Analyse Of Transient Confined-Unconfined Flow To A Partially Penetrating Well Considering Delayed Response

Pumping tests,especially the constant rate pumping tests,have been the important methods to obtain hydraulic parameters of aquifers and to calculate the drawdown of the aquifers in the geological and hydrological studies.However,most of the existing researched on the pumping tests are based on the Dupuit’s equation,which cannot be applied to complex geological situations.Pumping with a large rate or a long time pumping can convert a confined flow to a confined-unconfined one in a confined aquifer,and the unconfined flow is susceptible to the effect of the delayed response,which makes it more difficult to study on the law of groundwater seepage.In this study,with the method of the Laplace and the Finite Fourier Transform,a new solution is presented for the transient confined-unconfined flow to a partially penetrating well in a confined aquifer considering the delayed response from the unsaturated flow.This solution generalizes that of Xiao which accounts for the delayed response related to hydraulic conductivity and specific yield,and has been improved upon by introducing the model of the delayed response without considering the empirical constant α from Neuman’s work and by fully coupling the saturated zone with the unsaturated zone at the interface of the two regions and allowing both the horizontal flow and the vertical flow in the unsaturated region from Mishra and Neuman’s work.Based on the work of Mishra and Neuman,the proposed solution(1)considers ak and ac which are related to the relative hydraulic conductivity and specific moisture capacity,respectively,and(2)assumes that the conversion interface between the saturated and unsaturated region moves with the pumping time,and(3)assumes that the unsaturated flow is limited in a finite area.Based on the work of Neuman,specific hydraulic parameters which represent the boundary conditions of the delayed response are introduced to take place the empirical constant a in the work of Xiao.This solution investigates the aquifer anisotropy,and the effects of delayed response from the unsaturated zone on the drawdown and the development of the transient unconfined region.The acceptability of the proposed solution is verified in comparison with the the numerical solution of Visual MODFLOW Flex and the data from a pumping test from the U.S.Geological Survey,the results of which agree well with the actual observation data.The main conclusions are:(1)Similar to work by the Mishra and Neuman,the unsaturated zone has a significant impact on the transient unconfined flow,which is controlled by the relative hydraulic conductivity and specific moisture capacity of the unsaturated zone.(2)With the diminishment of the relative hydraulic conductivity and specific moisture capacity,the ability of the unsaturated region to transform water to the saturated region is decreased to a lower level,resulting in an increased drawdown in the unconfined.(3)In the parpartially penetrated well,the recharge to the unconfined region increases with the growth of the length of the screen,which makes the drawdown and the conversion radius to decrease.The results of this paper show great consistency with the preview studies,which offer much-needed insights into the field of mine dewatering and the application of geological and hydrological conditions considering delayer response during the transient confined-unconfined conversion.