單井垂直循環流場追蹤劑試驗利用充氣式封塞將單一口井的井篩分隔成上、下兩段井篩段，以下段抽水及上段注水的方式於含水層建立垂直循環流場。待流場達穩態後，於注水井篩段注入追蹤劑並在抽水井篩段量測濃度穿透曲線，使用適當數學模式分析其濃度穿透曲線及上、下井篩段洩降差，即可同時推估含水層水平徑向、垂直方向水力傳導係數與縱向延散度。由於過去利用流管法所建立的數學模式僅適用於縱向延散度小於追蹤劑移動距離的十分之一的範圍，且無法預測追蹤劑於含水層之傳輸移動行為，所以本研究發展全新的數學模式用以描述單井垂直循環流場追蹤劑試驗。模式首先求解穩態單井垂直循環地下水流場解析解，將所得孔隙流速分量配合二階延散張量理論，利用Laplace轉換有限差分法求解二維圓柱座標系統移流-延散方程式，即可計算追蹤劑於含水層之濃度分布及抽水井篩段濃度穿透曲線，並可藉由相關參數敏感度分析建立水文地質參數推估方法。此全新的數學模式可用於分析現地試驗資料，可同時推估含水層水平徑向、垂直方向水力傳導係數與縱向延散度，而且其適用性不受縱向延散度範圍限制。 The basic design of a single-well vertical circulation flow tracer test involves an injection and an extraction chamber separated by some vertical distance and isolated from one another both using an inflatable packer and utilize a pump to create a vertical circulation flow field in an aquifer. After a steady-state flow field is established and the pumping rate and drawdowns in these chambers are measured, the tracer mass is injected into injection chamber and the concentration breakthrough curve is recorded in the extraction chamber. Using an appropriate mathematical model to analyze the breakthrough curves and drawdown in chambers, the horizontal hydraulic conductivity, the vertical hydraulic conductivity and longitudinal dispersivity can be estimated. Existing models based on streamtube approach are only valid for interpreting vertical circulation flow tracer test in a certain condition that the longitudinal dispersivity is an order of magnitude smaller than the tracer travel distance. This study presents a novel mathematical model for interpreting solute transport in a single-well vertical circulation flow tracer test. In developing the mathematical model, a steady-state analytical solution for drawdown distribution is first obtained and the radial and vertical components of pore velocity are determined to serve as the input for the advection-dispersion equation. Subsequently, the two-dimensional advection-dispersion equation in cylindrical coordinates for describing tracer transport vertical circulation flow tracer test is derived based on the second order dispersion tensor theory. The Laplace transformed finite difference technique is applied to solve the two-dimensional transport equation. The novel model has an advantage over existing models because it can be valid over a wide range of the ratio of the longitudinal dispersivity to the distance traveled by the tracer. The new mathematical model can apply to determine the necessary relationships for estimating the longitudinal dispersivity as well as the radial and vertical hydraulic conductivities.
