Combined Effects of Bottom Flow and Wellbore Mixing on the Single-well Push-pull Test Using Large-diameter Well
-
摘要:
单井注抽（single-well push-pull，SWPP）试验因其成本低、周期短以及操作简单的优点，被广泛用于求取含水层弥散度等水文地质参数。依托干旱半干旱区常用的大口径井开展SWPP试验，常面临井底流渗漏和井筒混溶效应共同的影响。为此，本研究构建了同时考虑井底流和混溶效应的SWPP试验三阶段溶质运移模型，利用有限差分法对模型进行求解，并利用前人的渗流和溶质运移模型解析解验证其准确性，随后依托该模型探究大口径井附近渗流特征及井尺寸对SWPP试验的影响机制。研究结果表明：（1）新提出的考虑井底流的SWPP试验模型对抽水过程降深以及井壁处溶质运移过程的刻画，同前人解析解匹配良好，表明了该模型构建及求解的准确性；（2）随着井筛长度的逐渐减小，井底流对含水层整体流场的影响程度逐渐增大，流场从径向逐渐转变为球形流场；（3）粗井径相比细井径，注入阶段井中的溶质BTC（Breakthrough curve,穿透曲线）值更小，但抽出阶段的溶质BTC更大，井中混溶过程相比井底渗漏过程对SWPP试验的影响更为显著；（4）当井深小到井径的一半左右时产生类球形流场，井底的渗漏过程相比混溶过程对SWPP试验可能存在更为显著的影响；（5）对于本研究设置的模拟场景，即使不存在井底流，前人的解析解由于忽略井筒混溶，对弥散度的解译仍存在152.5%的误差，而随着井底埋深逐渐减小，井底流导致前人解析解的误差也逐渐增大。
Abstract:The single-well push-pull (SWPP) test is widely used for determining hydrogeological parameters such as dispersivity coefficient due to its advantages of low cost, short duration, and simple operation. Conducting SWPP experiments in large-diameter wells, commonly used in arid and semi-arid regions, often faces the combined effects of leakage at the well bottom and wellbore mixing. To address this, this study constructed a three-stage solute transport model for the SWPP test that considers both the influences of flow at the well bottom and wellbore mixing effects. The model was solved using the finite difference method, and its accuracy was verified against the analytical solutions of previous seepage and solute transport models. Subsequently, the study explored the seepage characteristics near large-diameter wells and the impact mechanism of well size on the SWPP test based on this model. The research results showed that: (1) The newly proposed SWPP test model, which considers well bottom flow, matches well with previous analytical solutions in depicting the drawdown process during pumping and the solute transport process at the well screen, indicating the accuracy of the model’s construction and solution. (2) As the length of the well screen gradually decreases, the influence of the well bottom flow on the entire flow field gradually increases, changing the flow field from radial to spherical. (3) Compared to a small well diameter, a larger well diameter results in a smaller breakthrough curve (BTC) value for solutes during the injection phase, but a larger BTC during the extraction phase, indicating that the mixing process within the well has a more significant impact on the SWPP test than the leakage process at the well bottom. (4) When the well depth is about half of the well diameter, creating a quasi-spherical flow field, the leakage process at the well bottom may have a more significant impact on the SWPP test than the mixing process. For the simulated scenarios set in this study, even in the absence of bottom flow, the previous analytical solution, due to the neglect of wellbore miscibility, still have an error of 152.5% in the interpretation of dispersivity coefficient. Moreover, as the burial depth of the wellbore bottom gradually decreases, the error in the previous analytical solution caused by the bottom flow also increases gradually.
-
-
表 1 不同井底埋深下解析解求出的弥散度及其误差
Table 1. The dispersivity coefficient and its error calculated from the previous analytical solutions under different well bottom burial depth conditions
井底埋深（l）(m) 1 2 3 4 5 6 7 8 9 10 α’L (m) 7.3 6.96 6.77 6.53 6.28 5.98 5.74 5.55 5.31 5.05 反演误差(%) 265.0 248.0 238.5 226.5 214.0 199.0 187.0 177.5 165.5 152.5 
下载: 导出CSV
-
[1] 顾昊琛,凡倩莹.2023.混合效应和表皮效应对单井注抽试验的影响机理[J]. 安全与环境工程,30(2):156-162.
