三種水層試驗部分貫穿井解析解之研究

Abstract

含水層試驗包括定流量抽水試驗、定水頭試驗、及微水試驗，通常為用來瞭解含水層水文地質參 數的重要工作。與水層試驗有關常用到的解析解，絕大多數是考慮井內的濾管(井篩)為全開的情況， 即濾管貫穿整個水層的厚度。在濾管是全開的假設下，水層內的流況可視為水平流，在這種情況下， 描述水層內水流的數學方程式不含垂直方向的份量，故較容易求得解析解。若考慮濾管只部份貫穿水 層，在井緣附近會有很顯著的垂直流，則描述水層內水流的數學方程式因含垂直方向的份量，而變得 非常難解。在過去文獻中，對於定水頭、定流量及微水試驗部分貫穿井，皆將井緣的邊界條件作簡化 而求得半解析解或解析解，然而這樣的解，計算得井緣附近的水位與流速場值，都會有誤差。 本研究計畫擬分成三年執行，第一年為求解定水頭試驗部分貫穿井的解析解；第二年擬針對定流 量抽水試驗與微水試驗，考慮部分貫穿井的情形推導相關的解析解。；第三年的計畫則進一步考慮鑿 井或完井過程所產生的井膚層，推求定水頭試驗部分貫穿且含井膚層的解析解。所推導得的解析解， 將具有下列用途：(1)用來描述水層內水位的時空分佈，(2)當數值解的驗核的工具，(3)結合最佳化方 法可用來推估水層的水文地質參數值。

The aquifer tests including constant head test, constant flux test, and slug test are usually used to investigate the hydrogeological properties of aquifers. Most analytical solutions related to the aquifer tests are based on the assumption that the pumping wells fully penetrate the aquifers. The flow in the aquifer is horizontal when assuming that the well is fully penetrated, and the resulting govern equation can be easily solved by conventional integral transform techniques. However, if the well partially penetrates the aquifer, the flow system will contain both horizontal and vertical flows. It is difficult to solve the problem with a partially penetrating well by the conventional methods. In the past, such problems were solved by simplifying the well boundary condition. However, these solutions will give significant errors in predicting the distribution of the hydraulic head and flow velocity near the wellbore. This study plans to solve the problem with a partially penetrating well for the aquifer tests such as constant head, constant flux and slug tests. In the first year, the new analytical solution for the partially penetrating well in a constant head test will be derived. In the second year, we will derive the solutions for constant-flux test and slug test which are also performed in a partially penetrating well. In the last year, we will further consider the wellbore skin, produced mainly by well drilling process, and derive the analytical solution for the constant head test. Those aquifer test solutions can be used to (1) describe the temporal and spatial distribution of hydraulic head in the aquifer system, (2) verify the numerical models, and (3) estimated the hydrogeological parameters if coupling with an optimization approach.