis of mine water inflow[J]. Yellow River, 2021, 43(S2): 66-68(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-RMHH2021S2027.htm
[17]	彭伏, 常勇, 郑秀清, 等. 地下水模型参数不确定性对晋祠泉流量预测的影响[J]. 水电能源科学, 2018, 36(10): 53-57. https://www.cnki.com.cn/Article/CJFDTOTAL-SDNY201810013.htm Peng F, Chang Y, Zheng X Q, et al. Influence of groundwater model parameter uncertainty on Jinci spring discharge prediction[J]. Water Resources and Power, 2018, 36(10): 53-57(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-SDNY201810013.htm
[18]	成建梅, 罗伟, 徐子东, 等. 火山岩体围岩隧道断层带涌水量计算方法综合研究: 以青云山隧道为例[J]. 地质科技情报, 2015, 34(6): 193-199. https://www.cnki.com.cn/Article/CJFDTOTAL-DZKQ201506028.htm Cheng J M, Luo W, Xu Z D, et al. Comprehensive study on calculation method of water inflow in fault zone of tunnel surrounding volcanic rock: Taking Qingyunshan tunnel as an example[J]. Geological Science and Technology Information, 2015, 34(6): 193-199(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-DZKQ201506028.htm
[19]	来永伟. "一孔多含水层分抽"技术应用研究[J]. 中国煤炭地质, 2022, 34(增刊2): 57-61. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGMT2022S2013.htm Lai Y W. Research on the application of "separate pumping in one hole with multiple aquifers" technology[J]. Coal Geology of China, 2022, 34(S2): 57-61(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-ZGMT2022S2013.htm
[20]	陈崇希. 地下水混合井流解析模型[J]. 水文地质工程地质, 2012, 39(5): 1-7. https://www.cnki.com.cn/Article/CJFDTOTAL-SWDG201205000.htm Chen C X. Analytical model of groundwater mixed well flow[J]. Hydrogeology & Engineering Geology, 2012, 39(5): 1-7(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-SWDG201205000.htm
[21]	齐跃明, 孙箐彬, 许天阳, 等. 一种确定多层含水层混合抽水等效井半径的方法[P]. 中国: ZL 2019 1 0039445.3, 2022-9-16. Qi Y M, Sun J B, Xu T Y, et al. A method for determining the equivalent well radius of mixed pumping in multilayer aquifers[P]. China: ZL 2019 1 0039445.3, 2022-9-16(in Chinese).
[22]	Kooper J. Beweging van het water in den bodem bij onttrekking door bronnen[J]. De Ingenieur, 1914, 29(38): 697-706.
[23]	Kochina P Y. Theory of ground water movement: by P. Ya. Polubarinova-Kochina, translated from the Russian by J.M. Roger de Wiest[M]. Princeton: Princeton University Press, 1962: 377-390.
[24]	Hemker C J. Steady groundwater flow in leaky multiple-aquifer systems[J]. Journal of Hydrology, 1984, 72(3/4): 355-374.
[25]	Hunt B. Flow to a well in a multiaquifer system[J]. Water Resources Research, 1985, 21(11): 1637-1641.
[26]	Maciek Lubczynski J G. Modeling of complex multi-aquifer systems for groundwater resources evaluation: Swidnica study case(Poland)[J]. Hydrogeology Journal, 2005, 13(4): 627-639.
[27]	Jaworska Szulc B. Groundwater flow modelling of multi-aquifer systems for regional resources evaluation: The Gdansk hydrogeological system, Poland[J]. Hydrogeology Journal, 2009, 17(6): 1521-1542.
[28]	陈崇希, 林敏, 成建梅. 地下水动力学: 第5版[M]. 北京: 地质出版社, 2011. Chen C X, Lin M, Cheng J M. Groundwater dynamics: Fifth Edition[M]. Beijing: Geological Publishing House, 2010(in Chinese).
[29]	薛禹群, 吴吉春. 地下水动力学: 第3版[M]. 北京: 地质出版社, 2010. Xue Y Q, Wu J C. Groundwater dynamics: Third Edition[M]. Beijing: Geological Publishing House, 2010(in Chinese).
[30]	马超, 孙箐彬, 邵光宇, 等. 淄河源区含水层介质特征及富水规律研究[J]. 干旱区资源与环境, 2020, 34(12): 173-180. https://www.cnki.com.cn/Article/CJFDTOTAL-GHZH202012026.htm Ma C, Sun J B, Shao G Y, et al. Multi method prediction and comparative analysis of mine water inflow[J]. Journal of Arid Land Resources and Environment, 2020, 34(12): 173-180(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-GHZH202012026.htm
[31]	林旺辉, 齐跃明, 邵光宇, 等. 谢家店水源地地质构造特征及其水文地质意义[J]. 中国科技论文, 2021, 16(9): 935-942. https://www.cnki.com.cn/Article/CJFDTOTAL-ZKZX202109003.htm Lin W H, Qi Y M, Shao G Y, et al. Geological structure characteristics of Xiejiadian water source area and its hydrogeological significance[J]. China Sciencepaper, 2021, 16(9): 935-942(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-ZKZX202109003.htm
[32]	袁冬梅, 齐跃明, 王俊萍, 等. 岩溶地下水源地的可开采资源量计算: 以淄博市谢家店水源地为例[J]. 科学技术与工程, 2020, 20(19): 7589-7595. https://www.cnki.com.cn/Article/CJFDTOTAL-KXJS202019003.htm Yuan D M, Qi Y M, Wang J P, et al. Calculation of exploitable resources in karst groundwater source area: Taking Xiejiadian water source area in Zibo City as an example[J]. Science Technology and Engineering, 2020, 20(19): 7589-7595(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-KXJS202019003.htm
[33]	Hunt B. Solutions for steady groundwater flow in multi-layer aquifer systems[J]. Transport in Porous Media, 1986(1): 419-429.
[34]	陈崇希, 唐仲华. 地下水流动问题数值方法[M]. 武汉: 中国地质大学出版社, 1990. Chen C X, Tang Z H. Numerical method of groundwater flow problems[M]. Wuhan: China University of Geosciences Press, 1990(in Chinese).
[35]	陈崇希, 王旭升, 胡立堂. 地下水流数值模拟中抽水井水位的校正[J]. 水利学报, 2007, 38(4): 481-485. https://www.cnki.com.cn/Article/CJFDTOTAL-SLXB200704015.htm Chen C, Wang X S, Hu L T. Emendation of drawdown in pumping wells for numerical modeling of groundwater flow[J]. Journal of Hydraulic Engineering, 2007, 38(4): 481-485(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-SLXB200704015.htm
[36]	陈崇希, 林敏, 叶善士, 等. 地下水混合井流的理论及应用[M]. 武汉: 中国地质大学出版社, 1998. Chen C X, Lin M, Ye S S, et al. Theory of multi-layer mixed well flow and its application[M]. Wuhan: China University of Geosciences Press, 1998: 1-43(in Chinese).