An approximate analytical solution for two-region non-Darcian flow toward a well in a leaky aquifer

作者：Wen Zhang^*; Huang Guan Hua; Liu Zhuang Tian; Li Jian

来源：Earth Science - Journal of China University of Geosciences, 2011, 36(6): 1165-1172.

DOI：10.3799/dqkx.2011.123

• Approximate analytical solutions
• Asymptotic values
• Critical distance
• Darcian flow
• Environment engineering
• Late stage
• Leakage effects
• Leaky aquifer
• Leaky aquifers
• Linearization procedures
• Non-Darcian flow
• Numerical Laplace inversion
• Pumping well
• Well bore storage

In this paper, we propose a two-region non-Darcian flow model near a pumping well in a leaky aquifer. The flow near the pumping well is assumed to be non-Darcian, with the area nearby defined as non-Darcian flow region, while the flow far away from the pumping well can be regarded as Darcian flow. The critical distance distinguishing the non-Darcian flow region and Darcian flow region can be determined by the critical Renolds number. We have used a linearization procedure coupled with Laplace transform to solve such a two-region non-Darcian flow model. The drawdowns both in the non-Darcian flow region and Darcian flow region have been obtained by using the so-called Stefest numerical Laplace inversion method. We have compared our results with those for the one-region Darcian flow model and the one-region non-Darcian flow model. The results indicate that: (1) The drawdowns in the non-Darcian flow region of different critical distances approach the same asymptotic value at early stages, as well as the result for the one-region non-Darcian flow model; while at late stages, significant difference has been found between the drawdowns obtained in this study; (2) A larger "non-Darcian hydraulic conductivity" kD results in a greater drawdown in the entire aquifer at early stages, while leads to a smaller drawdown in the non-Darcian flow region at late stages and has little impact on the drawdowns in the Darcian flow region; (3) The leakage effect on the drawdown is similar to that for the Darcian flow case, and it only exists at late stages; (4) When the wellbore storage is considered, all the drawdowns inside the well for different kD and dimensionless leakage parameter BD values approach the same asymptotic value at early stages and are straight lines in double logarithmic paper at early stages.

• 出版日期2011
• 单位中国农业大学