General analytical solutions of groundwater flow toward multi-dimensional sources/sinks in a confined aquifer with leakage and distributed recharge

Abstract

A variety of hydrogeologic conditions and parameters play roles in obtaining analytical solutions for groundwater flow in aquifers. Changes of these influencing conditions typically require finding a new solution. Therefore, it is very useful if a general approach and solution can be provided to conveniently construct the solutions corresponding to the condition changes. In this study, two general analytical solutions for multi-dimensional groundwater flow in homogeneous, confined aquifers are derived using Green’s function method for instantaneous and continuous sources/sinks. A library of analytical solutions can be readily obtained by combining the general solutions with directional solutions for a variety of hydrogeologic and geometric conditions. The aquifer can be one-, two-, or three-dimensional and vertically and horizontally finite, semi-infinite, or infinite. The geometry of sources/sinks can be point, line, areal, and volumetric. Leakage from adjacent aquifers and distributed precipitation recharge are also included. The general solutions are validated by reported analytical solutions. A series of typical solutions for one-, two-, and three-dimensional groundwater flow are presented. A computational example is provided to compare the drawdown distributions caused by point, vertical line, vertical areal, and volumetric sinks. A field investigation and design at a groundwater-contaminated site using the derived analytical solution suggests that drainage slots (vertical areal sinks) can be an effective alternative to pumping wells (vertical line sinks) in lowering the groundwater level for a shallow aquifer.