受壓含水層微水試驗考慮遲滯時間效應之分析

Abstract

本研究考慮地下水流與水力梯度間的相互延遲現象，發展出井部分貫穿侷限含水層並考慮膚層效應之微水試驗模式。利用拉普拉斯轉換與有限傅立葉餘弦轉換，可求得本模式的解，本解也能用來模擬分析全貫穿井與包含井膚層的例子。從無因次化的結果，可以看出延遲時間對於洩降的影響，在試驗初期相當顯著。敏感度分析則顯示洩降對導水係數最為敏感、對比出水係數較不敏感，而延遲係數則對洩降呈現相反的影響。此外，在正膚層中洩降對各項係數的敏感程度皆大於在負膚層中。美國地質調查局曾於南達科他州的Minnelusa含水層從進行微水試驗，此解被用來分析所取得的水位變化數據以逆推水層參數，根據所得水層參數，本新解預測的水位變化曲線與現地數據相當吻合，特別是在試驗的初期，比未考慮延遲效應的模式預測，更加貼近現地數據。

This study considers the phase lag effect between groundwater flux and drawdown gradient in the groundwater flow model for describing well water level (or drawdown) change during the slug test at a partially penetrating well with wellbore skin in a confined aquifer. The solution of the model can be derived by the use of Laplace transform technique and finite Fourier cosine transform. Additionally, the drawdown solution for the conditions of full penetrating well and no wellbore skin is also developed. The results show that the dimensionless phase lag significantly influences the dimensionless drawdown in the early time. The results of sensitivity analysis indicate that the drawdown is very sensitive to the change in hydraulic conductivity, less sensitive to the change in specific storage, and the phase lag parameters pose the adverse effect on the drawdown. The drawdown is more sensitive to all parameters in positive skin cases than those in negative skin cases. This new solution is also employed to analyze the measure data from slug test conducted by Greene et al. (1999) in South Dakota, US for the estimation of aquifer parameters. The predicted drawdown by the present solution based on the estimated parameters gives very good fit to field observed drawdown especially at early time test period as compared with those predicted without considering the phase lag effect.