Computerized Analytical Solutions To Well Problems Using Simple Numerical Techniques - Introduction

Analytical models for transient groundwater phenomena, such as those of Theis, Cooper, and Jacob, are important but often limited tools for aquifer evaluation and drawdown prediction. Most were developed using simplifying assumptions which compromise their treatment of complex boundaries and most also contain functions that are mathematically complex and difficult to solve explicitly. Examples of such functions are the Bessel functions, the exponential integral, and similar well functions for leaky confined and water table aquifers. This paper describes the joint use of simple numerical techniques and numerical approximations of these functions to extend many analytical models beyond their conventional applications. The enhanced analytical methods represent many hydrologic problems more easily and realistically, permit a wider range of application, and often provide insight into the response of pumped groundwater systems without the need to resort to more complex numerical flow models. Use of the enhanced analytical methods usually requires the use of microcomputers due to the large number of computations. Examples presented here are the development and extension of type curves and the determination of drawdown distributions.