[2] 江思珉,周念清,施小清,郑茂辉.2010.利用大口径井抽水初期试验数据确定含水层参数[J]. 工程勘察,38(9):32-35.
[3] 李旭. 2020. 抽/注水井附近非均质介质中溶质运移机理及数值模拟研究[D]. 中国地质大学博士学位论文.
[4] 李 旭,苏世林,文 章,许光泉.2022.单井注抽试验测算地下水流速的数值分析[J]. 地球科学,47(2):633-641. doi: 10.3321/j.issn.1000-2383.2022.2.dqkx202202019
[5] 刘玉舒,戴炆君,刘 洋,王全荣.2020.考虑弱透水层的单井注抽试验解析模型研究[J]. 安全与环境工程,27(6):1-6.
[6] 苏世林,李 旭,郭 强,张海涛,许光泉,朱 棋.2024.非完整井对单井注抽试验测算地下水流速影响机理[J]. 地球科学,49(1):288-298.
[7] 文 章,黄冠华,李 健,詹红兵.2009.承压含水层中大口径井附近非达西流的线性化近似解与数值解[J]. 水利学报,40(7):863-869. doi: 10.3321/j.issn:0559-9350.2009.07.014
[8] 肖 勋,施文光,王全荣.2020.井内混合效应与尺度效应对注入井附近溶质径向弥散过程的影响[J]. 地球科学,45(4):1439-1446.
[9] 薛禹群,吴吉春.1999.面临21世纪的中国地下水模拟问题[J]. 水文地质工程地质,(5):1-3.
[10] 阳 畅,刘 洋,刘世强,陈 思,王全荣.2023.微生物堵塞对单井注抽试验的影响机理[J]. 安全与环境工程,30(1):199-204+220.
[11] Barua G, Bora S N. 2010. Hydraulics of a partially penetrating well with skin zone in a confined aquifer[J]. Advances in Water Resources, 33(12): 1575-1587. doi: 10.1016/j.advwatres.2010.09.008
[12] Barua G, Hoffmann M R. 2005. Theory of Seepage into an Auger Hole in a Confined Aquifer[J]. Journal of Irrigation and Drainage Engineering, 131(5): 440-450. doi: 10.1061/(ASCE)0733-9437(2005)131:5(440)
[13] Chen Y, Wang Q R. 2021. The Effect of Boundary Conditions on the Single-Well Push-Pull Test in a Partially Penetrated Well[J]. Journal of Hydrology, 603(1): 127035.
[14] Gupta C P, Singh V S. 1988. Flow regime associated with partially penetrating large-diameter wells in hard rocks[J]. Journal of Hydrology, 103(3-4): 209-217. doi: 10.1016/0022-1694(88)90134-5
[15] Hebig K H, Zeilfelder S, Ito N, Machida I, Marui A, Scheytt T J. 2015. Study of the effects of the chaser in push-pull tracer tests by using temporal moment analysis[J]. Geothermics, 54: 43-53. doi: 10.1016/j.geothermics.2014.11.004
[16] Huang J Q, Christ J A, Goltz M N. 2010. Analytical solutions for efficient interpretation of single‐well push‐pull tracer tests[J]. Water Resources Research, 46(8): W08538.1-W08538.16.
