A Double-Porosity Model for Pumping in a Slant Fracture：The Distributed Parameter Approach

• Main Authors: Hsin-Wei Ho, 何信緯
• Other Authors: Chia-Shyun Chen
• Format: Others
• Language: zh-TW
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/jcfsne

碩士 === 國立中央大學 === 應用地質研究所 === 105 === 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.