An Approximate Analytical Solution for Two-Region Non-Darcian Flow Toward a Well in a Leaky Aquifer

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" k_D 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 k_D and dimensionless leakage parameter B_D values approach the same asymptotic value at early stages and are straight lines in double logarithmic paper at early stages.