[17] Lin J J, Ma R, Sun Z Y, Tang L S. 2023. Assessing the connectivity of a regional fractured aquifer based on a hydraulic conductivity field reversed by multi-Well pumping tests and numerical groundwater flow modeling[J]. Journal of Earth Science, 34(6): 1926-1939. doi: 10.1007/s12583-022-1674-5
[18] Mathias S A, Butler A P, Zhan H B. 2008. Approximate solutions for Forchheimer flow to a well[J]. Journal of Hydraulic Engineering, 134(9): 1318-1325. doi: 10.1061/(ASCE)0733-9429(2008)134:9(1318)
[19] Meng X M, Shao J Y, Yin M S, Liu D F, Xue X W. 2015. Low velocity non-Darcian flow to a well fully penetrating a confined aquifer in the first kind of leaky aquifer system[J]. Journal of Hydrology, 530: 533-553. doi: 10.1016/j.jhydrol.2015.10.020
[20] Papadopulos I S, Cooper Jr H H. 1967. Drawdown in a well of Large Diameter[J]. Water Resources Research, 3(1): 241-244. doi: 10.1029/WR003i001p00241
[21] Schroth M H, Istok J D. 2005. Approximate solution for solute transport during spherical-flow push-pull tests[J]. Ground Water, 43(2): 280-284. doi: 10.1111/j.1745-6584.2005.0002.x
[22] Shampine L F, Reichelt M W. 1997. The MATLAB ODE Suite[J]. ACM Transactions on Mathematical Software, 18(1): 1-22.
[23] Shampine L F, Reichelt M W, Kierzenka J A. 1999. Solving Index-1 DAEs in MATLAB and Simulink[J]. SIAM Review, 41(3): 538-552. doi: 10.1137/S003614459933425X
[24] Shi W G, Wang Q R, Zhan H B. 2020. New Simplified Models of Single-Well Push-Pull Tests With Mixing Effect[J]. Water Resources Research, 56(8): e2019WR026802. doi: 10.1029/2019WR026802
[25] Shi W G, Wang Q R, Salihu Danlami M. 2022. A novel analytical model of solute transport in a layered aquifer system with mixing processes in the reservoirs[J]. Environmental Science and Pollution Research, 29(45): 67953-67968. doi: 10.1007/s11356-022-20495-5
[26] Shi W G, Wang Q R, Zhan H B, Zhou R J, Yan H T. 2023. A general model of radial dispersion with wellbore mixing and skin effects[J]. Hydrology and Earth System Science, 27(9): 1891-1908. doi: 10.5194/hess-27-1891-2023
[27] Singh S K. 2007. Semianalytical model for drawdown due to pumping a partially penetrating large diameter well[J]. Journal of Irrigation and Drainage Engineering, 133(2): 155-161. doi: 10.1061/(ASCE)0733-9437(2007)133:2(155)
[28] Wang Q R, Jin A H, Zhan H B, Chen Y, Shi W G, Liu H, Wang Y. 2021. Revisiting simplified model of a single-well push-pull test for estimating regional flow velocity[J]. Journal of Hydrology, 601: 126711. doi: 10.1016/j.jhydrol.2021.126711
[29] Wen Z, Huang G H, Zhan H B. 2009. A numerical solution for non-Darcian flow to a well in a confined aquifer using the power law function[J]. Journal of Hydrology, 364(1): 99-106.
[30] Wang Q R, Shi W G, Zhan H B, Gu H C, Chen K W. 2018. Models of Single-Well Push-Pull Test With Mixing Effect in the Wellbore[J]. Water Resources Research, 54(12): 10155-10171.
[31] Wang Q R, Wang J X, Zhan H B, Shi W G. 2020. New model of reactive transport in a single-well push–pull test with aquitard effect and wellbore storage[J]. Hydrology and Earth System Science, 24(8): 3983-4000. doi: 10.5194/hess-24-3983-2020
[32] Wang Q R, Zhan H B, Wang Y X. 2017. Single-well push-pull test in transient Forchheimer flow field[J]. Journal of Hydrology, 549: 125-132. doi: 10.1016/j.jhydrol.2017.03.066
[33] Zhu Q, Wen Z, Jakada H. 2020. A new solution to transient single-well push-pull test with low-permeability non-Darcian leakage effects[J]. Journal of Contaminant Hydrology, 234: 103689. doi: 10.1016/j.jconhyd.2020.103689
-
图(4)
表(1)
计量
- 文章访问数: 88
- PDF下载数: 52
- 施引文献: 0