Full-Range Solution for the Theis Well Function

Abstract

AbstractPumping tests are used to determine the transmissivities and storage coefficients of aquifers. For nonleaky aquifers, the solution reduces to the exponential integral, which is also called the Theis well function. It is beneficial to have a simple and handy approximation for the Theis well function. A simple (minimum number of terms) and reliable approximation that is efficient, yet sufficiently accurate, is preferable. This research provides a simple and accurate approximation to the Theis well function valid for all values of its arguments. The approximation is constructed by a combination of two solutions that are valid for small and large arguments. The approximation contains unknown coefficients, which are determined by using an optimization procedure. An accurate approximation to the well function should also be able to accurately compute the derivative of the well function. The proposed approximation minimizes errors in both the well function and its derivative. The maximum relative error i...