背斜受限含水層中定流量抽水試驗之解析洩降解

Abstract

背斜地層是岩層受力彎曲後，形成向上拱起的褶皺地層。結構完整的背斜地層，可能作為廢棄物地下貯存或二氧化碳封存的場所。定流量抽水試驗藉由量測和分析觀測井的洩降反應，推求含水層的水文地質參數。本研究建立一個數學模式，用以描述定流量抽水試驗到達穩態時，背斜水層內的洩降分佈。在推導過程中，首先用三塊相連的長方體，近似模擬背斜地層的空間形體，接續採用傅立葉轉換和有限傅立葉餘弦轉換，推導得到轉換域的解後，進行傅立葉逆轉換以計算空間洩降的分佈值。使用此解進行模擬的結果，顯示兩翼較薄或是背脊較窄的水層，在井周圍會產生較大的洩降值。此外，在相同的抽水率條件下，縮減濾管開口長度和水層的異向性，會增加靠近井緣的無因次洩降。考慮不同設井位置的影響時，部分貫穿井若位於背斜脊中央上段處，在井周圍會產生較大的洩降。採用MODFLOW模擬地下水流時，取用適當的格網可近似模擬背斜形狀。與解析解結果相比，MODFLOW模擬結果所產生的洩降值較小。本研究所提出的解析解，也可應用於模擬平板形水層和斜坡水層的洩降分佈，將來亦可應用來逆推背斜含水層的水文地質參數值或做為廢棄物地下貯存場址篩選、設計的參考。

An anticline known as a convex-upward fold in layers of rock commonly forms during lateral compression, which may be elected as a potential site for underground waste storage or carbon sequestration. A constant-flux pumping test, which maintains a constant pumping rate at the test well, measures and analyzes the drawdown responses in one or several observation wells to determine the aquifer parameters. In this study, a mathematical model is developed for describing the steady-state drawdown distribution in the anticline aquifer during the constant-flux pumping. In the derivation, the topographical shape of the anticline is mimicked by three successive blocks. The infinite Fourier transform and finite Fourier cosine transform are applied to obtain the solution of the model in the transform spaces. The solution expressed as an integral form is then obtained from the Fourier inversion. Predicted results from the solution reveal that a thin-limbs or narrow-ridged anticline would cause a much larger head drop in the ridge zone. For a well of constant pumping rate, the dimensionless drawdown around the well increases with decreasing well screen length or/and aquifer anisotropy ratio. In examining the effect of well location, we find the partially penetrating well located at the top-middle of the ridge zone produces the largest drawdown. MODFLOW is a computer program that simulates the groundwater flow based on the block-centered finite difference method. Through the grid discretization, MODFLOW can imitate the antiform much closer to reality. The simulation for the flow in an anticline aquifer results in slightly smaller drawdown values when compared with those predicted by the present solution. The present solution can also be used to simulate the flow in a slab-shaped aquifer or a hillslope aquifer. It can be applied to identify the aquifer parameters and to design a potential site for waste disposal in the future as well.