徑向雙層侷限含水層定水頭與定流量抽水試驗之解析:考慮外邊界為Robin條件

地下水的含水層抽水試驗，普遍用來決定含水層參數值。若水層水井井緣有膚層或是井位於補綴水層中心，此問題可視水層為徑向雙層系統，它與均質水層的試驗結果會不同。本研究發展一解析模式用於描述定水頭試驗在雙區侷限含水層所產生的洩降分布，此模式考慮水層的外邊界為有限、且可用Robin條件描述，內邊界則是以定洩降來描述。本模式的解析解可透過拉普拉斯轉換、布朗維奇積分及留數定理求得。此外，基於達西定律利用此解可導得井緣流量的解。用同樣的方法，上述模式之內邊界條件改為固定流量即可求得定流量試驗的洩降解。目前多數定水頭與定流量的解析解，不管是穩態解的西姆公式、水層是單層或雙層，外邊界是定水頭條件或無流量條件，皆可視為本新解的特例。此新解可用來探討不同的外邊界條件、外邊界的距離、及傳導係數比對水洩降分布之影響。此外，本文也對此兩種含水層試驗做敏感度分析，探討在雙層中，各參數對於定水頭試驗之井緣流量或定流量試驗之洩降洩降分布影響。

關鍵字

含水層試驗；解析解；拉普拉斯轉換；複變逆轉；留數定理；徑向雙層；西姆公式；敏感度分析

並列摘要

Well pumping tests are commonly employed for the determination of the aquifer parameters. The well skin of finite thickness may exist around the wellbore during well installation. A patchy aquifer is referred to as an aquifer of which its hydraulic properties in the central portion is different from remaining part of the aquifer. In both cases, the aquifer can be considered as a two-zone system. The test results from a two-zone aquifer system should differ from those from a homogeneous one. This thesis develops an analytical model for describing drawdown distribution induced by a constant-head test (CHT) in a two-zone confined aquifer of finite extent with the Robin-type condition at outer boundary and a constant drawdown at inner boundary. The solution of the model is derived by the methods of Laplace transform, Bromwich integral and the residue theorem. Moreover, the wellbore flow solution may also be obtained by applying Darcy’s law to the new solution. Similarly, the drawdown solution for a constant-rate test (CRT) can be obtained in a similar manner when the condition of constant drawdown is replaced by a constant pumping flow rate in the model. Thus, most existing solutions, such as the steady state Thiem equation and the solutions for flow in confined aquifers including those for one-zone or two-zone finite aquifers with the Dirichlet or no-flow condition at outer boundary, could be considered as special cases of the present solutions. Those solutions may be used to investigate the effects of different kinds of outer boundary conditions, distance of outer boundary, and conductivity ratio on the drawdown distributions due to pumping. Furthermore, the sensitivity analysis is also performed to investigate the behavior of the wellbore flow for CHT and drawdown for CRT in response to the change of the parameters in each zone.

並列關鍵字

aquifer test ； analytical solution ； Laplace transforms ； complex inversion integral ； residue theorem ； composite aquifer ； Thiem equation ； sensitivity analysis

參考文獻

Abdul, A. S. (1992), A new pumping strategy for petroleum product recovery from contaminated hydrogeologic systems: Laboratory and field evaluations, Ground Water Monit. R., 12, 105-114.

Abramowitz, M., and I. A. Stegun (1970), Handbook of Mathematical Functions, Dover, New York.

Agarwal, R. G., R. Al-Hussainy, and H. J. Ramey, Jr. (1970), An investigation of wellbore storage and skin effect in unsteady liquid flow: I. Analytical treatment, Soc. Pet. Eng. J., 279-290.

Baker, J. A. and R. Herbert (1988), Pumping test in patchy aquifer, Ground Water, 20, 150–155.

Barry, D. A., J. Y. Parlange , and L. Li (2000), Approximation for theexponential integral (Theis well function), J. Hydrol., 227, 287–291.

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徑向雙層侷限含水層定水頭與定流量抽水試驗之解析:考慮外邊界為Robin條件

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