A semi-analytical solution for transient confined-unconfined flow toward the partially penetrating well

In this paper, a semi-analytical solution has been proposed for the transient confined-unconfined flow toward a partially penetrating well in a confined aquifer. It can be used to characterize the dynamic development of drawdown and the transient unconfined region during the transient confined-unconfined conversion. The proposed solution takes into account the delayed response recharge from the unsaturated region by the Neuman's upper surface recharge boundary condition, which is derived by the Laplace and Fourier transformations. The reliability of the semi-analytical solution has been proved by comparisons with numerical solutions from Visual MODFLOW Flex. In addition, a new model for the pumping flow in a pure unconfined aquifer is also developed by degradation analysis of the proposed solution, which has been used to fit well with the measured data from the pumping test in Cape Cod aquifer. The results indicate that both the use of partially penetrating pumping well and aquifer anisotropy have negative effects on the drawdown delayed responses and the development of transient unconfined region, which are disappeared at times > 10(5) S(r)b / K-r. The delayed response is positively related to the gravity storage and vertical hydraulic conductivity.