利用分布參數方法發展傾斜裂隙岩層 抽水試驗雙孔隙率模式;A Double-Porosity Model for Pumping in a Slant Fracture：The Distributed Parameter Approach

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Title:	利用分布參數方法發展傾斜裂隙岩層抽水試驗雙孔隙率模式;A Double-Porosity Model for Pumping in a Slant Fracture：The Distributed Parameter Approach
Authors:	何信緯;Ho, Hsin-Wei
Contributors:	應用地質研究所
Keywords:	雙孔隙率模式;抽水試驗;大傾角;捕集區
Date:	2017-01-11
Issue Date:	2017-05-05 17:42:49 (UTC+8)
Publisher:	國立中央大學
Abstract:	調查新竹尖石鄉含水層場址顯示一砂質岩層的裂隙帶傾角可大到30 度至60 度。如此大的傾角會在裂隙帶中引發區域性水流，使抽水試驗產生的地下水流場形成非徑向流場；抽水井上、下游地下水壓力變化不一致，於抽水井附近形成捕集區。過去已發展一雙孔隙率模式以分析裂隙岩層抽水試驗，並完成相關之理論和現地抽水試驗資料分析；該模式採用”集總參數(lumped parameter)方法模擬岩體母質流(matrix flow)”，假設岩體母質流與岩體母質和裂隙帶間的壓力差成正比。然而另有一種”分布參數(distributedparameter)方法，使用達西定律模擬岩體母質流”，假設岩體母質流與岩體母質和裂隙帶間的水力梯度成正比。集總參數和分布參數模式皆用於模擬岩體母質流，兩模式各有優缺點且被廣泛使用。因此本研究的目的為使用分布參數方法建立新的雙孔隙率模式以解決大傾角裂隙帶抽水試驗問題，比較兩種模式的理論分析和資料分析的結果，以了解和區分分布參數和集總參數兩種方法的理論差異和資料分析影響，並透過流場得出大時間的捕集區。本研究開發的模式為Laplace 域半解析解，在半對數圖中大時間洩降呈直線變化；其斜率可決定裂隙流通係數Tf，時間軸的截距則可決定裂隙和岩體母質儲水係數的總合Sf + Sm；利用所得小時間之解可決定岩體母質水力傳導係數Km、參數Sf與Sm。本研究得出分布參數與集總參數模式有相同之大時間漸近解，兩模式之差異在於中小時間的過渡變化；集總參數模式較為平坦，分布參數模式較為陡峭；因此視洩降資料過渡帶的變化，可決定使用何種模式進行資料分析與參數推估。另外本研究由模式推導出捕集區之解析解，並經由推導得知大時間後裂隙和岩體母質不再對抽水井供水，抽水井所抽的水由區域性水流提供；區域性水流i 越強或裂隙流通係數Tf越大，則抽水造成的捕集區越小。因此本研究認為，在分析抽水試驗時，必須考慮裂隙傾角造成的影響。;Investigating the sandstone aquifer from field in Jianshi township indicates that the dip angles of fractured zones can be as large as 30-60 degrees. Such large dip angles may induce a regional flow in the fractured zone, of which the interference with the pumping test will create a non-radial flow field that is asymmetric with respect to the pumping well. The pressure response in the down-gradient and up-gradient of the pumping well is different and a capture zone effect exists in the neighborhood of the pumping well. In the past, a new double-porosity mathematical model for large dipping angle fracture has been developed, and the important theoretical and field pumping test data have been done and analyses. In this model the “lumped-parameter” approach is employed to account for the matrix flow by assuming the flow between the matrix and fractured zone is proportional to the pressure difference between these two flow domains. However, there is another approach, the ”distributed-parameter” approach, for modeling the matrix flow. It invokes the Darcy’s law for the matrix flow by assuming that the matrix flow is proportional to the hydraulic gradient between the matrix and fractured zone. While each approach has certain advantages and disadvantages, they complement each other and are commonly used. Therefore the purpose of this research are employing the distributed-parameter approach to develop a new double-porosity model for pumping test in a large-dip angle fracture zone. Compare the theoretical and data analysis results from the two models in order to investigate and differentiate the impact and consequences associated with two approaches. Finally, the flow field is used to delimit the boundary of capture zone. The solution that we developed is in Laplace-domain, it is found that the large-time drawdown data exhibit a straight line on semi-log paper, and its slop can be used to estimate transmissivity of the fractured zone Tf while its intersection with the time abscissa to determine the sum of the storage coefficient of the fractured zone Sf and of matrix Sm. The matrix conductivity Km, Sf and Sm can be determined by fitting the small- and intermediate- time data by the solution without difficulty. Both the distributed- and lumped-parameter models can be approximated by the same asymptotic solution at large times. The major difference in these two models; however, lies in that the transition from small times to large times of the lumped-parameter model is flatter than that of the distributed-parameter model. Both the distributed- and lumped-parameter models are useful for data analysis, depending on the characteristics of the transition from small times to intermediate times. In addition, we derive the analytic solution for the capture zone. Due to prove of solution, regional flow substituted the water supply from matrix and fracture to pumping well. When the regional flow or transmissivity of the fractured zone Tf increase, the capture zone will be bigger. In this project, we think the dip angle is needed to consider during the pumping test.
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