Groundwater flow to a general well configuration in an unconfined aquifer overlying a fractured bedrock

Abstract

Unconfined aquifers sometimes overlie fractured bedrocks, consisting of unconfined-fractured aquifer systems. Pumping induced hydrodynamics in such aquifer systems has not received much attention as in other types of aquifer systems. This paper aims to obtain semi-analytical solutions of flow to a general well configuration in such an unconfined-fractured two-layer aquifer system. The examples of general well configuration, specifically discussed here, include: 1) a horizontal well, 2) a vertical well, 3) a vertical well with one horizontal collector, and 4) a vertical well with two horizontal collectors which are perpendicular with each other. The methodology is general and can be extended to other types of wells with minor modifications of solutions developed in this study. The point sink/source solution is first obtained using double infinite Fourier and Laplace transformations (where sink is for pumping and source is for injection). The line sink/source solution is then obtained via integrating the point sink/source along the desired direction and following the principle of superposition. The de Hoog numerical inverse Laplace transform and Gaussian Quadrature are used to obtain time-domain dimensionless drawdown solutions. The instantaneous drainage of water table and the inter-porosity flow of the underlying fractured aquifer are taken into account. The effects of the length of horizontal well on dimensionless drawdown and dimensionless drawdown derivative, and scaled sensitivity of the hydraulic parameters of the underlying fractured aquifer are explored. The dimensionless drawdowns and drawdown derivatives of a vertical pumping well, a vertical well with a single horizontal collector and a vertical well with two perpendicular horizontal collectors are also compared. The scaled sensitivity of dimensionless drawdown to the hydraulic parameters of the underlying fractured aquifer of these different pumping well structures is explored. The results of this study can be used to evaluate the hydraulic parameters using the drawdown data collected during a pumping test performed in a general well configuration in a unconfined-fractured two-layer aquifer system. Furthermore, the presented solutions can be utilized to design the pumping well to minimize drawdown in low-permeability or thin aquifers. By eliminating the inter-porosity flow term from the underlying fractured aquifer, the solutions are applicable to groundwater flow to a pumping well in leaky aquifers.