A new analytic function for modeling partially penetrating wells

Abstract

A new analytic function is presented to model three‐dimensional flow near a partially penetrating well. The function represents a sink distribution along the well axis, whereby equipotential conditions along the well perimeter are approximately satisfied by adjusting several degrees of freedom of the function. This procedure is well known and has led to rather accurate solutions provided a sufficient number of free parameters were incorporated. The values for these parameters are obtained by solving a system of linear equations. The function presented in this paper achieves the same accuracy as past solutions with a significant reduction in the number of degrees of freedom required and hence fewer equations to be solved. This increased efficiency is of little consequence when the well is modeled by itself. However, when combined with the solutions to the many other flow features in a regional aquifer, the savings become significant. In fact, if each of the individual solutions would have many degrees of freedom, the resulting system of equations may become unmanageable, thus restricting applications. To demonstrate the use of the new function, a hypothetical groundwater contamination problem is solved, whereby contaminants are intercepted by a partially penetrating well.