受限含水層定水頭試驗徑向雙層井緣流量之閉合解

Abstract

由於鑿井過程或完井工作的影響，水井附近的水層組成有顯著改變時，則此水層可視為徑向雙層系統。於受壓含水層做定水頭試驗，本文對地下水流方程式及定水頭邊界條件，推導得一個新的井緣流量閉合解；再者，也提出一個有效率的數值方法估算此閉合解的數值。估算得的流量值與用數值逆轉在拉普拉斯域解的結果，並列於表內，結果顯示這兩個解相吻合。這個新解不但可以用於估算徑向雙層地下水水井邊緣的流量，而且可評估水井膚層對井緣流量的影響。此外，於受壓單層含水層系統，存在兩種不同型式的井緣流量解析解，本文證明這兩個解與本文所推導得的解是相等的。本文所提的數值方法估算此閉合解的結果，精度至小數第五位，此數值可符合工程應用所需的精度。

An aquifer may be considered as a radial two-layer system if the formation properties near the well are significantly changed due to the well construction and/or well development. A closed-form solution for transient flow rate across the wellbore is derived under a constant-head test from a radial two-layer ground-water flow equation, which is subject to the boundary condition of keeping a constant head at the well radius in a confined aquifer. An efficient numerical approach is proposed to evaluate this solution. Values of dimensionless transient flow rate versus dimensionless time are provided in tabular forms and compared with those obtained by a numerical inversion technique for the Laplace-domain solution. The results show that the values of these two solutions are in good agreement. This newly derived solution can be used not only for predicting the transient flow rate across the wellbore but also for identifying the effects of a finite-thickness skin on the estimation of transient flow rates in a radial two-layer ground-water system. Furthermore, two other closed-form solutions for describing the same flow rate in a single-layer confined aquifer but in different forms can also be seen in the literature. This paper proofs the equality of these three solutions. The results estimated by the proposed approach are to five decimal places, which may meet the need of accuracy in engineering applications.