Analyses for constant-head test and constant pumping test in finite two-zone confined aquifers with the Robin condition at outer boundary
|關鍵字:||含水層試驗;解析解;拉普拉斯轉換;複變逆轉;留數定理;徑向雙層;西姆公式;敏感度分析;aquifer test;analytical solution;Laplace transforms;complex inversion integral;residue theorem;composite aquifer;Thiem equation;sensitivity analysis|
Well pumping tests are commonly employed for the determination of the aquifer parameters. The well skin of finite thickness may exist around the wellbore during well installation. A patchy aquifer is referred to as an aquifer of which its hydraulic properties in the central portion is different from remaining part of the aquifer. In both cases, the aquifer can be considered as a two-zone system. The test results from a two-zone aquifer system should differ from those from a homogeneous one. This thesis develops an analytical model for describing drawdown distribution induced by a constant-head test (CHT) in a two-zone confined aquifer of finite extent with the Robin-type condition at outer boundary and a constant drawdown at inner boundary. The solution of the model is derived by the methods of Laplace transform, Bromwich integral and the residue theorem. Moreover, the wellbore flow solution may also be obtained by applying Darcy’s law to the new solution. Similarly, the drawdown solution for a constant-rate test (CRT) can be obtained in a similar manner when the condition of constant drawdown is replaced by a constant pumping flow rate in the model. Thus, most existing solutions, such as the steady state Thiem equation and the solutions for flow in confined aquifers including those for one-zone or two-zone finite aquifers with the Dirichlet or no-flow condition at outer boundary, could be considered as special cases of the present solutions. Those solutions may be used to investigate the effects of different kinds of outer boundary conditions, distance of outer boundary, and conductivity ratio on the drawdown distributions due to pumping. Furthermore, the sensitivity analysis is also performed to investigate the behavior of the wellbore flow for CHT and drawdown for CRT in response to the change of the parameters in each zone.