Some approximate solutions of radial flow problems

Abstract

A large number of exact solutions to various boundary value problems in ground water flow have been solved in recent years using Laplace transformation. For most of the radial flow problems, the transform does not have a simple inverse and various methods such as the Mellin's inversion formula must be employed. The resulting exact solution is frequently in a form of a complex integral or an infinite series which is difficult to evaluate. It is shown that an approximate inversion formula for Laplace transforms, developed for the solution of visco-elastic problems, is applicable to most radial flow problems. Three cases are considered: (1) that of a well pumping a constant discharge from an infinite aquifer; (2) that of a well pumping a constant discharge from an infinite leaky aquifer; and (3) that of a well drawing an infinite leaky aquifer subject to a constant drawdown. The method leads to simple analytical solutions for each of the above cases and agreement between this method and the exact solution for each case is excellent.