Articles | Volume 20, issue 1
Research article
15 Jan 2016
Research article |  | 15 Jan 2016

Approximate analysis of three-dimensional groundwater flow toward a radial collector well in a finite-extent unconfined aquifer

C.-S. Huang, J.-J. Chen, and H.-D. Yeh

Abstract. This study develops a three-dimensional (3-D) mathematical model for describing transient hydraulic head distributions due to pumping at a radial collector well (RCW) in a rectangular confined or unconfined aquifer bounded by two parallel streams and no-flow boundaries. The streams with low-permeability streambeds fully penetrate the aquifer. The governing equation with a point-sink term is employed. A first-order free surface equation delineating the water table decline induced by the well is considered. Robin boundary conditions are adopted to describe fluxes across the streambeds. The head solution for the point sink is derived by applying the methods of finite integral transform and Laplace transform. The head solution for a RCW is obtained by integrating the point-sink solution along the laterals of the RCW and then dividing the integration result by the sum of lateral lengths. On the basis of Darcy's law and head distributions along the streams, the solution for the stream depletion rate (SDR) can also be developed. With the aid of the head and SDR solutions, the sensitivity analysis can then be performed to explore the response of the hydraulic head to the change in a specific parameter such as the horizontal and vertical hydraulic conductivities, streambed permeability, specific storage, specific yield, lateral length, and well depth. Spatial head distributions subject to the anisotropy of aquifer hydraulic conductivities are analyzed. A quantitative criterion is provided to identify whether groundwater flow at a specific region is 3-D or 2-D without the vertical component. In addition, another criterion is also given to allow for the neglect of vertical flow effect on SDR. Conventional 2-D flow models can be used to provide accurate head and SDR predictions if satisfying these two criteria.

Short summary
Existing solutions for the problem of pumping at a radial collector well (RCW) in unconfined aquifers either require laborious calculation or predict divergent results at a middle period of pumping. This study relaxes the above two limitations to develop a new analytical solution for the problem. The application of the solution is convenient for those who are not familiar with numerical methods. New findings regarding the responses of flow to pumping at RCW are addressed.