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標題: An Analytical Solution for Horizontal or Slanted Wells in Confined Aquifers near a Stream
作者: 鄒佩蓉
Tsou, Pei-Rong
關鍵字: 解析解;Analytical solution;河川滲漏;水平井;傾斜井;傅立葉轉換;Quasi-steady solution;Stream depletion rate (SDR);Horizontal well;Slanted well;Fourier transform
出版社: 水土保持學系所
引用: 1.Butler, J. J., Zlotnik, B. A. and Tsou, M. S. (2001)“Drawdown and stream depletion produced by pumping in the vicinity of a partially penetrating stream”, Ground Water, 39(5), 651-659. 2.Brunner, P., Cook, P. G., Simmons, C. T. (2009)“Hydrogeologic controls on disconnection between surface water and groundwater”, Water Resour. Res., 45(1), W01422, doi: 10.1029/2008WR006953. 3.Butler, J. J., Zhan, X., and Zlotnik, V. A. (2007)“Pumping-Induced Drawdown and Stream Depletion in a Leaky Aquifer System”, Ground Water, 45(2), 178-186, doi: 10.1111/j.1745-6584.2006.00272.x. 4.Chen, X. and Yin, Y. (2002)“Semianalytical solutions for stream depletion in partially penetrating streams”, Ground Water, 42(1), 92-96. 5.Folland, G. B. (2002)“Advanced calculus”, Prentice Hall, New Jersey. 6.Fox, G. A., DuChateau, P., and Durnford, D. S. (2002)“Analytical Model for aquifer response incorporating distributed stream leakage”, Ground Water, 40(4), 378-384. 7.Fox, G. A. and Gordji, L. (2007)“Consideration for unsaturated flow beneath a streambed during alluvial well depletion”, J. Hydrol. Eng., 12(2), 139-145, doi: 10.1061/(ASCE)1084-0699(2007)12:2(139). 8.Hunt, B. (1999)“Unsteady stream depletion from ground water pumping”, Ground Water, 37(1), 98-102. 9.Joshi, S. D. (2003)“Cost/Benefits of horizontal wells”, Society of Petroleum Engineers, 19-24. 10.Kawecki, M. W. (2000)“Transient flow to a horizontal water well”, Ground Water, 38(6), 842-850. 11.Kompani-Zare, M., Zhan, H., and Samani, N. (2005)“Analytical study of capture zone of a horizontal well in a confined aquifer”, J. Hydrol., 307(1-4), 48-59, doi: 10.1016/j.hydrol.2004.09.021. 12.Kreyszig, E. (1999)“Advanced engineering mathematics”, John Wiley & Sons Inc., New York. 13.Konikow, L. F. and Kendy, E. (2005)“Groundwater depletion: A global problem”, Hydrogeology Journal, 13(1), 317-320, doi: 10.1007/s10040-004-0411-8. 14.Langseth, D. E., Smyth, A. H., May, J. (2004)“A method for evaluating horizontal well pumping tests”, Ground water, 42(5), 689-699. 15.Linsley, R. K. and Franzini, J. B.(1979)“Water resources engineering”, McGraw-Hill Book Company, New York. 16.Park, E. and Zhan, H., (2002)“Hydraulics of a finite-diameter horizontal well with wellbore storage and skin effect in leady aquifers”, Adv. Water Resour., 25, 389-400. 17.Park, E. and Zhan, H. (2003)“Hydraulics of horizontal well in fractured shallow aquifer systems”, J. Hydrol., 281, 147-158. 18.Sun, D. and Zhan, H. (2006)“Flow to a horizontal well in an aquitard-aquifer system”, J. Hydrol., 321(1-4), 364-376, doi: 10.1016/j.jhydrol.2005.08.008. 19.Sun, D. and Zhan, H. (2007)“Pumping induced depletion from two streams”, Adv. Water Resour., 30(4), 1016-1026, doi: 10.1016/j.advwatres.2006.09.001. 20.Wang, W. and Zhang, G. (2007)“Numerical simulation of groundwater flowing to horizontal seepage wells under a river”, Hydrogeology Journal, 15(6), 1211-1220, doi: 10.1007/s10040-007-0171-3. 21.Yeh, H. D., Chang, Y. C. and Zlotnik, V. A. (2008)“Stream depletion rate and volume from groundwater pumping in wedge-shape aquifers”, J. Hydrol., 349(3-4), 501-511, doi: 10.1016/j.jhydrol.2007.11.025. 22.Zhan, H. (1999)“Analytical study of capture time to a horizontal well”, J. Hydrol., 217(1-2), 46-54. 23.Zlotnik, V. A. and Huang, H. (1999)“Effect of shallow penetration and streambed sediments on aquifer response to stream stage fluctuations (analytical model)”, Ground Water, 37(4), 599-605. 24.Zhan, H. and Cao, J. (2000)“Analytical and semi-analytical solutions of horizontal well capture times under no-flow and constant-head boundaries”, Adv. Water Resour., 23(8), 835-848. 25.Zhan, H., Wang, L. V. and Park, E. (2001)“On the horizontal-well pumping tests in anisotropic confined aquifers”, J. Hydrol., 252(1-4), 37-50. 26.Zhan, H. and Zlotnik, V. A. (2002)“Ground water flow to horizontal and slanted wells in unconfined aquifers”, Water Resour. Res., 38, 1108, doi: 10.1029/2001WR000401. 27.Zhan, H. and Park, E. (2003)“Hydraulics of horizontal wells in leaky aquifers”, J. Hydrol, 281, 129-146. 28.Zlotnik, V. A. and Tartakovsky, D. M. (2008)“Stream depletion by groundwater pumping in leaky aquifers”, J. Hydrol. Eng., 13(2), 43-50, doi: 10.1061/(ASCE)1084-0699(2008)13:2(43).
於河邊利用垂直井抽水會產生較大的洩降錐而可能導致地層下陷。本研究先推導出於河邊受壓含水層點源抽水之水頭分佈解析解,並根據疊加原則,將點源解沿著水平井與傾斜井之方向積分,而得到水平井與傾斜井之解析解。本研究為瞭解抽水後之地下水頭情形,忽略解析解中的指數項可簡化成半穩態解(quasi-steady solutions)。根據半穩態解比較井不同之位置以及長度所引起之洩降錐,進而獲得抽水井之設置參考依據。而河川滲漏量(Stream Depletion Rate, SDR)可由達西定律計算而得,且根據SDR之計算結果作為水平井或傾斜井之最佳設置方向參考。研究發現,含水層特性中垂直於河川方向之水力傳導度會影響達到半穩態SDR所需要之時間,此外,本研究亦進行井長及井與河川之距離對SDR之影響評估。

Pumping in a vertical well may produce a large drawdown cone near the well. In this paper, the solution is first developed for describing the groundwater flow associated with a point source in a confined aquifer near a stream. Based on the principle of superposition, analytical solutions for horizontal and slanted wells are then developed by integrating the point source solution along the well axis. The solutions can be simplified to quasi-steady solutions by neglecting the exponential terms to describe the late-time drawdown, which can provide useful information in designing horizontal well location and length. The stream depletion rate (SDR) implying the reduction of groundwater flow relative to infiltration from the stream can be obtained from Darcy's law. The direction of the well axis can be determined from the best SDR subject to the drawdown constraint. It is found that hydraulic conductivity in the direction perpendicular to the stream plays a crucial role in influencing the time required for reaching quasi-steady SDR. In addition, the effects of the well length as well as the distance between the well and stream on the SDR are also examined.
其他識別: U0005-0908201014430400
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